Roulette Forum
Roulette Forum => Roulette Strategy Discussion => Topic started by: Bayes on April 25, 2015, 11:22:50 AM

In my years of reading on forums, this is the one error I see time and time again. It concerns confusing the probability of a series with that of a single.
For example, there is a famous example in probability called the "Birthday Problem" which states that in a room of 23 people, there is a 50% chance that at least two will share a birthday. Does this suggest a system for roulette? what is the probability that in a sequence of spins, you will get at least one repeat?
If you do the math, it turns out that in any 8 spin sequence, there is a roughly 56% chance that there will be at least one repeat in the sequence. No problem with that, but the error occurs when you make a statement like this:
"So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 56% chance that one of the 7 will repeat on the next spin."
This is saying that there is a 56% chance that you will get a win when betting on 7 numbers! but any casino which offered the equivalent of such odds would soon be out of business. The mistake lies in assuming that you can apply the probability of the series (7 spins with at least one repeat) to that of a single outcome. But once the 7 spins have gone, probability applies to the next spin only, so the original probability is now meaningless. All you can do is bet the last 7 numbers and hope that one of the last 7 repeats. What is the chance of that?
The answer is 7/37, no more and no less. If you doubt this, assume that the last 7 numbers were 17,1,32,25,8,12,28. The chance that 17 will hit on the next spin (and so result in a repeat) is 1/37, the chance that 1 will repeat is again 1/37. Similarly for each of the others. Since these are mutually exclusive outcomes, we can add the results, which gives 7/37.
You can indeed make a system out of the knowledge that there is at least one repeat with probability 56% in the last 8 spins, but in order for the probability to remain valid, you have to place your bets from spin 1, not after spin 7. So on spin 1 you put one chip on the last outcome, on spin 2 add another chip to whatever just hit, and so on, until you get a repeat (a win). But in that case, your profit will vary according to when you get the repeat, assuming you do get it. 56 times out of 100 you will indeed get at least one, but what you cannot say is that you will win 29 chips 56 times out of 100, betting 7 numbers!
Making this mistake is no different, in principle, to "calculating" that because there is a 99.9% chance of getting at least 1 black in 10 spins, then after 9 spins with no blacks the chance of a black on the next spin is 99.9%. This is of course, none other than the gambler's fallacy, but it may not be so easy to recognize it in more unusual or complex scenarios such as the probability of repeats.

In my years of reading on forums, this is the one error I see time and time again. It concerns confusing the probability of a series with that of a single.
For example, there is a famous example in probability called the "Birthday Problem" which states that in a room of 23 people, there is a 50% chance that at least two will share a birthday. Does this suggest a system for roulette? what is the probability that in a sequence of spins, you will get at least one repeat?
If you do the math, it turns out that in any 8 spin sequence, there is a roughly 56% chance that there will be at least one repeat in the sequence. No problem with that, but the error occurs when you make a statement like this:
"So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 56% chance that one of the 7 will repeat on the next spin."
This is saying that there is a 56% chance that you will get a win when betting on 7 numbers! but any casino which offered the equivalent of such odds would soon be out of business. The mistake lies in assuming that you can apply the probability of the series (7 spins with at least one repeat) to that of a single outcome. But once the 7 spins have gone, probability applies to the next spin only, so the original probability is now meaningless. All you can do is bet the last 7 numbers and hope that one of the last 7 repeats. What is the chance of that?
The answer is 7/37, no more and no less. If you doubt this, assume that the last 7 numbers were 17,1,32,25,8,12,28. The chance that 17 will hit on the next spin (and so result in a repeat) is 1/37, the chance that 1 will repeat is again 1/37. Similarly for each of the others. Since these are mutually exclusive outcomes, we can add the results, which gives 7/37.
You can indeed make a system out of the knowledge that there is at least one repeat with probability 56% in the last 8 spins, but in order for the probability to remain valid, you have to place your bets from spin 1, not after spin 7. So on spin 1 you put one chip on the last outcome, on spin 2 add another chip to whatever just hit, and so on, until you get a repeat (a win). But in that case, your profit will vary according to when you get the repeat, assuming you do get it. 56 times out of 100 you will indeed get at least one, but what you cannot say is that you will win 29 chips 56 times out of 100, betting 7 numbers!
Making this mistake is no different, in principle, to "calculating" that because there is a 99.9% chance of getting at least 1 black in 10 spins, then after 9 spins with no blacks the chance of a black on the next spin is 99.9%. This is of course, none other than the gambler's fallacy, but it may not be so easy to recognize it in more unusual or complex scenarios such as the probability of repeats.
Aaaah ! Seems that you have accessed my website “ fergusleesroulette.co.uk “. and found my “ Birthday Method “.
The main function of roulette websites is to put forward ideas for discussion that REAL players have used PROFITABLY.
I had used this method profitably but , as I said, I sometimes had to wait for a long time to have a bet. So not for me. The Long Run argument that critics use is invalid unless you can specify how long your long run is.Furthermore, Probability Theory deals with Expectations and not the Certainties that our critics claim. It is a tool to be used and not the Holy Grail that our critics claim it to be.
So now that you have accessed my site would you be kind enough to programme my Double Dozen strategy  which I use profitably. I would like to know just when I should stop betting it before losing not only my bankroll but all my profits from it .
I am pleased that we now have a programmer who is able to programme any strategy. Thanks in anticipation.

Nobody can predict the outcome of the next spin.
The chance of a repeater is for the EC 50%. A sampl of 8 spins has 256 possible different sequences. Every sequence need 8 results. The number of all the outcomes is 256x8=2048 spins
One of the sequences has not a single repeater.
A 10 spins sample contents one sequence of 10 red on 1024 sequences.This is 0,098% .

The Long Run argument that critics use is invalid unless you can specify how long your long run is.Furthermore, Probability Theory deals with Expectations and not the Certainties that our critics claim. It is a tool to be used and not the Holy Grail that our critics claim it to be.
hmmm... I'm not sure what you mean by this, but it seems a little strange that you've used probability on your site to support a system but are now dismissing it because it turns out that the chances aren't as favorable as you thought they were.
Anyway, regarding your system, it's not easy to understand, so do you have any further examples or explanations here? How long have you been playing it (number of placed bets) and with what results?

Hi Slacker,
In the absence of zero there are 81 possibilities in 4 spins of the wheel when betting the dozens 3x3x3x3 = 81. Grouping these 81 into 9 groups of 9 , my Blocks  or Groups guarantees 3 correct no matter the result .
Using Block 1 , which is
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
2 3 1 3 1 2 1 2 3
2 3 1 1 2 3 3 1 2 an example would be if the 4 spins are won by numbers in the dozens 1 1  3  2 it can be seen that 3 of these are in the first line of the block
.As will be seen we cannot actually bet the first 2 "spins " as we would need to bet all 3 each time for no profit but a loss should zero occur.Hence these need to be used as " virtual spins "and used only as a guide as to what to bet on spins " 3 " and "4".
4 combinations of 3 are needed to ensure 3 correct from 4 spins. These are 123 / 124 / 134 / and 2 /3 /4 and so is a 1 in 4 shot for a payoff of 7 / 2 and so , even allowing for the zero , gives an advantage to the player.
It may be thought that as there are nine combinations of spins 3 and 4 then it is really a 2 in 9 shot for a payoff of 7 /2 but we finish when any 3 win so we cannot bet the 4th of a winning 123. Even if we did we would need to bet all 3 dozens which would be silly.
As the 3rd spin , if won , pays only 2 /1 we do not bet it but place 1 chip on each of the other 2 dozens and , if one of them wins , put the resulting 3 chips on the 4th number.
Read and digest .
With volatility and the need for virtual spins I think programming it
would be challenging  but then , I am not a programmer.The best of luck.

Scepticus,
I'm none the wiser, I'm afraid. This is far too vague, computers are completely stupid and only do what they're told to do, no more and no less, so if I can't play your system manually (which I can't, at the moment), then I certainly won't be able to tell the computer how to do it.
If you could show how you play these 20 spins with stepbystep instructions, I might be able to get a handle on it. Thanks.
21
19
29
36
7
7
16
12
20
2
7
11
6
34
24
35
12
8
23
24

Hi slacker. Thanks for your question .To keep things tidier I have given my reply in Scep's Roulette Strategies.

In my years of reading on forums, this is the one error I see time and time again. It concerns confusing the probability of a series with that of a single.
You can indeed make a system out of the knowledge that there is at least one repeat with probability 56% in the last 8 spins, but in order for the probability to remain valid, you have to place your bets from spin 1, not after spin 7. So on spin 1 you put one chip on the last outcome, on spin 2 add another chip to whatever just hit, and so on, until you get a repeat (a win). But in that case, your profit will vary according to when you get the repeat, assuming you do get it. 56 times out of 100 you will indeed get at least one, but what you cannot say is that you will win 29 chips 56 times out of 100, betting 7 numbers!
Yes your logic complies with probability theory. But there is another force that enters the picture.
If you study many many numbers, you will find that this 56% or any other percentage, takes place MORE FREQUENTLY within a range determined by empirical research. In your example, will the repeat occur in the very 1st spin, or will it occur in the 8th spin? Very unlikely. Lets say after processing hundreds of thousands of numbers, you will find that the 56% remains true to its probability, however the 56% happens a lot more often within the range of the 3rd spin to the 7th spin. Meaning that if the 56% chance of a repeat stands, it is more likely to happen between the 3rd and the 7th spin. If that's true, doesn't make more sense to bet this range, instead of the entire 8 spin range?
Secondly, who says that if you have to bet all 8 spins to enjoy the 56% chance, you can't bet $0.50 in the first 2 spins, then $10 from spin 3 to 7 and then stop?
Empirical research, is not against probability. It goes a further step to determine the range within which, the action is most likely to happen.
These are the issues that probability theory does not address. It can only assign values for individual events or series of events. The range of action is something only a player can determine, after extensive research. And that results in probabilities of occurrence within a specific range. What's wrong with using these probabilities?
Police departments are on guard for driving violators. Y are they more vigilant between 1 am and 4 am? And far more relaxed between 9 am and 5 pm?
Range of occurrences is part of every day life. Roulette is not an exception.

Guys,
Again, you can't step outside of probability with your virtual bets and take advantage of bets that you believe are "due". Again, gambler's fallacy. Look it up.

Guys,
Again, you can't step outside of probability with your virtual bets and take advantage of bets that you believe are "due". Again, gambler's fallacy. Look it up.
How is the fact that the probability of 8 black in a row is [18/37]^8, outside probability? And how "what is due" fits in? We are talking about at least one event happening within a series of events.

Secondly, who says that if you have to bet all 8 spins to enjoy the 56% chance, you can't bet $0.50 in the first 2 spins, then $10 from spin 3 to 7 and then stop?
Of course you can do that, it's called a progression. My point was that you cannot take the probability of the series and apply it to the next spin.
These are the issues that probability theory does not address. It can only assign values for individual events or series of events.
Umm... there are ONLY individual events and series of events, they encompass the totality of possibilities, so what is it that probability theory can't deal with?
The range of action is something only a player can determine, after extensive research. And that results in probabilities of occurrence within a specific range. What's wrong with using these probabilities?
There are not two kinds of probabilities  "theoretical" and "empirical". Assuming a fair wheel, all empirical probabilities will conform to the theoretical probabilities. I think the problem is that people don't understand that the word "theoretical" in this context doesn't mean a guess, or something that hasn't been verified by experience. In fact it means the opposite.
In science, the term "theory" refers to "a wellsubstantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment."^{[14]}^{[15]} Theories must also meet further requirements, such as the ability to make falsifiable predictions with consistent accuracy across a broad area of scientific inquiry, and production of strong evidence in favor of the theory from multiple independent sources.

I do not understand what you mean with the error in propability.
From my point of view the propability theory fails for a short run event.The propability theory is very interested for researching large events. A roulette player plays always small events.

Secondly, who says that if you have to bet all 8 spins to enjoy the 56% chance, you can't bet $0.50 in the first 2 spins, then $10 from spin 3 to 7 and then stop?
Of course you can do that, it's called a progression. My point was that you cannot take the probability of the series and apply it to the next spin.
These are the issues that probability theory does not address. It can only assign values for individual events or series of events.
Umm... there are ONLY individual events and series of events, they encompass the totality of possibilities, so what is it that probability theory can't deal with?
The point is that the probability of series stands, whether you are in the second spin or third or fifth. As long as you start the betting process form spin one. When you deal with a series of bets, there is only one probability from the beginning until what you are aiming for happens, or till the end of the series. Is that understood?
The value doesn't change if you missed the first 2 or 3 spins in an 8 preplanned spin series.
If you missed one or a few spins, that doesn't mean that the probability of series is invalid, and it only counts what happens after the missed spins. Otherwise it would make no sense to have probability of series. So my question in your example is this. Is the probability of a repeat in 8 spins still 56%, after missing the first 6 spins? (Yes the betting process started form spin 1). The probability of series specifies a specific percentage of at least one success in a preplanned 8 series of bets. That percentage does not and should not change just because the first 6 spins missed the target.
Of course seeing 6 missed spins somewhere on a score board, is not the same as being part of the betting process from spin 1. Ready made virtual losses do not count (up to a certain extend). The player HAS TO BE in the betting process from the start. The bet amounts is another issue, and that's where a construction of a good system starts.

I do not understand what you mean with the error in propability.
From my point of view the propability theory fails for a short run event.The propability theory is very interested for researching large events. A roulette player plays always small events.
Yup. I forgot to mention that. Though probability is correct in large data, when it comes to roulette and short data probability is always WRONG. And that's what a smart player can take advantage of.

when it comes to roulette and short data probability is always WRONG. And that's what a smart player can take advantage of.
No, it's just your comprehension of it that is wrong. And no, the smart player can't consistently take advantage of several short run plays, since the house payoff is short of what probability dictates fair.
Real

So my question in your example is this. Is the probability of a repeat in 8 spins still 56%, after missing the first 6 spins? (Yes the betting process started form spin 1). The probability of series specifies a specific percentage of at least one success in a preplanned 8 series of bets. That percentage does not and should not change just because the first 6 spins missed the target.
Yes, the probability of a repeat in 8 spins is always the same, but this is irrelevant to past spins, the probability of which is always 1, assuming we know what the outcomes were, of course.
Again, I have to stress that the error made by scepticus and many others, is that you cannot assign a probability of a complete series to the next single outcome, or part of that series. What's past is gone, and probability does not apply, certainty does.
So on the 8th spin the chance of any of the previous 7 numbers repeating is 1x 1 x 1 x 1 x 1 x 1 x 1 x 7/37 ~ 19%, not 56%.
The casino does not let us bet directly on a series; we have to bet one spin at a time. And even if it did, they would adjust the payouts accordingly so that they have the edge.
when it comes to roulette and short data probability is always WRONG. And that's what a smart player can take advantage of.
In a sense, you're correct. Probability is an average and averages become more meaningful as the sample size increases, but the "best guess" for the next single outcome is the average. If this were not true, the probability of a series would also be wrong, since it is by definition the probability of a sequence of SINGLE events.
Also, the concept of variance is needed to complete the picture. A data set is specified by the average and also the variance (how much the data is "spread out" around the average). All this can be quantified quite precisely.
And I don't see how you can take advantage of something being wrong if you don't know what is RIGHT! If you know nothing about how likely the next outcome is, as you say probability cannot tell you this, then how does this help or give any advantage? In that case you can say nothing at all, and you may as well bet randomly.

I will not say I am a smart player, but I take my advantage of the knowledge of the short run theory.

dobbelsteen, what is the difference between the short run theory and the long run theory? Isn't the short run theory just the long run theory applied to the short run?
The thing is, probability is just so basic a concept that it's hard to define, although everyone knows what it means. You might remember that guy Ashley Revell who some years ago went to LV and put his entire life savings on red. But if probability theory is WRONG in the short term, why didn't he put all his money on number 17? After all, the payoff is much higher!
But of course, you don't need to be a math geek to realize that your chance of success is much higher betting on an even chance, even when betting just one spin.
https://www.youtube.com/watch?v=zGCdBsOIKYA (https://www.youtube.com/watch?v=zGCdBsOIKYA)
But still, he was foolish not to find a singlezero wheel.

So my question in your example is this. Is the probability of a repeat in 8 spins still 56%, after missing the first 6 spins? (Yes the betting process started form spin 1). The probability of series specifies a specific percentage of at least one success in a preplanned 8 series of bets. That percentage does not and should not change just because the first 6 spins missed the target.
Yes, the probability of a repeat in 8 spins is always the same, but this is irrelevant to past spins, the probability of which is always 1, assuming we know what the outcomes were, of course.
Again, I have to stress that the error made by scepticus and many others, is that you cannot assign a probability of a complete series to the next single outcome, or part of that series. What's past is gone, and probability does not apply, certainty does.
So on the 8th spin the chance of any of the previous 7 numbers repeating is 1x 1 x 1 x 1 x 1 x 1 x 1 x 7/37 ~ 19%, not 56%.
The casino does not let us bet directly on a series; we have to bet one spin at a time. And even if it did, they would adjust the payouts accordingly so that they have the edge.
when it comes to roulette and short data probability is always WRONG. And that's what a smart player can take advantage of.
In a sense, you're correct. Probability is an average and averages become more meaningful as the sample size increases, but the "best guess" for the next single outcome is the average. If this were not true, the probability of a series would also be wrong, since it is by definition the probability of a sequence of SINGLE events.
Wait a minute now. Y do we have probability of series, if according to your reasoning is being canceled after every spin? and it turns to a probability of a single event? Just because I bet one spin at a time? What if I lay out an amount enough to cover 8 spins and instruct a robot to bet after every spin? The moment I decide to commence a series of bets and stop at any time I hit the target once, then I am locked into the series. Not the single event. And the key word is hit at least once. I don't aim to hit all or half or three of the 8 spins. Just one at any point in the 8 bet range. Then my mission is over. A single event implies the expectation to hit the next spin according to the probability of the expected result happening. But this is not the case if you decide in advance to bet a series of bets and terminate them when the target is hit at least once.
1x1x1x1x1x1x1x 7/37 is only valid if you happen to see a score board and there is no repeat 7 times, and bet the 8th spin. When you see something already formed is not part of a series because it happened without your input. The probability of series counts only when you are there from the beginning and apply your guessing power or luck from SPIN 1. Not from spin #8. Can you name a situation where the probability of series applies, without betting after every spin?
You can only bet one spin at a time, flip a coin once at a time. Scratch a lottery ticket one at a time.
There in no such thing as betting a series at once as a bulk bet. and if you bet in several roulettes at the same time, then this is not a series bet. It is a multiple single bet.

As far as taken advantage of the wrongness of probability in the short run there is a word for it. EXPERIENCE AND RESEARCH. It doesn't have to be what's missing and what is due. It could be following an obvious trend. Or many other things that only experience can pinpoint.
In my systems what is RIGHT is to hit the target just once. I don't aim in continuous wins. One hit and abandon. That's not too much to ask.
I find these issues extremely important and I am glad I have resolved them.
Whether I will win one of the series of bets is the LEAST of my worries, that's y I am not searching for a winning system. My Biggest worry is when the time comes to bet, if someone else is using cash chips for inside bets, which prevents me from betting. The least I am concerned with is whether I'll win one of the next few bets. The expected result is crystal clear to me, and if the rare event happened, I only lose very little because I stop on time. easily recoverable in the next round.

Again, I have to stress that the error made by scepticus and many others, is that you cannot assign a probability of a complete series to the next single outcome, or part of that series. What's past is gone, and probability does not apply, certainty does. Slacker
Slacker,
Above is the biggest problem confronting many gambler's. The logic required to comprehend it is just out of reach for most of them. No matter how many different ways you explain it, they can't grasp it. There's a level of intellect that is missing that prevents them from ever fully understanding it, and accepting it. Try as you might, you will never convince most of them.
It's often been said by public officials that taxes on gambling and cigarettes is a tax on the poor and ignorant. They're not entirely wrong. The gambler's fallacy is part of that proof.

Again, I have to stress that the error made by scepticus and many others, is that you cannot assign a probability of a complete series to the next single outcome, or part of that series. What's past is gone, and probability does not apply, certainty does. Slacker
Slacker,
Above is the biggest problem confronting many gambler's. The logic required to comprehend it is just out of reach for most of them. No matter how many different ways you explain it, they can't grasp it. There's a level of intellect that is missing that prevents them from ever fully understanding it, and accepting it. Try as you might, you will never convince most of them.
It's often been said by public officials that taxes on gambling and cigarettes is a tax on the poor and ignorant. They're not entirely wrong. The gambler's fallacy is part of that proof.
like I said a million times this problem
Again the expert of repeating the same thing over a million times, without substantiation. The only attempt to substantiate is to parallel unrelated situations with a humorous twist.
Contradicting yourself in the process.
Biased and defective roulettes do not produce unbiased and independent results. When it comes to your methods some roulettes are terribly defective. When it comes to systems they are the poster boy of mechanical perfection. Defects and bias are mutually exclusive with independence of spins.
Sorry. Just the facts. Rather than gathering members to agree with you, prove your points. Then offer in detail your own winning methods for others to comment on.
Prove what you say, rather than referring to textbooks, when it's a well known fact short runs do not necessarily comply with probability. Or tell us what the long run is, so we can have something to work with.
This is what Slacker said: You can indeed make a system out of the knowledge that there is at least one repeat with probability 56% in the last 8 spins, but in order for the probability to remain valid, you have to place your bets from spin 1, not after spin 7
I guess you are asking him to contradict himself.
Or tell the math experts that the probability of series is a myth.
Looking at the picture one can easily conclude that the issue is made up of 2 questions. Not one question. It further implies that a compromise has to be made.

I'm sorry Palestis,
It's unlikely that you will ever comprehend the reasons written above. Furthermore, you keep changing the arguments in a way that doesn't even make sense to other readers.
My suggestion is that you keep your bets low, and increase the number of virtual bets that you place. This will slow the rate at which you inevitably lose your bankroll.
Cheers,
Real

@ Real,
You may be right, but as palestis says, this is very important so I'm going to continue trying. Besides, I find it an interesting challenge. I may not be able to convince palestis, but he's not the only one reading this thread.
palestis, I'm not sure what point you're trying to make because you've repeated some of the arguments I made in previous posts, for example about being able to bet only one spin at a time. I'm not sure where you and I disagree, so can you tell me what precisely you think is wrong with the argument in my first post?
Are you saying that scepticus is correct: that the chance of getting a repeat (a win) on the last spin of the series, given that there have been no previous repeats, really is 56% and not 19%?
Please answer yes or no without going off on a tangent. The issue is really very simple, and I may have in fact muddied the waters by using the idea of series versus single events. It actually comes down to the question of whether spins are independent or not.
Fortunately, we don't have to argue endlessly about any of this, because it would be quite easy to test palestis' theory on some spins.
 The so called NULL hypothesis is that there is no difference between waiting for virtual losses and just betting randomly from the first spin. i.e., Waiting for losses and not waiting will, on average, result in the next win coming just as quickly in both cases.
 The ALTERNATIVE hypothesis is that there IS a difference, so that you are likely to get at least one winner within a shorter number of spins than would be the case if you had NOT waited for the "virtual losses".
However, I'm not so naive that I think palestis will change his mind even with empirical evidence. The trouble is that if you don't understand the principle, then you might be inclined to think that the result only applies to THAT particular system or scenario under test, but what about the infinite number of other possible roulette systems?
I think this is where you're correct, Real. Some people won't ever be able to abstract from the particular details of a system and see that it's built on the same fallacy.

I'm sorry Palestis,
It's unlikely that you will ever comprehend the reasons written above. Furthermore, you keep changing the arguments in a way that doesn't even make sense to other readers.
My suggestion is that you keep your bets low, and increase the number of virtual bets that you place. This will slow the rate at which you inevitably lose your bankroll.
Cheers,
Real
For your info, I don't know what losing is (never mind losing the entire bankroll). The worst thing that has happened is come back from the casino with just $20 over my bankroll. I haven't experience a losing session yet, because I simply don't allow it to happen. Patience has been proven to be the player's greater asset. Nowhere in my play, I find your theories to be valid. So I don't know what you are talking about. Your advice probably better serves a new gambler.

@ Real,
You may be right, but as palestis says, this is very important so I'm going to continue trying. Besides, I find it an interesting challenge. I may not be able to convince palestis, but he's not the only one reading this thread.
palestis, I'm not sure what point you're trying to make because you've repeated some of the arguments I made in previous posts, for example about being able to bet only one spin at a time. I'm not sure where you and I disagree, so can you tell me what precisely you think is wrong with the argument in my first post?
Are you saying that scepticus is correct: that the chance of getting a repeat (a win) on the last spin of the series, given that there have been no previous repeats, really is 56% and not 19%?
Please answer yes or no without going off on a tangent. The issue is really very simple, and I may have in fact muddied the waters by using the idea of series versus single events. It actually comes down to the question of whether spins are independent or not.
The way you are asking the question has nothing to do with the probability of series. You set the condition GIVEN THAT THERE WERE NO PREVIOUS REPEATS. This is simply asking what the next spin will be. In that case it's 19%. Because YOU SET A CONDITION.
The probability of series has no conditions. Just a stipulation to win once out of 8 tries. Provided you place a bet (virtual or real and regardless of $ amount ) in all 8 tries. In that case is 56% till the end of the series. it can happen with the first spin or it can happen with the 8th spin, or it might not happen at all.
If you meant no repeat in the previous 7 spins (provided that you have placed all 7 bets), then there is no answer. What's the importance of the 8th spin anyway, when you had 7 more spins to play?
Probability of series looks at the whole picture, not parts of the picture.
The biggest fallacy of all is to dwell on probabilities, as a means to win the roulette.
THE PLAYER PLAYS IN THE SHORT RUN. And in the short run the rules of probability do not apply.
That's y we have forums. To get information on how to exploit instabilities in the short run and win. . If you think like real, then there should be no need for forums, and no need to play roulette at all. I don't see any FUN in playing a game where losing money is a certainty. I don't even like roulette. The only part I like is that you can create money out of nothing, without manual labor but one's brains. Players who are guided by probability alone, are doing themselves a disservice.
It is the short run we are dealing with, and experience supersedes probability and math.
The goal in playing roulette is not to validate probability theory. it is to leave the casino with more money that you went in with.. If someone doesn't know how, then this is a good place to ask for help.
Comments that I am ignorant of probability and math are redundant. It's a replacement for valid arguments and lack of proof to the contrary. I've been playing roulette too long. And I know exactly where I'm standing. Theories of the "real" type are more suitable for a new kid on the block.

palestis,
I think you misunderstand me, I'm not in the "Real" camp regarding math. I do have a lot of respect for the guy because he really is an expert in advantage play, but as far as he's concerned the mathematical expectation tells you EVERYTHING you need to know about the "game". He takes the view that the random game is unbeatable, so you have to target the physical device, environmental conditions, dealer "signature" and so on. It's not that he's seriously tried the other way and found it wanting, it's just that he dismisses it as a fallacy, because the mathematical expectation of the "ideal" game says that you will inevitably lose "in the long run" owing to the unfair payout, no matter what fancy systems or MM you use.
I know he's mistaken, because I and others do consistently make a profit without using physics. Mathematical expectation is not the ONLY thing that determines whether you win or lose, and I'm not talking about the stuff that gambler's bang on about as being crucial, like "quitting while ahead" (which is meaningless unless you plan to never play again) or selfdiscipline, which is necessary of course, but not sufficient.
There is a kind of "toolbox" of techniques which I use in order to keep the deviations within reasonable limits. and once you can do that, MM takes care of the rest. One of those techniques is to exploit anomalies in the random stream, just as you do. I wouldn't be surprised if we play in a very similar way.
In a nutshell, I attack an anomaly for one or two spins, betting that it will end. If it doesn't I bet that it will continue, then when it does end I switch again and bet that it won't immediately repeat. I have one eye on my W/L results and switch to a different target if things aren't going well. I never "chase" a target with steep progressions, and I always follow a pattern as long as it continues to win. It's that simple.
I have written various programs which track spins and reveal patterns and anomalies, extreme events etc. There are countless opportunities occurring all the time, and I never wait for "triggers", but bet every spin.
I've attached a screenshot of one sequence of my morning's play. After the two long losing sequences (marked with black circles) I started betting for a return to some kind of normality. An event like this (6 wins out of the last 34 spins) is obviously an extreme event and cannot continue. Even if it HAD continued for a bit longer it wouldn't have been a disaster because I would just have kept my bets low until there was some indication of leveling off.
I strongly disagree about your assessment of probability as being useless, or worse, as an aid to playing roulette.
THE PLAYER PLAYS IN THE SHORT RUN. And in the short run the rules of probability do not apply.
In the first place, there is no definite line of demarcation between the "short run" and the "long run"; it's a matter of degree. And isn't the long run just a succession of short runs? In statistical jargon, the "sample" MUST resemble the "population" in some degree in terms of the relative frequency of events.
As I said in my previous post, the probability in the long run of an event (which is what you say IS valid, but useless for the short run  namely, playing roulette), is the BEST GUESS in the short run. If there was not a tendency for a series of single outcomes or events to converge towards their long run probability, then the long run probability would be something OTHER than what it is. That's just common sense.
And you seem to be ignoring the point I made earlier about Ashley Revell. Does probability really have NOTHING to say about what may be the best strategy to use for someone who wants to make his bank last as long as possible during an evening in the casino? This is surely the "short run", but according to you, it makes no difference whether he bets his entire bank on number 17 in one spin or splits it into 100 pieces and plays one piece at a time on red!
Then there's the issue of the house edge. Some games have a much higher house edge than others, does it really make no difference what game you play, since probability is irrelevant in the short run? obviously not.
That's y we have forums. To get information on how to exploit instabilities in the short run and win.
And probability theory is one way of getting that information. You don't have to use it, but it's there to be used, and it can often suggest different lines of attack.
The problem is that guys like Real encourage the view that math and probability is just a stick with which to beat system players over the head with. "The math says you can't win". So end of story. It is so much more than that. It's also worth pointing out that the definition of probability as a "long run relative frequency" is just one interpretation, which is not always useful. See the Wikipedia article:
http://en.wikipedia.org/wiki/Probability_interpretations (http://en.wikipedia.org/wiki/Probability_interpretations)
It's true that the mathematical rules or laws of probability are the same in all interpretations, but these rules have more to do with logic than math; they are just a way of keeping you from contradicting yourself when reasoning with probabilities.

I know he's mistaken, because I and others do consistently make a profit without using physics. Mathematical expectation is not the ONLY thing that determines whether you win or lose, and I'm not talking about the stuff that gambler's bang on about as being crucial, like "quitting while ahead" (which is meaningless unless you plan to never play again) or selfdiscipline, which is necessary of course, but not sufficient.
Sorry Slacker,
But I suspect that you're simply experience the waves of variance in a diminished number of trials. But if you're having fun with it, then have at it.
There is a kind of "toolbox" of techniques which I use in order to keep the deviations within reasonable limits. and once you can do that, MM takes care of the rest. One of those techniques is to exploit anomalies in the random stream, just as you do. I wouldn't be surprised if we play in a very similar way.Slacker
"No betting system can convert a subfair game into a profitable enterprise... "— Probability and Measure(second edition, page 94) by Patrick Billingsley
"The number of ‘guaranteed’ betting systems, the proliferation of myths and fallacies concerning such systems, and the countless people believing, propagating, venerating, protecting, and swearing by such systems are legion. Betting systems constitute one of the oldest delusions of gambling history. Betting systems votaries are spiritually akin to the proponents of perpetual motion machines, butting their heads against the second law of thermodynamics." — The Theory of Gambling and Statistical Logic (page 53) by Richard A. Epstein

Real,
You're so predictable.
But I suspect that you're simply experience the waves of variance in a diminished number of trials.
I've placed well over 100,000 bets each year for the last 3 years or so. Variance? I don't think so.
There ARE those who win consistently without using advantage play. You can choose to believe it or not. That doesn't mean I subscribe to the gambler's fallacy or any other fallacies.

Slacker,
How many units were won over the 100k bets?
A live wheel or an RNG wheel online in fun mode?

palestis,
I know he's mistaken, because I and others do consistently make a profit without using physics. Mathematical expectation is not the ONLY thing that determines whether you win or lose, and I'm not talking about the stuff that gambler's bang on about as being crucial, like "quitting while ahead" (which is meaningless unless you plan to never play again) or selfdiscipline, which is necessary of course, but not sufficient.
There is a kind of "toolbox" of techniques which I use in order to keep the deviations within reasonable limits. and once you can do that, MM takes care of the rest. One of those techniques is to exploit anomalies in the random stream, just as you do. I wouldn't be surprised if we play in a very similar way.
Well there you go. You covered a lot in your post and I'm certainly impressed.
The bottom line is that you win consistently. And it's not by physics or device exploitation.
According to Real, NOBODY can win consistently, unless you take the physics route. If you played that many spins and you are ahead of the game it's definitely not a coincidence. I doubt if Real will believe you, but I have no reason to doubt you because I'm at the same level. And I know people who win consistently. By the way I too play in a similar way. I look for trends and short term anomalies. The secret is to limit the bets to a minimum, whether following an anomaly or betting that it will stop. That way you can never lose your shirt, especially with aggressive progression if the exception happens. If it doesn't work in one cycle, it is highly unlikely that it won't work in the next cycle of anomalies. And with a good MM system you can recover and also you can neutralize the effects of the HE
When we talk about probabilities, it's not always about "what is due to happen". I'm sure you have your own probability figures regarding the chances of an anomaly being continued for one more time or the probability to stop after a certain point. But I can't let probability and the unfair payout prevent me from winning, as there are opportunities emerging all the time that can be taken advantage of.
Probability is only a part of the game. there are other things involved as long as you know how to spot opportunities. That is y I don't spend much time philosophizing about probability. My focus is to identify opportunities. Whatever probability is behind it, I don't care. It automatically kicks in because all these opportunities fall into identifiable groups. Once you have established a plan of action there is no need to consult with probabilities. They are built in the plan of action.
But anyway, after saying that you have been winning consistently, you obviously admit that there are ways to win roulette with systems, So the argument is settled.
Because from your initial posting, you came across as a non believer of systems. And as your reasoning seemed to be the probability disadvantage.
Now the question is, can you convince another member in this forum?
Because he's already started to ask you questions about your play. If it was live wheel or RNG or play for fun. Obviously he doesn't believe that you have consistent winnings, even if he initially agreed with your reasoning.
Maybe you should post one of your systems regarding anomalies or trends so we can analyze it.
That would be for more productive, instead of dwelling on probability theories.
As far as physics and VB and bias and defects, in the pic below the expert author describes his encounter with casino stuff, after watching and clocking the wheel.
Not after playing and winning, but simply by watching.

For your info, I don't know what losing is (never mind losing the entire bankroll). I The worst thing that has happened is come back from the casino with just $20 over my bankroll. I haven't experience a losing session yet, because I simply don't allow it to happen. Patience has been proven to be the player's greater asset. Nowhere in my play, I find your theories to be valid. So I don't know what you are talking about. Your advice probably better serves a new gambler.Palestis
Oh my! So you've never even lost before! Bedazzling!
(https://forum.roulette30.com/proxy.php?request=http%3A%2F%2Fwww.myhusbandateallmyicecream.com%2Fwpcontent%2Fuploads%2F2013%2F02%2Fbedazzled_g1.jpg&hash=5e68af304f3410eeed80f1dbc3f25532)
According to Real, NOBODY can win consistently, unless you take the physics route. If you played that many spins and you are ahead of the game it's definitely not a coincidence. I doubt if Real will believe you, but I have no reason to doubt you because I'm at the same level.Palestis
Palestis,
That is correct! Nobody can win consistently, unless they're exploiting the gaming device. And it's not just my opinion, it's history's as well. Furthermore, you can win some serious money if you can prove that it can be done!
$30,000 Betting System Challenge
http://vegasclick.com/gambling/bettingsystemchallenge.html
A positive variance after 300k spins? Maybe, depends on how many numbers you bet, on how many spins bets are actually placed, and whether or not you're flat betting or running a progression. An internet friend, named Kelly, had one survive over a million trials. I've also seen it done when people have played in free mode via online sites and using an rng source from the older versions of Excel. However, it's much like playing slots in the free mode online. Everyone seems to win on that free app as well. (By the way, I really doubt Bayes is playing in free mode. I'm sure he knows the difference, but many of "the holy grail searchers" on the forums aren't aware of the difference.)
If someone repeated the test and won a relevant amount after one million trials from random.org, flat betting, then I'd be more impressed. Unfortunately, too many people are working from some of the Wiesbaden and other public board data samples, where you'll likely find board misreads and or repeats. Corrupt data samples are sometimes the source of such anomalies.
Furthermore, surviving after thousands of spins and winning 20, 30, or even 100 units also isn't a break through. It's usually nothing more than variance, or corrupt data. If someone had to play that way for a living, then they'd certainly starve to death.
Palestis, I have to say, you're on an entirely different level! You're above and beyond the rest of us... having never lost and all. I mean, you're definitely better than Bayes and me, because I sometimes lose. I suspect he's lost, like me, before as well. ( Yes, really, I lose sometimes.) Perhaps it's because the rest of us play in the real world though, ya think???
Cheers,
Really


Slacker,
How many units were won over the 100k bets?
A live wheel or an RNG wheel online in fun mode?
I mostly play a nozero RNG, even chances. With no house edge I shouldn't be making ANY profit at all over time, but I'm way up. I'd rather not say exactly how much, but I'll create some vids of playing sessions with running commentary to give you an idea of the techniques I use and the win rate. I'll upload the vids to youtube and post the links here.

For your info, I don't know what losing is (never mind losing the entire bankroll). I The worst thing that has happened is come back from the casino with just $20 over my bankroll. I haven't experience a losing session yet, because I simply don't allow it to happen. Patience has been proven to be the player's greater asset. Nowhere in my play, I find your theories to be valid. So I don't know what you are talking about. Your advice probably better serves a new gambler.Palestis
Oh my! So you've never even lost before! Bedazzling!
According to Real, NOBODY can win consistently, unless you take the physics route. If you played that many spins and you are ahead of the game it's definitely not a coincidence. I doubt if Real will believe you, but I have no reason to doubt you because I'm at the same level.Palestis
Palestis,
That is correct! Nobody can win consistently, unless they're exploiting the gaming device. And it's not just my opinion, it's history's as well. Furthermore, you can win some serious money if you can prove that it can be done!
$30,000 Betting System Challenge
http://vegasclick.com/gambling/bettingsystemchallenge.html
I lost before as I was gaining experience. Now days I almost never lose. That doesn't mean I always win.
I avoid losing by stopping on time. I simply exercise the roulette player's greatest advantage, You can stop anytime and walk away. Whether winning at this point or losing very little compared to the average session winnings. There is no CONTRACT in roulette playing, to wage your bets indefinitely. And neither a contract to bet a specified amount. The player has absolute freedom to come and go as he pleases. Let's not forget that.
What history and experts are you talking about?
Show me the work of an expert, where I can read an in depth study that should've
taken years to complete, and then I might pay some attention. With specific approaches and details. There is none. It's all hearsay.
As far as the Vegas click challenge you have to be naïve to take it seriously. Part of the conditions are to play for 200,000 spins. Impossible in live roulette. Possible in simulation, but simulation does not allow for instant (spurr of the moment) player's input. Preprogrammed plans of action, do not resemble real life situations. Like quitting. And waiting for conditions to change. Simulation has to have all those factors preplanned before it can proceed. On top of it, it doesn't allow for a player's 6th sense. Which is very much active during the game. So the possibility that someone will take the challenge does not exist.
The only way you can resolve the roulette challenge is for a team of players to get together and spend 1 year in a casino. Then they can lay out their systems and methods and test them out in a real environment and see the results.
Since that's unlikely to happen, the debate will go on for ever.
At the end what counts is the player's own experience. Only he knows where he stands with the game of roulette.
For you all those who are winning consistently are liars. Because according to your ghost experts they shouldn't be winning. Beating the device is easy to say.
Y do you avoid posting its details, so others can comment?

Palestis,
There's no difference between playing 200k consecutively or off and on over several weeks.

Beating the device is easy to say.
Y do you avoid posting its details, so others can comment?
That wouldn't be such a great idea on a public forum. Casinos don't care about mathematical systems, but they are interested in methods which target the wheel, dealer etc, and would take steps if they were made aware of any weaknesses. Real obviously doesn't want to share trade secrets, and who can blame him?
The terms of that challenge are actually pretty good, but I doubt whether anyone will ever beat it. Ideally, a system should be as mechanical as possible, but it would be a lot of work programming it, and assuming it did "work", where would the fun be in playing any more? I play as much for fun as the money, but then, it's not much fun losing.

FWIW, an interesting article by Al Krigman (casinocitytimes.com)
Betting Systems: Verity or Voodoo?
A primary gambling theorem holds that betting systems can't alter expectation  expected percentage gain or loss  in independenttrial games of chance. For instance, raising or lowering bets in some pattern from hand to hand at baccarat doesn't change house advantage. Likewise, big bucks on pass with full odds at craps has the same house edge as an equal amount on pass and one or more come bets with comparable odds.
Yet, gamblers galore believe strongly that how they bet affects their chances to win. And a surfeit of "systems" can be found claiming to exploit secrets about simultaneous and sequential wagering schemes the casino bosses don't want anyone to know.
Who's right: the cerebral statisticians or the superstitious solid citizens? Surprise! Both are correct. The apparent conflict only arises because they're talking about different things.
Expectation, which betting systems don't change, is an objective criterion. It's what the casino earns by virtue of its edge. And, it's a longterm average which stabilizes after tens or hundreds of thousands of decisions  many more than a single bettor would encounter even after protracted play.
Individual success, which may be influenced by systems, is a subjective goal. It may involve a host of nonmonetary factors such as obtaining free meals or maximizing playing time, along with targets ranging from breaking even or showing a small profit to doubling a bankroll or hitting a lifestylechanging jackpot. Moreover, it's a shortterm effect which may be dominated by statistical properties of the game other than expectation.
To see the implications, picture seven players, all of whom gamble two weeks in a row with budgets first of $240 then of $480. Their goals are to double their bankrolls at roulette each week or lose the money trying. They'll all bet $12 a pop, but will use different betting systems. These are summarized below, with associated probabilities of winning and payoffs.
Player System
Al $12 on a single number (2.63 percent, pays $420)
Betty $6 on each of two numbers (5.26 percent pays $204)
Carl $4 on each of three numbers (7.89 percent, pays $132)
Dee $3 on each of four numbers (10.52 percent, pays $96)
Ed $2 on each of six numbers (15.79 percent, pays $60)
Fran $1 on each of 12 numbers (31.58 percent, pays $24)
Gail $6 on 112 and $6 on 1324 (63.16 percent, pays $6)
The players all have the same expectation  a theoretical loss of 5.26 percent or $0.6312 per round on their $12 bets. The casino, which takes the long view, would rate them equally. Their systems are irrelevant in this respect.
Chances the players will double their money each week before tapping out differ, however, owing to singleround risk and reward characteristics and the bettobankroll sizes. The probabilities of success are shown below.
Player $240 $480
Al 48% 47%
Betty 47% 44%
Carl 45% 40%
Dee 43% 37%
Ed 39% 29%
Fran 33% 20%
Gail 11% 2%
These probabilities suggest that to double a stake before losing it, chances of success improve as bets become a) greater longshots with larger payoffs but steeper odds, and b) higher fractions of the starting bankroll. Players having other criteria  say, extending a streak of winning games without regard to amount, minimizing the chance of going bellyup, or testing the air in a highlimit pit  might find this strategy disastrous.
Betting systems can be optimized for any specified gambling goals. High likelihood is no guarantee, of course. And, don't forget the insidious law of unintended consequences. Raising the chance of meeting a specified set of goals may have an unpleasant downside, like excessive loss when things go wrong, too long a required playing time, sacrifice of a desirable fallback position, or sneers from dealers you're trying to impress.

A session of two weeks says nothing.The final result depends on the number of spins.This example is easy to symulate on the computer. I predict, together they will lose and one or two will have a small profit. Nobody shall double his start amount.

I'll upload the vids to youtube and post the links here.
Can we expect this anytime soon?

The $30,000 Challenge doesn't actually dismiss the possibility of a winning system. He says that no one who had a winning system would sell it . His target is scammers who GUARANTEE that their system wins all the time.

The $30,000 Challenge doesn't actually dismiss the possibility of a winning system. He says that no one who had a winning system would sell it . His target is scammers who GUARANTEE that their system wins all the time.
If there was a HG then would be any interest at all for its creator to reveal,publish,sell it???
I think the common sense says a big NO.
BUT,this doesn't mean that someone out there winning consistently while staying under the "radars"...

LOL. The players are like robots in his example. Why? Because he wants to have an easy time writing an article while sounding intelligent.

Slacker. Just an explanation. When I read or hear about an unusual comment made by a mathematician I ask myself " Can I use that idea in roulette ? " You read my Birthday Problem Method " but failed to point out that it was derived from the birthday problem supposition that if 23 people were in a room then the probability of two of them sharing the SAME birth date was just over 50 %. I merely applied that argument to roulette by reducing the 356 to 37 and adjusting the maths. So , IN THEORY , there NEEDS to be 23 already in the room and so the NEED for 8 numbers to have already been spun . So your view that you need to start from a base of one is wrong.
It is just an idea I put on the table and , like my others , put there on a take it or leave it basis.

I merely applied that argument to roulette by reducing the 356 to 37 and adjusting the maths. So , IN THEORY , there NEEDS to be 23 already in the room and so the NEED for 8 numbers to have already been spun . So your view that you need to start from a base of one is wrong.
I think the point trying to be made was not that you should start from a base of one but that if you calculate in advance the probability of a series you cannot then wait for the series to be partially completed and then calculate the chance of the remaining spins given what has already happened. To do that assumes that outcomes are not independent. It's just the gambler's fallacy rearing its ugly head again.

No Mike, the point Slacker was making was that I WAS indulging in the Gamblers ' Fallacy and you are doing the same here.
I was merely taking the maths of the Birthday Problem adjusting it from 365 Days to 37 spins. and finding that 8 was the resultant number. Waiting does NOT necessarily apply here . If 23 people are already in the room then the calculation can be applied.So, like Slacker , you misunderstand the nature of the problem.
Incidentally,it should be noted that the Birthday Problem refers only to the Probability of two people sharing the same birthday  not the certainty that they will do so.
What I was doing is what I said I did  take something a mathematician said that seemed unusual and tried to apply it to roulette.

I merely applied that argument to roulette by reducing the 356 to 37 and adjusting the maths. So , IN THEORY , there NEEDS to be 23 already in the room and so the NEED for 8 numbers to have already been spun . So your view that you need to start from a base of one is wrong.
I think the point trying to be made was not that you should start from a base of one but that if you calculate in advance the probability of a series you cannot then wait for the series to be partially completed and then calculate the chance of the remaining spins given what has already happened. To do that assumes that outcomes are not independent. It's just the gambler's fallacy rearing its ugly head again.
The probability of series has one value and one value only. And that value remains the same from the beginning of the series till the end, because we don't know when the expected result will happen. Of course looking for 2 results that already happened (partially completed as you say), and they are against the expected outcome of that series (virtual loss), technically cancel the series and a new probability of series is needed for the remainder of the series. But as I have described many times, that's not the case the way I look at it.
I actually bet the entire series. And I'm there on top of the roulette when the actual guessing/betting starts from spin 1 in the series till the end or until the expected outcome occurs. .
I just chose to stick with the situation where my first 2 bets for example lost and then carry the series till the end. I stop the series bet if one of my 2 first guesses won, and then look again for a new series where my first 2 guesses lost (cost free of course). Just because I wait for that particular situation it doesn't mean that the probability of series changes. As by definition probability of series is at least one desired outcome at any point in the series (which is unknown), and then the series ends. Whether the series ended after a LW result or a LLLLW doesn't change its predetermined value. I arbitrarily chose a situation where after guessing AND BETTING my first 2 results were LL.
But I actually placed bets in those 2 results. it just happened that the betting amount in those 2 bets to be $0.001. Don't forget that I didn't look to find those 2 results ready made. I actually placed bets.
So instead of betting a planned $510204080 amount I chose to bet $0.01  0.0151020. For obvious reasons. The question is: does the probability of series change if the bet amounts are of the first kind or they are of the second kind? No it doesn't.
To make things simpler I only bet profit yielding amounts in the most frequent WINNING RANGE of the series. A fact that can only be determined after a long time empirical research.
But as long as I bet all the 5 spins in a 5 event series the probability value is always the same.
That's not the same as looking around for an LL situation first. Because it then becomes a 3 series event, and it has a different (lesser ) value.
The $ amount in each bet doesn't change the value of the series.
That is what you are failing to understand.

scepticus and palestis,
I am not failing to understand anything. On scepticus' website it says that
So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 50% chance that one of the 7 will repeat on the next spin.
scepticus, are you still insisting that this is true? I assume so, because you haven't removed it. :(

scepticus and palestis,
I am not failing to understand anything. On scepticus' website it says that
So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 50% chance that one of the 7 will repeat on the next spin.
scepticus, are you still insisting that this is true? I assume so, because you haven't removed it. :(
It was DERIVED from the Birthday Problem . If THAT is true then it follows that the 8 numbers is also true.
UNLESS you can show that my maths derivation from the Birthday Problem scenario is wrong. So give it a go
Mike and if you do then I will remove it.
It is a theory Mike , nothing more  there are no certainties in roulette.
Since you appear to think that only AP have " educated " guesses then perhaps you will prove that my Double Dozen idea is also a gamblers' fallacy.

scepticus,
Why do you guys have to make everything so complicated? It's very simple, the chance of a hit on any number or group of numbers in one spin is just however many numbers you're betting on, divided by the total possible number of outcomes. You are betting on 7 numbers and there are 37 possible outcomes, so the probability is 7/37, which is very far from 50%.
Obviously, the birthday problem can only apply to spins which have already occurred, not to future spins (unless taken as a series). So if you look at all the consecutive 7 spin sequences in a spin file you will find that around 50% of them do have at least one repeat.

scepticus and palestis,
I am not failing to understand anything. On scepticus' website it says that
So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 50% chance that one of the 7 will repeat on the next spin.
scepticus, are you still insisting that this is true? I assume so, because you haven't removed it. :(
It was DERIVED from the Birthday Problem . If THAT is true then it follows that the 8 numbers is also true.
UNLESS you can show that my maths derivation from the Birthday Problem scenario is wrong. So give it a go
Mike and if you do then I will remove it.
It is a theory Mike , nothing more  there are no certainties in roulette.
Since you appear to think that only AP have " educated " guesses then perhaps you will prove that my Double Dozen idea is also a gamblers' fallacy.
Excuse me Scept,but what has to do the ''birthday paradox'' and a double dozen bet?
I fail to see the connection,also I don't get why every column on your board has (?) three wins,could you analyze your thinking?
It's like you consider three wins in every possible permutation of dozens as sure thing,how come?

scepticus,
Why do you guys have to make everything so complicated? It's very simple, the chance of a hit on any number or group of numbers in one spin is just however many numbers you're betting on, divided by the total possible number of outcomes. You are betting on 7 numbers and there are 37 possible outcomes, so the probability is 7/37, which is very far from 50%.
Obviously, the birthday problem can only apply to spins which have already occurred, not to future spins (unless taken as a series). So if you look at all the consecutive 7 spin sequences in a spin file you will find that around 50% of them do have at least one repeat.
It's not 7 numbers,must be 8 in order to have 53% chance of repeat.

scepticus,
Why do you guys have to make everything so complicated? It's very simple, the chance of a hit on any number or group of numbers in one spin is just however many numbers you're betting on, divided by the total possible number of outcomes. You are betting on 7 numbers and there are 37 possible outcomes, so the probability is 7/37, which is very far from 50%.
Obviously, the birthday problem can only apply to spins which have already occurred, not to future spins (unless taken as a series). So if you look at all the consecutive 7 spin sequences in a spin file you will find that around 50% of them do have at least one repeat.
Get a grip Mike,get a grip. You say that my claim that after 7 spins one is likely to repeat on the next spin is nonsense .Then you claim that if I " look at all the consecutive 7 spin sequences in a spin file I will find that around 50% of them DO have at least one repeat " !!??!!
So I am wrong when I say something but you are right when you say the same thing.
ALL I was doing was floating an idea  nothing more so lighten up .
Anyway, I could do a better demolition job on the idea than you have ! Get the blinkers off Mike.

scepticus and palestis,
I am not failing to understand anything. On scepticus' website it says that
So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 50% chance that one of the 7 will repeat on the next spin.
scepticus, are you still insisting that this is true? I assume so, because you haven't removed it. :(
It was DERIVED from the Birthday Problem . If THAT is true then it follows that the 8 numbers is also true.
UNLESS you can show that my maths derivation from the Birthday Problem scenario is wrong. So give it a go
Mike and if you do then I will remove it.
It is a theory Mike , nothing more  there are no certainties in roulette.
Since you appear to think that only AP have " educated " guesses then perhaps you will prove that my Double Dozen idea is also a gamblers' fallacy.
Excuse me Scept,but what has to do the ''birthday paradox'' and a double dozen bet?
I fail to see the connection,also I don't get why every column on your board has (?) three wins,could you analyze your thinking?
It's like you consider three wins in every possible permutation of dozens as sure thing,how come?
Hi Blue Angel .
Forget about the birthday paradox. That was only in reply to Mike. He was selective in his choice of my ideas so I asked him to look at the Double Dozen Method.
As for the blocks.
You already know that we allocate the numbers to a particular dozen .
112 is Dozen 1
1324 is Dozen 2 and
25  36 is Dozen 3.
Think of ANY four consecutive dozens from those three. . They can all be the same  or different
1111 / 1321 , whatever.
Look at ANY block and EACH downward foursome and you will find that at least one of them contains 3 correct
While these 9 particular blocks are mine I have copied the idea from the work of REAL mathematicians .
They were made initially for " football pools " in the UK away back in the 1940 / 1950 s. I have just adapted them for roulette.
If you are still not sure then just ask .

By saying 3 correct what exactly do you mean?
Do you mean that if you bet in a certain way then you are going to win 3 times guaranteed??

By saying 3 correct what exactly do you mean?
Do you mean that if you bet in a certain way then you are going to win 3 times guaranteed??
No . Only that there will be three wins in one of the columns in each block. To guarantee 3 together , in the absence of a zero , needs 36 bets. As we only get 27 returned when one wins this is not viable although there will be times that there will be 4 threesomes.  so 4 x 27 .
To get a better understanding I suggest that you look only at the first 3 . After the first two spins look at the number below them .It SHOULD win roughly 1 in 3 so might appeal to those who use dozens in a progression.
After that look at the probabilities of having 3 and 4 parlayed.
The problem ? We must choose which to parlay from the 9 available ? Can we reduce this number to give us an edge ? I say we can . Others differ . So what's new , pussycat ?

Get a grip Mike,get a grip. You say that my claim that after 7 spins one is likely to repeat on the next spin is nonsense .Then you claim that if I " look at all the consecutive 7 spin sequences in a spin file I will find that around 50% of them DO have at least one repeat " !!??!!
So I am wrong when I say something but you are right when you say the same thing.
scepticus,
They are not at all the same thing. It's not me who is wearing the blinkers. Let's take it step by step. Suppose you start tracking and your first number is 17 (1)
17
the probability of a repeat in the next spin is now 1/37, because there is only 1 way a repeat could occur.
21 hits
17, 21
the probability of a repeat in the next spin is now 2/37, because there are 2 ways a repeat could occur.
11 hits
17, 21, 11
the probability of a repeat in the next spin is now 3/37, because there are 3 ways a repeat could occur.
8 hits
17, 21, 11, 8
the probability of a repeat in the next spin is now 4/37, because there are 4 ways a repeat could occur.
32 hits
17, 21, 11, 8, 32
the probability of a repeat in the next spin is now 5/37, because there are 5 ways a repeat could occur.
12 hits
17, 21, 11, 8, 32, 12
the probability of a repeat in the next spin is now 6/37, because there are 6 ways a repeat could occur.
19 hits
17, 21, 11, 8, 32, 12, 19
the probability of a repeat in the next spin is now 7/37, because there are 7 ways a repeat could occur.
But according to your reckoning, the probability of the next spin resulting in repeat at this point (1 spin remaining) is 53%. Do you see how this is mistaken?
If you don't agree, please point out where you think I have made a mistake.

The average is between 7 and 8. And of course for each more numbers, the probability for a repeat
increase.
Here is such a large variance, the average is not so frequent, it can be much usefull.
Compare to say RED happens on average every second spin on NOZ, it do not help very much to make a staking plan.
I have played around with betting system on repeating numbers a lot, and found it is not easy to make a negative progression. To frequent runs which dig us Deep.
A positive progression works much better. And make it bold. If we use 69 numbers, for example
the first fallen. We won't win if a hit delay after 7 numbers fallen. I use to progress
1,3,7,15 on a hit (I use low stake), and then will get faster back on 1 or 2 hits.

Get a grip Mike,get a grip. You say that my claim that after 7 spins one is likely to repeat on the next spin is nonsense .Then you claim that if I " look at all the consecutive 7 spin sequences in a spin file I will find that around 50% of them DO have at least one repeat " !!??!!
So I am wrong when I say something but you are right when you say the same thing.
scepticus,
They are not at all the same thing. It's not me who is wearing the blinkers. Let's take it step by step. Suppose you start tracking and your first number is 17 (1)
17
the probability of a repeat in the next spin is now 1/37, because there is only 1 way a repeat could occur.
21 hits
17, 21
the probability of a repeat in the next spin is now 2/37, because there are 2 ways a repeat could occur.
11 hits
17, 21, 11
the probability of a repeat in the next spin is now 3/37, because there are 3 ways a repeat could occur.
8 hits
17, 21, 11, 8
the probability of a repeat in the next spin is now 4/37, because there are 4 ways a repeat could occur.
32 hits
17, 21, 11, 8, 32
the probability of a repeat in the next spin is now 5/37, because there are 5 ways a repeat could occur.
12 hits
17, 21, 11, 8, 32, 12
the probability of a repeat in the next spin is now 6/37, because there are 6 ways a repeat could occur.
19 hits
17, 21, 11, 8, 32, 12, 19
the probability of a repeat in the next spin is now 7/37, because there are 7 ways a repeat could occur.
But according to your reckoning, the probability of the next spin resulting in repeat at this point (1 spin remaining) is 53%. Do you see how this is mistaken?
If you don't agree, please point out where you think I have made a mistake.
Brains can’t handle the compounding power of exponents,we expect probabilities to be linear.
Here’s an example: What’s the chance of getting 10 heads in a row when flipping coins?
The untrained brain might think like this:
“Well, getting one head is a 50% chance,getting two heads is twice as hard, so a 25% chance,getting ten heads is probably 10 times harder… so about 50%/10 or a 5% chance.”
And there we sit, smug as a bug on a rug,no dice bub!:)
After pounding your head with statistics, you know not to divide, but use exponents.
The chance of 10 heads is not .5/10 but .510, or about .001.
It’s like asking “What’s the chance of getting one or more heads in 23 coin flips?”
There are so many possibilities: heads on the first throw, or the 3rd, or the last, or the 1st and 3rd, the 2nd and 21st, and so on.
How do we solve the coin problem? Flip it around (Get it? Get it?).
Rather than counting every way to get heads, find the chance of getting all tails, our “problem scenario”.
If there’s a 1% chance of getting all tails (more like .5^23 but work with me here), there’s a 99% chance of having at least one head.
I don’t know if it’s 1 head, or 2, or 15 or 23: we got heads, and that’s what matters.
If we subtract the chance of a problem scenario from 1 we are left with the probability of a good scenario.
The same principle applies for birthdays.
Instead of finding all the ways we match, find the chance that everyone is different, the “problem scenario”.
We then take the opposite probability and get the chance of a match.
It may be 1 match, or 2, or 20, but somebody matched, which is what we need to find.
square root (n) is roughly the number you need to have a 50% chance of a match with n items.
sqrt(365) is about 20.
Exponential growth rapidly decreases the chance of picking unique items (aka it increases the cranes of a match). Remember: exponents are nonintuitive.
Remember how we assumed birthdays are independent? Well, they aren’t.
If Person 1 and Person 3 match, and Person 3 and 5 match, we know that 1 and 5 match also.
The outcome of 1 and 5 depends on their results with 3, which means the results aren’t an independent 1/365 chance (in our case, it’s a 100% chance of a match).
When counting pairs we did math as if birthdays were like independent coin flips, and multiplied probabilities.
This assumption isn’t strictly true but it’s “good enough” for a small number of people (23) compared to the sample size (365).
It’s unlikely to have multiple people match and screw up the independence, so it’s a good approximation.
It’s unlikely, but it can happen. Let’s figure out the real chances of each person picking a different number:
The first person has a 100% chance of a unique number (of course)
The second has a (1 – 1/365) chance (all but 1 number from the 365)
The third has a (1 – 2/365) chance (all but 2 numbers)
The 23rd has a (1 – 22/365) (all but 22 numbers)
When x is close to 0, a coarse firstorder Taylor approximation for ex is:
\displaystyle{e^x \approx 1 + x}
so
\displaystyle{ 1  \frac{1}{365} \approx e^{1/365}}
Using our handy shortcut we can rewrite the big equation to:
\displaystyle{p(different) \approx 1 \cdot e^{1/365} \cdot e^{2/365} \cdots e^{22/365}}
\displaystyle{p(different) \approx e^{(1 2 3 ... 22)/365}}
\displaystyle{p(different) \approx e^{(1 + 2 + ... 22)/365}}
But we remember that adding the numbers 1 to n = n(n + 1)/2.
Don’t confuse this with n(n1)/2, which is C(n,2) or the number of pairs of n items.
They look almost the same!
Adding 1 to 22 is (22 * 23)/2 so we get:
\displaystyle{p(different) \approx e^{((23 \cdot 22) /(2 \cdot 365))} = .499998}
This approximation is very close and good enough for government work, as they say.
If you simplify the formula a bit and swap in n for 23 you get:
\displaystyle{p(different) \approx e^{(n^2 / (2 \cdot 365))}}
and
\displaystyle{p(match) = 1  p(different) \approx 1  e^{(n^2 / (2 \cdot 365))}}
Let’s generalize the formula to picking n people from T total items (instead of 365):
\displaystyle{p(different) \approx e^{(n^2 / 2 \cdot T)}}
If we choose a probability (like 50% chance of a match) and solve for n:
\displaystyle{p(different) \approx e^{(n^2 / 2 \cdot T)}}
\displaystyle{1  p(match) \approx e^{(n^2 / 2 \cdot T)}}
\displaystyle{1  .5 \approx e^{(n^2 / 2 \cdot T)}}
\displaystyle{2ln(.5)\cdot T \approx n^2}
\displaystyle{n \approx 1.177 \sqrt{T}}
If you take square root(T) items (17% more if you want to be picky) then you have about a 5050 chance of getting a match.
If you plug in other numbers you can solve for other probabilities:
\displaystyle{n \approx \sqrt{2ln(1m)} \cdot \sqrt{T}}
Remember that m is the desired chance of a match (it’s easy to get confused, I did it myself).
If you want a 90% chance of matching birthdays, plug m=90% and T=365 into the equation and see that you need 41 people.
For Roulette numbers is the same,just replace 365 with 37 and 23 with 8 and you arrive approximately on 53%
Wikipedia has even more details (https://en.wikipedia.org/wiki/Birthday_problem) to satisfy your inner nerd!:)

Figuring probabilities using intuitive leaps very often results in errors. There's no substitute for the plodding, methodical approach.

It is a very low probability we will get 16 heads in a row! Yes it is, nothing to discuss.
In a game it is hard to use this fact.
Unless somebody gave you odds over 50% on each flip. Even then it is hard, if you not have plenty of time, and/or a lot of Money.
Betting plans can overcome most of the variance, but NOT all, and it will end up in a sudden loss, or
a slow drain, depending of how we play. It can process fast, from the first trial, and it can delay
so the game is over Before any nasty happen.
When Florence Martingale makes the last bet at the table limit on red (NOZ), the rare case has happen
already with a probability of 100%, Her Destiny is judged by if a even more rare case should happen,
the probability of the extended event is 50% , win or lose, recover +1 in that spin or lose all bets on that run.
I am not free from thinking of and using rare cases, but I know it would not help me calculating
the odds, it never does on Roulette, we know it Before. I know as well it will not harm, if
I hit the bet I win otherwise I lose.
There is no "You must lose" and there is no "You must win"! Some care can make loss less.

Mike. If we are to think outside of the box then we must challenge the " received wisdom". You blindly accept that "You cannot use past numbers "so you continue to be trapped inside the box. So you are blinkered until you accept that there MAY be a different way to look at things.
What I presented was only a different way of looking at things. It DOES need at least 23 people in a room for
there to be a better than 50% chance that two of them having the same birthday . That does not mean that there WILL be  or even in the next HUNDRED series of 23 ONLY the probability.
I have only transferred the idea to roulette . If there NEEDS to be 8 then 7 is a good starting point because the Probability does not kick in until 8.Start from the 7th and bet the last 7 numbers for 5 spins MIGHT give a profit .
You yourself gave credibility to the idea when you said that previous lists of 7 gave a 50 % probability of two being the same .

scepticus,
Can we stick to the SPECIFIC case? You have stated that :
the probability of the next spin resulting in repeat at this point is 53%.
And I have just shown using simple arithmetic why this cannot be true. What, SPECIFICALLY, do you object to and where have I gone wrong, in your view?
Presumably you don't object to the "received wisdom" that 2 + 2 = 4?
Accusing me of being "trapped in the box" etc, is not helpful.
You yourself gave credibility to the idea when you said that previous lists of 7 gave a 50 % probability of two being the same .
That's your interpretation, but it was not my intention. I'm curious how you calculated this probability anyway, could you show me?

scepticus,
Can we stick to the SPECIFIC case? You have stated that :
the probability of the next spin resulting in repeat at this point is 53%.
And I have just shown using simple arithmetic why this cannot be true. What, SPECIFICALLY, do you object to and where have I gone wrong, in your view?
Presumably you don't object to the "received wisdom" that 2 + 2 = 4?
Accusing me of being "trapped in the box" etc, is not helpful.
You yourself gave credibility to the idea when you said that previous lists of 7 gave a 50 % probability of two being the same .
That's your interpretation, but it was not my intention. I'm curious how you calculated this probability anyway, could you show me?
Since we are into " specifics" Mike , I don't recall saying "the probability of the next spin resulting in repeat at this point is 53% " I am not saying that I didn't , just that I don't recall doing so. So please be " specific" and tell me the " specific " post. If I did not say it I am not required to show you how I calculated it .
And since you claim that my interpretation of your post of June22nd is not what you "intended " it to mean would you now tell us WHAT you did mean ?
You still do not understand that I was only extending the Birthday Paradox into roulette .Perhaps I could make the same claim as you that your interpretation is not what I intended ?

scepticus,
It's on your web site, in two places. The actual numbers I quoted aren't important, it's the logic that's flawed:
THE "BIRTHDAY" METHOD
Anyone who has come across The Birthday Problem will remember how it at first seems ridiculous. You will remember that despite there being 365 days in a year it only needs 23 strangers in a room for there to be a 50% chance that at least two will share the same birthday. Not every time , of course, but over any extended period.
Recalling that I had last read it in Amir D. Aczel's book " Chance " I was intrigued to find that he also gives the formula for calculating this .So, naturally, I wondered if it could be used in roulette. In p.72 he states that " 1.2 times the square root of the number of categories gives the number of " balls " required for even odds that at least two share some characteristics."
Now the square root of 37 is 6 .08 which , multiplied by 1 . 2 is 7.296 which , rounded up is 8. So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 50% chance that one of the 7 will repeat on the next spin.
I found that waiting for 8 consecutive non  repeat numbers before betting them was a profitable proposition .The downside is that you will sometimes have to wait for some time before you can actually start betting .
If you test this yourself remember that it is a"rolling " eight numbers or , simply , the last EIGHT numbers at each and every stage. And you have to revise after each win. The strategy is up to you to devise . Your Money  Your Choice.
A NINE NUMBER BET.
Similar to the 8 number bet is the 9 number bet.
After 9 different numbers appearing in 9 consecutive spins there is a 95% chance of the tenth spin showing one of those 9. Strange but true if we are to believe the mathematicians.
1.6 times the square root of 37 "categories " gives 95% chance that two will share the same characteristics.
The square root of 37 is 6.08 and that multiplied by 1.6 gives the answer 9.73..
Remember that this is a "rolling" 9 which needs to be adjusted after each spin.
Assuming , that is , that I properly understand the maths.as given by mathematicians.
Remember, though, that the Long Run is "towards infinity" and you may not live that long.

For someone who wants to stick to " specifics " , Mike , you certainly avoid answering questions . Perhaps because you cannot answer them ? So where did I claim 53 % ?
The " received wisdom " that I am questioning is the view that we cannot use previous numbers .And the LOGIC of the Birthday Paradox supports it ! If the Birthday Paradox is " logical " then . by extension  so is my Birthday Method. As is often the case,it is a matter of perception .
AP advocates USE past numbers which they claim points to a wheel being flawed , so you actually DO use past numbers.Why if WE cannot use past numbers ? " Because the wheel has no memory " is the mantra. Have you EVER heard anyone claim that the wheel HAD a memory . Stupidity dressed up as wisdom !
Even if it were the case that we must start from bet one you don't allow for the possibility that someone sitting at the table so , in your view, I cannot use their stats. ?
If you had the courage to now tell us what you meant by series of seven producing a repeat number in 505 of cases you would see that your conclusion is illogical.
You will be forever blinkered , Mike, until you ditch your idea that AP is the ONLY WAY to beat roulette.

For someone who wants to stick to " specifics " , Mike , you certainly avoid answering questions . Perhaps because you cannot answer them ? So where did I claim 53 % ?
Like I said, the exact probability isn't important, but since you bring it up, the 50% you mention in the first highlighted part above (from your website) isn't correct either. And you switch from 7 numbers in that paragraph to 8 in the following paragraph.
The " received wisdom " that I am questioning is the view that we cannot use previous numbers .And the LOGIC of the Birthday Paradox supports it ! If the Birthday Paradox is " logical " then . by extension  so is my Birthday Method. As is often the case,it is a matter of perception .
No, your extension isn't logical. Do I really have to point out why? I'm beginning to suspect that you're being deliberately obtuse.
AP advocates USE past numbers which they claim points to a wheel being flawed , so you actually DO use past numbers.Why if WE cannot use past numbers ? " Because the wheel has no memory " is the mantra. Have you EVER heard anyone claim that the wheel HAD a memory . Stupidity dressed up as wisdom !
Again, the difference is obvious. The meaning and significance of past numbers is completely different in the case of the bias player and system player, and VB doesn't even use past numbers at all, only physics.
If you had the courage to now tell us what you meant by series of seven producing a repeat number in 505 of cases you would see that your conclusion is illogical.
LOL, courage? scepticus, you should really learn some basic probability, because until you do, you won't understand what I mean when I tell you what I meant.
http://www.mathgoodies.com/lessons/vol6/intro_probability.html (http://www.mathgoodies.com/lessons/vol6/intro_probability.html)

For someone who wants to stick to " specifics " , Mike , you certainly avoid answering questions . Perhaps because you cannot answer them ?
I could say the same thing about you. I asked you a question after giving a stepbystep analysis of why the probability of a repeat after 7 different numbers had come up is NOT 50% (or thereabouts), but only 7/37. I repeat it here, since you avoided answering it.
What, SPECIFICALLY, do you object to and where have I gone wrong, in your view?
One question answered for another. Seems fair to me!

Mike
You are STILL dodging my questions so stop prevaricating.
1 )There DOES need to be 23 people in the room BEFORE the maths kick in.So it IS logical that there needs to be 7 numbers on the board before the 8th kicks in. Seven are NEEDED , 8 gives extra assurance.
3 ) Please point out the " obvious difference " .It is a difference of perception.
I know that VB ( Visual Ballistics ) does not use past numbers but many APs use them.Real claims that he has loads of past numbers.You may not use past numbers . Hibbert showed that a flawed wheel could be detected by using past numbers so that IS an AP method in itself so doesn't need wheel tracking. I have said before that what you claim to do could work but I claim that you don't .Your confidence is misplaced if you think it is better than random.
4 ) Another typical evasion and demoshes your previous contention that you don't insult others on the forum.
So come on , Mike. Stop your prevarication and answer my questions . Your contention that we cannot beat the odds is far from being proved so remove the blinkers.

scepticus,
In regard to the use of past spins, it should be obvious that the purposes are very different in the two cases.
1. Where an AP is recording past spins, it is either for purposes of detecting dealer signature or bias. I can't say much about dealer signature because as far as I'm concerned it's debatable whether there is really any merit in it, but with respect to bias tracking, past spins are used to detect whether there is some bias (D'uh!), although as Real has pointed out, to rely solely on past spins for this purpose is very inefficient.
2. The system player who uses past spins to create "triggers" is being inconsistent. On the one hand, he assumes that the wheel is fair (that reds and blacks, for example, come up equally often), but thinks that because (for example) 10 reds in a row have just come up, then black is "due". But if this were true, the wheel would not be fair after all because outcomes would not be independent (certain patterns would reliably indicate future patterns).
Strictly speaking, independence is a matter of empirical testing, not logic. However, the expression "the wheel has no memory" is not a "mantra", or "stupidity dressed up as wisdom", as you put it, but is just a way of describing the process of what is called in probability "sampling with replacement".
The usual scenario given in probability tutorials is an urn with different colored balls in it. Suppose there are 5 balls in an urn, 3 white and 2 red. The probability of drawing a red ball is 2/5, because there are 5 possible outcomes and only 2 of them give the result you're looking for. Now take out a ball, replace it, then draw another, what is the probability of drawing a red ball?
Obviously the same as before, because nothing has changed.
On the other hand, suppose you draw a red ball, but this time DON'T replace it. What is the chance of drawing another red ball? this time the chance is not 2/5, because there are only 4 balls left and only 1 red, so the chance is 1/4. This is called "sampling without replacement".
Roulette follows the "with replacement" model, because on each spin every pocket is "replaced". In other words, for any number or group of numbers, the number of ways it can come up does not change from spin to spin. Those who like to use triggers seem to prefer using the "without replacement" model! they somehow come to the conclusion that the probability changes after "drawing" some particular pattern or other, as though some of the pockets have been taken off the wheel (or perhaps new ones added).
Having said that, as I mentioned before, independence is not something that can be proved mathematically or logically, but even so, it's not very reasonable to assume that there is a lack of independence or that the roulette does NOT conform to the "with replacement" model, because it clearly does. Of course it COULD be the case that there is some other source of nonindependence, but this would be a rare pathological case, and anyway, you would have to know precisely how the nonindependence manifested (it wouldn't do to just assume that numbers are "due", across the board).
Blackjack is an example of "sampling without replacement", so it makes sense (given that it was discovered that the lack of certain cards can give an advantage) to track past results, because when the count reaches a certain point, you have an advantage.
The ideas of "with replacement" and "without replacement" only refer to independence and nonindependence, not bias. So the AP who is tracking past numbers isn't doing it because he thinks the "without replacement" model is valid; he is not looking for any triggers, but an imbalance in outcomes which means that some numbers tend to come up more often than others due to defects or irregularities in the wheel. He is not committing any fallacy, unlike the system player.

I am neither supporting or defending anyone else's strategy but mine . So be specific.
! ) You keep claiming that I don't understand Probability Theory but produce No evidence other than what is in your deeply prejudiced mind.
Collecting past numbers
1 ) for WHATEVER reason is USING past numbers .Claims of sole ownership to use them is illogical .
2 ) Why do Advantage Players spend countless hours collecting past numbers if they don't utilise them ?
They are either stupid or they do utilise them. You continue to be evasive here.
3 ) Although you " despise " the use of triggers you seem blissfully unaware that you in fact DO use triggers when you WAIT for signals to bet.
If Real claims that using the Last Five numbers is a good idea why then is my 8 number idea nonsense unless you also claim that he is talking nonsense ?
Until you understand that an uncertain future is unpredictable and so any attempt to predict it can only be built on assumptions you will remain blinkered. AP is built on assumptions as are Methods the difference is that Method players know this but AP don't so your pathetic attempts to " educate" us is akin to the blind leading the blind .

scepticus,
Strictly speaking, independence is a matter of empirical testing, not logic. However, the expression "the wheel has no memory" is not a "mantra", or "stupidity dressed up as wisdom", as you put it, but is just a way of describing the process of what is called in probability "sampling with replacement".
The usual scenario given in probability tutorials is an urn with different colored balls in it. Suppose there are 5 balls in an urn, 3 white and 2 red. The probability of drawing a red ball is 2/5, because there are 5 possible outcomes and only 2 of them give the result you're looking for. Now take out a ball, replace it, then draw another, what is the probability of drawing a red ball?
Obviously the same as before, because nothing has changed.
Hi Mike,
No arguement with the above, BUT, if you keep taking out one ball and replacing it several thousand times and record all the results You can establish the average gap between white and red balls being drawn. Theory cannot readily answer that, yet it is the most important requirement for betting. The odds are meaningless against this info as you can virtually bet until that average is reached.
Obviously there wil be many missed betting opportunities, but the general success rate will be higher.
Regards,
Harry
P.S. the more balls there are in the bag the more efective this strategy becomes. H.

I'm not so sure, guys, ..Probability Theory regarding roulette ASSUMES independence it does not require Empirical Evidence beforehand .. Even three standard deviations does not produce certainty It is only a Best Guess.
Just as advocates of The Long Run are required to state how long their Long Run is , advocates of Empirical Evidence are required to state how many spins are required for their calculations .. Such a figure can only be ASSUMED . In other words a guess.
You agreed Mike that sets of 7 spins do have a 50% chance of a repeat .That being so that 50% expectation continues throughout the 7 spins so it doesn't really matter at which stage we start betting does it ?
All you keep parroting is that we cannot beat the odds. You fail to understand that roulette is a gambling game and gambling is about " Beating The Odds ". We already understand that so your presence here is only to boost your ego
As for how I calculated the 50 % I gave it in my website page so your question merely underlines your lack of understanding. Self styled Roulette Experts ! LOL

Probably Mike doesn't want to understand that we calculate the probability for the whole series,not separately/independently each and every spin.
It's 2 different things,the probability for any EC to occur within a single spin of the ball is 48.65%, while the probability to happen once within 4 spins is approximately 96%
It's not possible to have the same chance for a single apeareance with only 1 trial and with many trials,the longer we try,the more probable becomes,BUT we are risking more money in order to win the same amount.
Therefore,yes,it becomes more possible but it's not in our best interest to adapt such strategies because they provide no advantage.
This is how we arrive on 53% possibility that the next result will be a repeat when 8 different numbers have already occurred.
By adapting the strategy of virtual bets,you gain no advantage because from one hand you are risking less money,but from the other you are going to win less too.
You cannot affect the win/loss ratio and the fixed payouts!
The key to a winning strategy lies elsewhere...

And I think the key , BA , is Bet Selection. Unless you have a reasonable bet selection method then it becomes more difficult to win .
And while our AP criticise our methods they don't have the courage to post their own method.
Point out that if past spins DO actually indicate a biased wheel then that in itself is an AP method they say that they don't actually do that. So why do they collect past spins if they don't use them ?
Point out that if Dealers' Signature is true then that in itself they say that it is a rather ineffective method.
Point out that bonafide mathematicians and physicists would not agree that theirs is a valid system they produce the likes of Ed Thorp . Why would Thorp use a computer if it was as simple as our self styled Roulette Experts claim.
They claim that they discuss matters in a forum where COMPUTERS are sold .
They say we cannot win using a strategy yet even The Wizard of ODDS admits that it is possible  so he is also wrong ?
Maths Experts admit that we CAN win in the short term but not in the Long Term and since we only bet in the short term then it is obvious that CAN win though APs deny it.
Mike admits that he guesses  but fails to tell us how his " educated guesses" allow him to claim that AP is the ONLY WAY to beat roulette . A " guess " is Proof ?

1)Roulette devices is not my cup of coffee.
2)What they do and claim,I don't know and I don't care to be true.
3)Long term is many short terms all together,if you can do it on most of your sessions,the you have achieved the overall winning.
A battle could be lost,but the final result of the war depends from many battles.
4)If you are asking me,then yes,for me bet selection is fundamental and a progression is secondary and/or optional element of a winning strategy.
I know most of you would disagree with me,but I'm not here to say what you want to listen.

Well, i agree with you BA . I think few, if any, on the forum agree with MY approach !
If we win more than we lose then we are winners despite warnings that we will EVENTUALLY lose .
Talk is cheap . The only time that counts is the time we actually bet . We put our money where our mouths are .

I am neither supporting or defending anyone else's strategy but mine . So be specific.
! ) You keep claiming that I don't understand Probability Theory but produce No evidence other than what is in your deeply prejudiced mind.
My evidence is the fallacious reasoning on your web site.
Collecting past numbers
1 ) for WHATEVER reason is USING past numbers .Claims of sole ownership to use them is illogical .
2 ) Why do Advantage Players spend countless hours collecting past numbers if they don't utilise them ?
They are either stupid or they do utilise them. You continue to be evasive here
Apparently you believe that any "use" of past numbers is legitimate, which is absurd. Is it ok to use past numbers based on astrology or the phases of the moon? perhaps based on your birthday?
3 ) Although you " despise " the use of triggers you seem blissfully unaware that you in fact DO use triggers when you WAIT for signals to bet.
No AP uses triggers or waits for signals to bet based on past numbers alone. There is always some other data that is taken into account (physics). System players use past numbers exclusively and refer to generic statistics, and the triggers are always based on a lack of understanding of statistical independence of outcomes. Again, you seem unable to discriminate and make conceptual distinctions, or perhaps you just don't want to.
If Real claims that using the Last Five numbers is a good idea why then is my 8 number idea nonsense unless you also claim that he is talking nonsense ?
Real claimed that backing the last 5 numbers can reduce the house edge. I personally haven't tried it but it's not an unreasonable system given that if there is any bias present then this will take advantage of it. Your system is nonsense because waiting for 7 different numbers does not mean that the 8th number has a 50% chance of being one of the previous 7.
Until you understand that an uncertain future is unpredictable and so any attempt to predict it can only be built on assumptions you will remain blinkered. AP is built on assumptions as are Methods the difference is that Method players know this but AP don't so your pathetic attempts to " educate" us is akin to the blind leading the blind .
Some assumptions are always made, the point is, are those assumptions reasonable? system players assume that outcomes are not independent, which is not a reasonable assumption. AP assumes that roulette is ultimately a deterministic system which obeys the laws of physics, and that any physical device is always less than ideal, both of which are reasonable assumptions.

Hi Mike,
No arguement with the above, BUT, if you keep taking out one ball and replacing it several thousand times and record all the results You can establish the average gap between white and red balls being drawn. Theory cannot readily answer that, yet it is the most important requirement for betting. The odds are meaningless against this info as you can virtually bet until that average is reached.
Obviously there wil be many missed betting opportunities, but the general success rate will be higher.
Regards,
Harry
P.S. the more balls there are in the bag the more efective this strategy becomes. H.
Hi Harry,
Theory can easily find the average gap; it's just the inverse of the probability. In other words, the average gap between hits for a single number (probability = 1/37) is 37 spins, the average gap between hits of a particular street is (ignoring the zero) 12 spins, because the probability of a hit is 1/12, and so on.
Why is the average gap the most important requirement for betting? The concept of virtual bets is flawed and based on the gambler's fallacy. The truth is, virtual betting does not give you one iota of advantage. This can easily be proved empirically, it's not just "theory".

You agreed Mike that sets of 7 spins do have a 50% chance of a repeat .That being so that 50% expectation continues throughout the 7 spins so it doesn't really matter at which stage we start betting does it ?
NO, it does NOT continue throughout the 7 spins, that is the mistake which Slacker was trying to highlight in this thread. The probability of a series is not the probability of a single outcome, surely that's obvious?
I've attached a file of spins which show the probabilities of 8 spin sequences. Here are the first few lines:
17 18 29 1 8 11 33 15
29 19 18 26 9 4 10 13
10 25 31 35 31 24 31 32 (R) 0.333
34 26 21 17 3 2 30 19
32 3 3 14 29 26 8 26 (R) 0.400
9 23 28 15 18 13 8 23 (R) 0.500 / 0.167
31 28 20 31 21 29 6 23 (R) 0.571
34 3 4 16 2 28 26 14
27 1 24 17 33 32 34 2
14 25 32 24 28 13 16 25 (R) 0.500 / 0.200
18 9 20 20 30 15 33 33 (R) 0.545
32 36 3 34 2 24 6 11
At least one repeat in a sequence is indicated by an (R), after that is the (running) empirical probability of at least one repeat (obtained by dividing the current number of sequences which have at least one repeat by the total number of sequences). At the end of the file you will see that this is 0.557, or 55.7% which is in fact also the theoretical probability of at least one repeat in 8 spins.
In some lines there is an additional probability after the forward slash. This is the the probability of a series given that there are NO repeats in the first 7 spins, but the last spin results in a repeat. For example:
9 23 28 15 18 13 8 23 (R) 0.500 / 0.167
There was 1 repeat but it occurred at spin 8 (#23). In the prior 7 spins there were no repeats. This is the scenario you refer to in your system where you claim that there is a 50% chance of a repeat on the 8th spin given that the prior 7 numbers are different.
As you can see from the results, this is not correct; the probability of the series in question is only around 10%, but how could this be if as you say, the 50% expectation continues throughout the series? The conclusion is that it doesn't, and it can't. This must be the case, because the scenario of no repeats in the first 7 and a hit on the 8th is only one possible outcome of the series, of which there are many (a single repeat first occurring on any of the spins 2 through 8, first repeat on the 2nd spin, another repeat on the 3 etc), and all of these have their own probabilities, but you are attributing a full 50% to just one of them. If you were right, there would not be "room" for the all the others (mutually exclusive outcomes must add up to 100%).

I am neither supporting or defending anyone else's strategy but mine . So be specific.
! ) You keep claiming that I don't understand Probability Theory but produce No evidence other than what is in your deeply prejudiced mind.
My evidence is the fallacious reasoning on your web site.
Collecting past numbers
1 ) for WHATEVER reason is USING past numbers .Claims of sole ownership to use them is illogical .
2 ) Why do Advantage Players spend countless hours collecting past numbers if they don't utilise them ?
They are either stupid or they do utilise them. You continue to be evasive here
Apparently you believe that any "use" of past numbers is legitimate, which is absurd. Is it ok to use past numbers based on astrology or the phases of the moon? perhaps based on your birthday?
3 ) Although you " despise " the use of triggers you seem blissfully unaware that you in fact DO use triggers when you WAIT for signals to bet.
No AP uses triggers or waits for signals to bet based on past numbers alone. There is always some other data that is taken into account (physics). System players use past numbers exclusively and refer to generic statistics, and the triggers are always based on a lack of understanding of statistical independence of outcomes. Again, you seem unable to discriminate and make conceptual distinctions, or perhaps you just don't want to.
If Real claims that using the Last Five numbers is a good idea why then is my 8 number idea nonsense unless you also claim that he is talking nonsense ?
Real claimed that backing the last 5 numbers can reduce the house edge. I personally haven't tried it but it's not an unreasonable system given that if there is any bias present then this will take advantage of it. Your system is nonsense because waiting for 7 different numbers does not mean that the 8th number has a 50% chance of being one of the previous 7.
Until you understand that an uncertain future is unpredictable and so any attempt to predict it can only be built on assumptions you will remain blinkered. AP is built on assumptions as are Methods the difference is that Method players know this but AP don't so your pathetic attempts to " educate" us is akin to the blind leading the blind .
Some assumptions are always made, the point is, are those assumptions reasonable? system players assume that outcomes are not independent, which is not a reasonable assumption. AP assumes that roulette is ultimately a deterministic system which obeys the laws of physics, and that any physical device is always less than ideal, both of which are reasonable assumptions.
1 ) In your OPINION.
2 ) Read it again Mike.
3 ) Thanks for emphasising my point that yo DO use triggers. WAITING for your data to tell you when to bet IS a trigger. A different kind of trigger but a trigger nevertheless.
4 ) Utter nonsense . And real made NO mention of that excuse in his original post .
5 ) So you DO agree with me that we must use assumptions ! Agreed that those assumptions must be reasonable. It follows then that you can only claim that your assumptions are better than others and not, as you claim, that AP is THE ONLY WAY !

You agreed Mike that sets of 7 spins do have a 50% chance of a repeat .That being so that 50% expectation continues throughout the 7 spins so it doesn't really matter at which stage we start betting does it ?
NO, it does NOT continue throughout the 7 spins, that is the mistake which Slacker was trying to highlight in this thread. The probability of a series is not the probability of a single outcome, surely that's obvious?
I've attached a file of spins which show the probabilities of 8 spin sequences. Here are the first few lines:
17 18 29 1 8 11 33 15
29 19 18 26 9 4 10 13
10 25 31 35 31 24 31 32 (R) 0.333
34 26 21 17 3 2 30 19
32 3 3 14 29 26 8 26 (R) 0.400
9 23 28 15 18 13 8 23 (R) 0.500 / 0.167
31 28 20 31 21 29 6 23 (R) 0.571
34 3 4 16 2 28 26 14
27 1 24 17 33 32 34 2
14 25 32 24 28 13 16 25 (R) 0.500 / 0.200
18 9 20 20 30 15 33 33 (R) 0.545
32 36 3 34 2 24 6 11
At least one repeat in a sequence is indicated by an (R), after that is the (running) empirical probability of at least one repeat (obtained by dividing the current number of sequences which have at least one repeat by the total number of sequences). At the end of the file you will see that this is 0.557, or 55.7% which is in fact also the theoretical probability of at least one repeat in 8 spins.
In some lines there is an additional probability after the forward slash. This is the the probability of a series given that there are NO repeats in the first 7 spins, but the last spin results in a repeat. For example:
9 23 28 15 18 13 8 23 (R) 0.500 / 0.167
There was 1 repeat but it occurred at spin 8 (#23). In the prior 7 spins there were no repeats. This is the scenario you refer to in your system where you claim that there is a 50% chance of a repeat on the 8th spin given that the prior 7 numbers are different.
As you can see from the results, this is not correct; the probability of the series in question is only around 10%, but how could this be if as you say, the 50% expectation continues throughout the series? The conclusion is that it doesn't, and it can't. This must be the case, because the scenario of no repeats in the first 7 and a hit on the 8th is only one possible outcome of the series, of which there are many (a single repeat first occurring on any of the spins 2 through 8, first repeat on the 2nd spin, another repeat on the 3 etc), and all of these have their own probabilities, but you are attributing a full 50% to just one of them. If you were right, there would not be "room" for the all the others (mutually exclusive outcomes must add up to 100%).
Of course the 8th IS only one outcome but if there have been NO wins in the previous 7 of that 8 then the 50 % still applies . Assume that my mate betting all 8 was sitting at the table recording the numbers. No repeats were made in the last 7. HE has a better chance than me of winning on the 8th spin ?
What I argued was that IF the 23 people in a room scenario was valid then, by extension, then so woould be the 8th after 7 non recurrences.
You claim that virtual bets are useless. I say that NOT using virtual bets in my Nine Block idea is stupidity. So go on, genius, prove me wrong !
I make the same challenge to you Mike , as I did to real . Post your idea on a site where Physics students discuss physics. See if they agree with you ., I doubt it

Hi Mike,
No arguement with the above, BUT, if you keep taking out one ball and replacing it several thousand times and record all the results You can establish the average gap between white and red balls being drawn. Theory cannot readily answer that, yet it is the most important requirement for betting. The odds are meaningless against this info as you can virtually bet until that average is reached.
Obviously there wil be many missed betting opportunities, but the general success rate will be higher.
Regards,
Harry
P.S. the more balls there are in the bag the more efective this strategy becomes. H.
Hi Harry,
Theory can easily find the average gap; it's just the inverse of the probability. In other words, the average gap between hits for a single number (probability = 1/37) is 37 spins, the average gap between hits of a particular street is (ignoring the zero) 12 spins, because the probability of a hit is 1/12, and so on.
Why is the average gap the most important requirement for betting? The concept of virtual bets is flawed and based on the gambler's fallacy. The truth is, virtual betting does not give you one iota of advantage. This can easily be proved empirically, it's not just "theory".
Hi Mike,
The above quote leaves me with the idea that while you like playing with maths you have never played roulette seriously.
I do not play single numbers or even streets so I have not researched those areas. I am very certain that those who have will tell you that your calculatiions are wrong. I play almost exclusively DS ( double streets ,lines, sixaines etc). By your reconing the average gap between appearances should be 6 spins. As I have played many thousands DS bets over the years and I can say positvely that your theory is wrong.
The rule of thirds, which is accepted mathematically gives the average number of DS seen in 6 spins as 4. There may be more, there may be less, BUT THE AVERAGE IS 4.
Counting the number of each DS, in an extended trial, and then dividing by 6 does not give the average gap.
You ask why knowing the average is important for betting. The answer is simple !!
If you know the average gap you need only bet around that spin or spins. You can call the spins before the average and after the average virtual bets or wasted time. It doesn't matter. there is no money at stake !! By restricting the betting to few spins around the average you obtain a better hit rate. This translates into an advantage.
Harry

The word "time" before spins in the second row of the last paragraph should be deleted. I tried to do so but nothing happened. Perhaps someone can tell me how to edit posts.
Harry

In the right upper corner of your message is link "Modify".
It appears only in messages that you have written.

1 ) In your OPINION.
NO, it's not my opinion, it's a fact. I admit though, that the file I uploaded didn't conclusively prove this, but I'll upload another one later, which will.
2 ) Read it again Mike.
Read what again?
3 ) Thanks for emphasising my point that yo DO use triggers. WAITING for your data to tell you when to bet IS a trigger. A different kind of trigger but a trigger nevertheless.
No, I specifically denied that AP's use triggers in the way that system players do. You're just playing with semantics now.
4 ) Utter nonsense . And real made NO mention of that excuse in his original post .
scepticus, I'm not responsible for the meaning of Real's posts. You asked me why I don't think his "system" is nonsense and I told you what I thought the thinking might be behind it. If you want a definitive answer you'll have to ask Real. If I hadn't given you an answer you would have accused me of evading the issue in your usual bombastic way.
5 ) So you DO agree with me that we must use assumptions ! Agreed that those assumptions must be reasonable. It follows then that you can only claim that your assumptions are better than others and not, as you claim, that AP is THE ONLY WAY !
I want to be clear about one thing: AP is the only way to get a real edge playing roulette. Playing with patterns, virtual bets, and progressions does absolutely nothing to the house edge. It does not even reduce it slightly.

Thanks December, I did try that, but when I checked it was still there. I see that it is gone now so perhaps I didn't give it enough time to change.
Harry

Harry,
Counting the number of each DS, in an extended trial, and then dividing by 6 does not give the average gap.
You're correct. The average gap is obtained by dividing the number of spins by the number of hits, but a quicker way is just to turn the probability upside down. So for a DS, the probability is 6/37, and therefore the average gap is 37/6 or about 6.167. Slightly more than 6, of course, because of the house edge.
I'm curious what you think the average gap is for a DS? do you think it is less or more than 6?
If you know the average gap you need only bet around that spin or spins. You can call the spins before the average and after the average virtual bets or wasted time. It doesn't matter. there is no money at stake !! By restricting the betting to few spins around the average you obtain a better hit rate. This translates into an advantage.
So when do you start the betting and when do you quit? I'd like to try it.

And I think the key , BA , is Bet Selection. Unless you have a reasonable bet selection method then it becomes more difficult to win .
And while our AP criticise our methods they don't have the courage to post their own method.
Point out that if past spins DO actually indicate a biased wheel then that in itself is an AP method they say that they don't actually do that. So why do they collect past spins if they don't use them ?
Point out that if Dealers' Signature is true then that in itself they say that it is a rather ineffective method.
Point out that bonafide mathematicians and physicists would not agree that theirs is a valid system they produce the likes of Ed Thorp . Why would Thorp use a computer if it was as simple as our self styled Roulette Experts claim.
They claim that they discuss matters in a forum where COMPUTERS are sold .
They say we cannot win using a strategy yet even The Wizard of ODDS admits that it is possible  so he is also wrong ?
Maths Experts admit that we CAN win in the short term but not in the Long Term and since we only bet in the short term then it is obvious that CAN win though APs deny it.
Mike admits that he guesses  but fails to tell us how his " educated guesses" allow him to claim that AP is the ONLY WAY to beat roulette . A " guess " is Proof ?
And he just keeps slicing them..
P.S. With that sharp mind as yours I bet that you have won at least 75% of all those "an argument per day"s. :)

NO, it's not my opinion, it's a fact. I admit though, that the file I uploaded didn't conclusively prove this, but I'll upload another one later, which will.
The FACT is that the 8th number is part of the series and GIVEN that you concede that series of seven contain at least ONE repeat how can you claim that it is a single . ( As has already been pointed out to you the correct figure is OVER 7 so we must consider it inapplicable and use 8 )
I wrote;
Collecting past numbers 1 ) for WHATEVER reason is USING past numbers .Claims of sole ownership to use them is illogical .
So how did you construe it to mean
Apparently you believe that any "use" of past numbers is legitimate, which is absurd. Is it ok to use past numbers based on astrology or the phases of the moon? perhaps based on your birthday?
You claim that you said you " specifically denied that AP's use triggers in the way that system players do". You're just playing with semantics now.
Refer me to that post Mike. In the post I read you just said triggers were useless and made no reference at all about APs using them .
In an earlier post I said you lacked the courage of your conviction  and now you provide more evidence !
scepticus, I'm not responsible for the meaning of Real's posts. You asked me why I don't think his "system" is nonsense and I told you what I thought the thinking might be behind it. If you want a definitive answer you'll have to ask Real. If I hadn't given you an answer you would have accused me of evading the issue in your usual bombastic way.
You, me, and most everyone on this forum KNOW that Real's Last Five Number bet doesn't meet the criteria of Probability. Yet you cravenly don't admit that it is nonsense ! The answer you gave is Real's own excuse so it seems that you have discussed this with Real . Nor do you understand that you have undermined your own argument that Method players will lose " eventually " because , having conceded to Real a biased wheel you must concede it to everyone ! So according to you , the reason we win is not because of our Method but because of a biased wheel ! Know something Mike ? I don't care if a biased
wheel IS the reason  i'll take a profit whatever the reason.
Pontificating again mike when you say
Some assumptions are always made, the point is, are those assumptions reasonable? system players assume that outcomes are not independent, which is not a reasonable assumption. AP assumes that roulette is ultimately a deterministic system which obeys the laws of physics, and that any physical device is always less than ideal, both of which are reasonable assumptions.
Method players do NOT assume that outcomes are not independent except in series  which you have previously accepted . We KNOW that any man made physical device is flawed . The question to be answered is " is it flawed enough to give us an advantage ". In modern wheels,in the major casinos, the answer is " Extremely unlikely " . You provide no proof to the contrary , Mike , and even if you did I think a Physicist would not accept it .
Anyway, as I have said before, my patience is limited so unless you stop evading rather than answering my questions I will be ending this discussion / argument. So;
If the Wizard of Odds accepts that roulette can be beaten by using a strategy why don't you ?
I have asked you to prove that my Virtual bets are not useless as you claim  so answer.
Those two will do for starters , Mike . so come on , stop prevaricating and " educate " me .

And I think the key , BA , is Bet Selection. Unless you have a reasonable bet selection method then it becomes more difficult to win .
And while our AP criticise our methods they don't have the courage to post their own method.
Point out that if past spins DO actually indicate a biased wheel then that in itself is an AP method they say that they don't actually do that. So why do they collect past spins if they don't use them ?
Point out that if Dealers' Signature is true then that in itself they say that it is a rather ineffective method.
Point out that bonafide mathematicians and physicists would not agree that theirs is a valid system they produce the likes of Ed Thorp . Why would Thorp use a computer if it was as simple as our self styled Roulette Experts claim.
They claim that they discuss matters in a forum where COMPUTERS are sold .
They say we cannot win using a strategy yet even The Wizard of ODDS admits that it is possible  so he is also wrong ?
Maths Experts admit that we CAN win in the short term but not in the Long Term and since we only bet in the short term then it is obvious that CAN win though APs deny it.
Mike admits that he guesses  but fails to tell us how his " educated guesses" allow him to claim that AP is the ONLY WAY to beat roulette . A " guess " is Proof ?
And he just keeps slicing them..
P.S. With that sharp mind as yours I bet that you have won at least 75% of all those "an argument per day"s. :)
I wish GNO I wish. But I can't complain . After all she gives me pocket money !

Hello to all,
In my opinion scepticus is right.
The following theorem is based on the same probabilistic logic that yields the wellknown “Birthday Paradox” in Probability theory and asserts that in roulette the probability of distinct outcomes without repetitions decreases exponentially as the number of spins increase.
Let Prob(N,r,) be the probability of r distinct outcomes resulting from r
successive spins (r < or = N) of a roulette wheel with N slots. Then
Prob(N,r) < or = e –r(r1)/2N

scepticus,
It would be helpful if you formatted your reply so that it is at least readable. Surely this is not beyond the capability of a "sharp" mind?
My patience is limited too, but I will at least respond to this:
If the Wizard of Odds accepts that roulette can be beaten by using a strategy why don't you ?
He doesn't. If you believe otherwise, please post a link to where he said anything of the kind. This is what he thinks about gambling systems: http://wizardofodds.com/gambling/bettingsystems/
The rest of your reply is just repetition of comments and questions I have already responded too. Evidently your tactic is to ignore my answers and keep slinging mud in the hope that some of it sticks.
Back to the specific subject of this thread, and in particular, your claim that after 7 different numbers there is a 50% chance (or thereabouts) that the next spin will be a repeat.
I've attached another file of spins: sequences of 8 where the first 7 spins are different. Here's the first few lines:
25 12 1 31 6 4 32 33
23 0 12 18 20 6 3 23 1/2 = 0.500
32 9 13 16 29 27 35 28
1 2 19 13 6 22 14 28
22 10 19 23 12 7 2 1
36 29 0 22 8 16 24 35
35 20 5 22 34 3 25 1
34 22 8 19 31 13 21 7
23 20 21 33 2 13 8 9
23 24 30 9 7 8 17 30 2/10 = 0.200
35 18 21 5 17 15 12 3
1 17 2 19 28 27 7 18
0 27 19 28 11 22 12 35
14 15 24 35 18 25 26 8
28 27 33 6 11 32 35 8
19 8 6 18 23 17 26 21
9 15 31 1 19 30 33 5
1 15 34 14 36 3 21 4
20 16 6 22 10 13 33 28
18 16 11 10 14 13 23 1
9 13 29 18 17 26 15 31
23 34 13 26 28 36 32 16
36 3 11 9 22 10 19 32
23 12 27 11 8 14 33 18
26 10 25 32 11 4 9 25 3/25 = 0.120
Lines which have a probability alongside mark those sequences which have a repeat on the last spin, so the first sequence like this is the 2nd sequence in the file, and this is the first such sequence with a repeat on the 8th spin, so the probability is 1/2 = 0.5. The next such sequence occurs at the 10th sequence in the file, and it's the second occurrence of a sequence with a repeat, so the probability (so far) is now 2/10 = 0.2.
As successive probabilities are calculated further down the file, you'll see that it converges to around 0.19 (19%), which, surprise surprise! is 7/37, the probability which I showed it must be in a previous post.
You are betting on 7 numbers, so the probability is just 7/37, period. WHAT HAS GONE BEFORE IS TOTALLY IRRELEVANT.
scepticus, try repeating to yourself 100 times before going to sleep:
PAST SPINS DO NOT AFFECT FUTURE SPINS.
It might help.
@ parrondo,
In my opinion scepticus is right.
I am not, and never was, disputing either the birthday problem or his extension of it to roulette, what I am saying is wrong is just what Slacker pointed out in his first post: IT IS INVALID TO TAKE THE PROBABILITY OF A SERIES AS THE PROBABILITY OF THE NEXT SPIN. The whole fallacious concept of "virtual bets" is based on this error, which in turn hinges on the gambler's fallacy (not understanding that successive spins are independent and have no connection with each other).
The rot runs deep, I'm afraid. Even Slacker, who started this whole thread, later admits that he waits for deviations before betting because he thinks it's superior to betting randomly! BA also posts systems which have a gambler's fallacy component, even though I have seen posts by him in which he criticizes it in other systems. People don't even realize they are doing it, but it's so much a part of the world of gambling systems that it's hard not to (perhaps unconsciously) indulge in virtual bets.
Someone has to counter the proliferation of ignorance.

and it goes on and on...!
Where is the bottom line??

Where is the bottom line??
PAST SPINS DO NOT AFFECT FUTURE SPINS.

No answer to my questions . Instead HE asks ME another question ! The answer is simple .Read WOO 's Question s thread . better still, ASK the wizard of Odds ! The usual bluff and bluster from an AP.
He doesn't realise that we don't claim that past spins AFFECT future spins  .only that past spins can be a GUIDE to future spins  AS DO AP ! He cannot answer my questions because it would reveal his ignorance.
I am from a generation that finds difficulty with modern technology .So ?
Where does it end Blue Angel. .It ends here ! I am fed up with his evasions.

scetpicus has presented a strategy for playing roulette in which a player has a positive expected gain per spin in contrary to the popular belief that in the long run the House always has the edge. It is, however, to be noted that one may have to play a large number of spins in order to realize an overall gain.
GREAT scepticus.

Hi Mike,
I can see where we are going to disagree. You are right in saying that the important fact is the number of hits. To arrive at an average I list the number of hits on each DS(sixline) and the gap between the last hit.
I then list the times each gap is recorded. I play 40 spin sessions and stop and restart the count.
In most 40 spin cycles Gaps of 1,2,3. are the most numerous Gaps of 4 to 7 are slightly less numerous. 8 to 10 will register a hit or 2, but hits over 10 are rare you are unlikely to see more than one or two in a cycle. These are considered out of range and discarded.
There are on average about 35 hits in a cycle if we divide this by 6 as the number of DS we end up with just under 6. which is very similar to your calculation .BUT we have gathred a lot of infomation along the way as to which gaps are the most likely. This
enables us to set a betting range. We will find that by far the bulk of the hits will be betwen spins 1 and 7 The bulk of these(about 3/4) will fall between 1 and 5.
If I were betting single DS I would either use a very strong progression between 1 and 6 or a weak progression between 1 and 10. There will be plenty of losses along the way but the overall result should be positive.
That's a fairly good example of how I arrive at averages and betting ranges.
Harry

No answer to my questions . Instead HE asks ME another question ! The answer is simple .Read WOO 's Question s thread . better still, ASK the wizard of Odds ! The usual bluff and bluster from an AP.
The Wiz has never said, and never will say, that it's possible to win using betting systems. Why on earth would he contradict the statements made in the page I linked to when replying to a question? again, where is the specific link where he says this? and you accuse ME of bluff and bluster! A lot of people have told him that they or others are winning using systems and he sometimes replies that it's due to "luck and progressions"  LUCK and progressions. Progressions don't affect the house edge and luck is just luck, so this cannot be interpreted as endorsing betting systems.
He doesn't realise that we don't claim that past spins AFFECT future spins  .only that past spins can be a GUIDE to future spins  AS DO AP ! He cannot answer my questions because it would reveal his ignorance.
[SIGH]
scepticus, you're just playing with words. "Guide", "affect", "indicate" etc. mean the same thing in this context. Although to be more precise, it should really be "past spins don't affect the PROBABILITY of future spins". To repeat myself yet again, in the case of AP, yes past spins can indicate something ABOUT THE WHEEL, if you record enough of them.
What do past spins, as collected by system players, indicate? System players aren't interested in the fitness of the wheel. Mostly, they BELIEVE that certain patterns of spins will be reliably followed by certain other patterns, even though the independence of outcomes doesn't justify this belief. This is a logical error, but it is not illogical to believe that past spins can tell you something about the WHEEL (i.e., that it may be biased).
Also, the bias player has to collect many spins (thousands) in order to be sure that any apparent bias is not just natural variance (which is why it's much better to confirm in other ways  visually if possible  that there is indeed a bias). On the other hand, to the system player, the natural variance IS the trigger. He attempts to USE the variance, not eliminate it, which is why so few spins are needed for his triggers. The methodology and meaning of the past spins are very different, and yet you insist that because AP and system players both "use" past spins, then each of the strategies are equally effective. That's being either naive or dishonest.
And you have the nerve to talk about ME being evasive. You guys are always on about how EMPIRICAL research trumps theory and maths. I have uploaded a spin file which PROVES that the chance of the 8th spin being a repeat after 7 different numbers have shown is NOT 50%, as you keep claiming, but less than 20% (7/37, to be exact), and yet you have completely ignored it.
I have given the empirical evidence, the least you can do is be a man and admit that you're wrong.

Nobody on this forum claims the past spins influence the future spins. By study the random rows my conclusion is that the features of a short run sample are not the same as the features of a long run sample.
Players use the anomalies and unbalance of small samples to game roulette.Strategies are based on the random rows of the different chances.
ECs, dozens , columns and DSs are the most popular random sequences.

Nobody on this forum claims the past spins influence the future spins.
dobbelsteen,
Yes, they do. scepticus believes that IF the last 7 numbers are all different, the 8th number has a 50% chance of being a repeat, even though there are only 7 ways in which the 8th number could be a repeat. If the 7 numbers are NOT all different, he thinks the probability of the 8th number is something else. So whether you choose to call it "influence", or "guide" or whatever, isn't really the issue.

Mike
Just let me ask you a philosophical question.
Forget about past spins influencing future spins.
Do you believe that information has no value whatsoever?
What and how much information it is and how it can be interpreted and used is a very important and different issue. Lets ignore the specifics.
The question is more general/principal: does information about a random, chaotic, stochastic or whatever system has value or not?

The question is more general/principal: does information about a random, chaotic, stochastic or whatever system has value or not?
Kav,
Yes of course it has value. If there were no such information then casinos wouldn't be able to calculate the odds so that they have the edge. But as you rightly acknowledge, the crux of the matter is, for whom is the value and for what reason(s)?

@ Harry,
Thanks for the explanation.

Mike after RB RBRBRBRB I shall bet contrary the last color. The probability theory tells me that an event of 20 ECs has an appearence of once in 2^20 spins. I wager that that should not happen.

Hi everyone  anyone.
The Wizard of Odds site has changed a bit since the takeover . The Wizard of Odds no longer answers questions and refers me to his Wizard of Vegas site.
I was barred from that site because I forgot my password I got impatient when the robot continually asked me for it , so registered anew with a new username. Against the rules so they were quick and glad to be rid of another roulette player.
So would anyone with access to WOV please ask him the following question.
" Did the Wizard of Odds ever accept that roulette might be able to be beaten using a Strategy ? Thanks."
If anyone does so would they kindly post the answer here ? Whatever the answer .
Thanks

Mike after RB RBRBRBRB I shall bet contrary the last color. The probability theory tells me that an event of 20 ECs has an appearence of once in 2^20 spins. I wager that that should not happen.
dobblesteen,
As long as you're clear that betting the opposite of the last 10 spins doesn't give you an advantage compared to betting any other sequence, there's no harm in it.
The chance that the next 10 spins will be a repeat of the first is 2^{10}. If you believe it's 2^{20}, then you're making the same mistake as scepticus and many others.

The question is more general/principal: does information about a random, chaotic, stochastic or whatever system has value or not?
Kav,
Yes of course it has value. If there were no such information then casinos wouldn't be able to calculate the odds so that they have the edge. But as you rightly acknowledge, the crux of the matter is, for whom is the value and for what reason(s)?
Mike,
Probability equations are not information; it is not data.
Information is acquired for example by observation.
Principally, observation proceeds any theoretical law. The physical law is the bitch of observation. Don't be fooled by the fact that nature "follows laws". It is the observation of nature that created these laws and just one (different) observation is enough and can easily break/refute the "law". Data is king, laws are the slaves that breathlessly try to describe observation, not the other way around. This is why a physical law can never be proven; only disproven by observation. You can consider all "valid" physical laws as descriptions of reality that are not yet disproven.
Science may be described as the art of systematic oversimplification — the art of discerning what we may with advantage omit.
In so far as a scientific statement speaks about reality, it must be falsifiable; and in so far as it is not falsifiable, it does not speak about reality.
Our knowledge can only be finite, while our ignorance must necessarily be infinite.
Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve.
Karl Popper
Isn't strange that you seem to have more blind belief in (probability) laws as the beall endall of random systems than one of the greatest philosophers of science?

Kav,
Of course observation must be prior to theory, and equations are not data. No argument from me there. Reality has the final say, yes!
Formulas, theory, and equations are MATHEMATICAL MODELS. A model is considered appropriate and a good "fit" if it accurately reflects and/or predicts the data, and given certain basic assumptions, probability formulas DO fit the data very well.
The basic formula of classical probability, which was developed in connection with games of chance like roulette, is very simple, it is just the number of ways an event can occur divided by the total number of possible events. So the probability of getting a red is just 18/37, because out of the total number of possible numbers, 18 of them are red. The assumption is that the events in question are equally likely.
Empirical probability is the number of times the event has occurred divided by the number of trials. There is no assumption that the events are equally likely. If the empirical probability matches the theoretical probability, we can be sure that the assumptions of theoretical probability were correct, agreed?
I'm not sure where you get the idea that I have "blind belief" in probability laws. The data I provided was empirical and it confirmed the accuracy of the model  the empirical probability (just using the data and counting) was very close to that given by the theoretical model.
More complex distributions such as the binomial distribution follow logically from the basic model, they are not arbitrary.
Of course models are a simplification of reality. But that doesn't mean that they can't "work" over a large range of phenomena. The models work well enough for the casinos.

Thanks for your thoughtful reply Mike.
I try to find some common ground. That's why I'm not talking about past spins per se. I'm not even talking about the specific usability of information.
I just want to make an admittedly very vague point about the value of information.
In that general sense, we can say that past spins offer information about the system at hand (the roulette wheel).
By agreeing to this general/principal statement, that any information (including past spins) has value, one doesn't have to agree neither that past spins influence future results in a specific way, nor that we can take advantage of this information in any practical way.
I just want to point out a scientifically sound reasoning why past spins have "some value" in understanding a random system like roulette.

]
scepticus,
They are not at all the same thing. It's not me who is wearing the blinkers. Let's take it step by step. Suppose you start tracking and your first number is 17 (1)
17
the probability of a repeat in the next spin is now 1/37, because there is only 1 way a repeat could occur.
21 hits
17, 21
the probability of a repeat in the next spin is now 2/37, because there are 2 ways a repeat could occur.
11 hits
17, 21, 11
the probability of a repeat in the next spin is now 3/37, because there are 3 ways a repeat could occur.
8 hits
17, 21, 11, 8
the probability of a repeat in the next spin is now 4/37, because there are 4 ways a repeat could occur.
32 hits
17, 21, 11, 8, 32
the probability of a repeat in the next spin is now 5/37, because there are 5 ways a repeat could occur.
12 hits
17, 21, 11, 8, 32, 12
the probability of a repeat in the next spin is now 6/37, because there are 6 ways a repeat could occur.
19 hits
17, 21, 11, 8, 32, 12, 19
the probability of a repeat in the next spin is now 7/37, because there are 7 ways a repeat could occur.
But according to your reckoning, the probability of the next spin resulting in repeat at this point (1 spin remaining) is 53%. Do you see how this is mistaken?
If you don't agree, please point out where you think I have made a mistake.
...
Counting the first trial, I show the mean is 8.408797, the median is 8, and the mode is 7.
The probability of two numbers without a repeat is 37/38 = 97.37%.
The probability of three numbers without a repeat is (37/38)×(36/38) = 92.24%.
The probability of four numbers without a repeat is (37/38)×(36/38)×(35/38) = 84.96%.
Following this pattern, the probability of no repeats in 8 numbers is (37/38)×(36/38)×(35/38)×...×(31/38) = 45.35%.
So the probability of a repeat within 8 numbers is 100%  45.35% = 54.65%.
The Wizard of Odds
( on a 38 number table.)

scepticus,
I'm afraid you still don't get it. The wizard's calculation which you have copied and pasted here does not invalidate mine, they are calculating different things entirely. The crux of your mistake is this:
if there have been NO wins in the previous 7 of that 8 then the 50 % still applies
WRONG. You are confusing a simple probability (the next spin) with a compound probability (two or more spins). In my calculations, I was working out the chance of a repeat on the NEXT spin, not the chance of at least one repeat in the next two or more spins.
Look, if you work out the chance of one or more repeats (at least one) in the next 8 spins the probability is 55.7% (single zero wheel), which is quite close to the Wiz's calculation (the difference is due to the extra zero). No argument from me there.
But the 55.7% does NOT apply when any of the 8 spins has come and gone, because the "probability" of them is now 100%, understand? How can the 55.7% probability remain throughout the length of the 8 spin sequence when you have observed successive spins? It must reduce after each spin up to the 8 spins.
Think about it and try to work out what the successive probabilities are after each spin.

The following gives the probabilities of at least one repeat after the 1st, 2nd, etc spins up to the 7th. They are similar to the Wiz's calculations.
Since we're only interested in repeats, it doesn't matter what the first spin is. After the 1st, the probability of NO repeats up until the 8th is
36/37 x 35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37
and since there can only be one of two outcomes in the sequence: either there is a no repeat or at least 1, the probability of at least 1 is
1  36/37 x 35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37
The remaining calculations show the probability of at least 1 repeat from the 2nd spin up to the 8th, 3rd up to the 8th, etc.
After spin #1: 1  36/37 x 35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.55682
After spin #2: 1  35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.54451
After spin #3: 1  34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.51848
After spin #4: 1  33/37 x 32/37 x 31/37 x 30/37 = 0.47599
After spin #5: 1  32/37 x 31/37 x 30/37 = 0.41247
After spin #6: 1  31/37 x 30/37 = 0.32067
After spin #7: 1  30/37 = 0.18919
So after spin #7, the probability is 0.18919, which is 7/37. I hope this makes sense to you.

Last reply on this Mike.
I am not arguing anything other than that if 22 people are ALREADY in the room then the 23 rd DOES give the probability that two of them will have the same birthday . If that is so then the same applies to roulette. You
think differently to me . So what ? Many members here disagree with me  on a number of things . The object of a forum is to put forward ideas . We discuss STRATEGIES
I have put forward some ideas  you have contributed little but smug criticism.
You keep banging on about "systems " and seem to think that a " strategy " is the same as a "system ". It is not. I am super  confident that the Wizard of Odds DID say that he never said roulette could not be beaten by a strategy so your knowledge of " the history of roulette " is sadly lacking in " fact ".
You still avoid posting your promised AP versus Method thread AND you still haven't proved dobbelsteen wrong as you so arrogantly claimed .
so, Mike , it DOES end here . You won't convince me and I won't convince you and I am not continuing to indulge in an interminable discussion / argument . I'll keep using Method and you keep betting your   whatever it is that you are a Roulette Expert at .
'bye 1

Ok scepticus. let's leave it at that then. We'll let readers decide. Some things are nonnegotiable, and if you can't recognize the authority of logic and mathematics ( not MY authority ), maybe some will.

Ok scepticus. let's leave it at that then. We'll let readers decide. Some things are nonnegotiable, and if you can't recognize the authority of logic and mathematics ( not MY authority ), maybe some will.
If the authority of math is the determining factor in roulette, how do you explain, that in the absence of the HE, absolutely nothing would change in the results of a system player? If a lousy 2.7% was eliminated today, those who lose, they will keep on losing the same amounts they lose today.
And those who win, will not win any substantial amount over the usual. No system that has been described till today will start winning or breaking even if the payouts begin to be fair. And neither casinos will start reporting any substantial reduction of their profits from roulette.
Things will remain basically the same had the HE been eliminated today.
That leads me to conclude that there are factors present besides basic statistics.
Math deals with pure numbers.
When money and profitability enters the play, the dynamics change, and they are not only guided by math alone. There is a lot more to it than math.
What is involved is up to the player to research and draw his own conclusions.

Ok scepticus. let's leave it at that then. We'll let readers decide. Some things are nonnegotiable, and if you can't recognize the authority of logic and mathematics ( not MY authority ), maybe some will.
If the authority of math is the determining factor in roulette, how do you explain, that in the absence of the HE, absolutely nothing would change in the results of a system player? If a lousy 2.7% was eliminated today, those who lose, they will keep on losing the same amounts they lose today.
And those who win, will not win any substantial amount over the usual. No system that has been described till today will start winning or breaking even if the payouts begin to be fair. And neither casinos will start reporting any substantial reduction of their profits from roulette.
Things will remain basically the same had the HE been eliminated today.
That leads me to conclude that there are factors present besides basic statistics.
Math deals with pure numbers.
When money and profitability enters the play, the dynamics change, and they are not only guided by math alone. There is a lot more to it than math.
What is involved is up to the player to research and draw his own conclusions.
After all is just theory and for those with gambling experience know very well that theory could be far from what really happens during action.
That's why I believe one should give a priority on his/her empirical observations rather than what theory indicates.

That's why I believe one should give a priority on his/her empirical observations rather than what theory indicates.
No argument from me, which is why I uploaded a file showing that the probability of the next spin following 7 different numbers was 7/37, not 55.7% (the probability of the series). scepticus ignores this EMPIRICAL observation and instead tries to make out that we just "think differently", as though it's all a matter of opinion.
Guys, it's not a matter of fancy math, but simple logic.

YAAW N !

Ok scepticus. let's leave it at that then. We'll let readers decide. Some things are nonnegotiable, and if you can't recognize the authority of logic and mathematics ( not MY authority ), maybe some will.
If the authority of math is the determining factor in roulette, how do you explain, that in the absence of the HE, absolutely nothing would change in the results of a system player? If a lousy 2.7% was eliminated today, those who lose, they will keep on losing the same amounts they lose today.
And those who win, will not win any substantial amount over the usual. No system that has been described till today will start winning or breaking even if the payouts begin to be fair. And neither casinos will start reporting any substantial reduction of their profits from roulette.
Things will remain basically the same had the HE been eliminated today.
That leads me to conclude that there are factors present besides basic statistics.
Math deals with pure numbers.
When money and profitability enters the play, the dynamics change, and they are not only guided by math alone. There is a lot more to it than math.
What is involved is up to the player to research and draw his own conclusions.
Well said Palestis.
I've noticed that the guys who are constantly repeating "in the end, no matter what you do your losses will always be around the HE percentage" are those who learnt the game by the books and don't have real experience. Or if they did have, they are were not paying enough attention.
Most of these guys join the forums just to promote aff links to some online RNG casino or link from a roulette book selling on Amazon or link for selling a computer and these guys are not here to learn or share what they've learned while playing, but they are trying to mislead the newbies into buying some of the stuff they are promoting, and this way making quick buck through commissions.

In my years of reading on forums, this is the one error I see time and time again. It concerns confusing the probability of a series with that of a single.
For example, there is a famous example in probability called the "Birthday Problem" which states that in a room of 23 people, there is a 50% chance that at least two will share a birthday. Does this suggest a system for roulette? what is the probability that in a sequence of spins, you will get at least one repeat?
If you do the math, it turns out that in any 8 spin sequence, there is a roughly 56% chance that there will be at least one repeat in the sequence. No problem with that, but the error occurs when you make a statement like this:
"So it appears that after 7 consecutive numbers have appeared and none are repeats there is a 56% chance that one of the 7 will repeat on the next spin."
This is saying that there is a 56% chance that you will get a win when betting on 7 numbers! but any casino which offered the equivalent of such odds would soon be out of business. The mistake lies in assuming that you can apply the probability of the series (7 spins with at least one repeat) to that of a single outcome. But once the 7 spins have gone, probability applies to the next spin only, so the original probability is now meaningless. All you can do is bet the last 7 numbers and hope that one of the last 7 repeats. What is the chance of that?
The answer is 7/37, no more and no less. If you doubt this, assume that the last 7 numbers were 17,1,32,25,8,12,28. The chance that 17 will hit on the next spin (and so result in a repeat) is 1/37, the chance that 1 will repeat is again 1/37. Similarly for each of the others. Since these are mutually exclusive outcomes, we can add the results, which gives 7/37.
You can indeed make a system out of the knowledge that there is at least one repeat with probability 56% in the last 8 spins, but in order for the probability to remain valid, you have to place your bets from spin 1, not after spin 7. So on spin 1 you put one chip on the last outcome, on spin 2 add another chip to whatever just hit, and so on, until you get a repeat (a win). But in that case, your profit will vary according to when you get the repeat, assuming you do get it. 56 times out of 100 you will indeed get at least one, but what you cannot say is that you will win 29 chips 56 times out of 100, betting 7 numbers!
Making this mistake is no different, in principle, to "calculating" that because there is a 99.9% chance of getting at least 1 black in 10 spins, then after 9 spins with no blacks the chance of a black on the next spin is 99.9%. This is of course, none other than the gambler's fallacy, but it may not be so easy to recognize it in more unusual or complex scenarios such as the probability of repeats.
Slacker  I have deleted my Birthday Method from my site "fergusleesroulette.co.uk".
But MOST DEFINITELY not for the reasons you give.
Nor will I even discuss it ! Make of that what you will !

Well done scepticus, you did the right thing.

Well done scepticus, you did the right thing.
So why don't you do THE RIGHT THING and answer my question about your " Calculation " ?
WHAT were you calculating .?

Most of these guys join the forums just to promote aff links to some online RNG casino or link from a roulette book selling on Amazon or link for selling a computer and these guys are not here to learn or share what they've learned while playing, but they are trying to mislead the newbies into buying some of the stuff they are promoting, and this way making quick buck through commissions.
And WHERE are these links? I don't recall a single post or thread here which is trying to get members to buy anything (apart from Kav's). It's a bit hypocrital you being concerned about misleading the newbies when you are doing exactly that by recommending virtual bets.

So why don't you do THE RIGHT THING and answer my question about your " Calculation " ?
WHAT were you calculating .?
What question and calculation?

So why don't you do THE RIGHT THING and answer my question about your " Calculation " ?
WHAT were you calculating .?
What question and calculation?
OOPS !Sorry Mike I did not put the question to you. I should have but didn't because I was still trying to understand the point of it .The Wiz said that the chance of a repeat was over 53% in a series of 8 while you appeared to be saying that the chance DIMINISHES with each spin. That was what puzzled me .I think the chance is more likely to increase .So Mike educate me.

The Wiz said that the chance of a repeat was over 53% in a series of 8 while you appeared to be saying that the chance DIMINISHES with each spin. That was what puzzled me .
The Wiz's calculation is ok as far as it goes for a series of 8. But once you have observed successive spins the chance does indeed diminish, as per my calculations.
I think the chance is more likely to increase .
If you think about it, this cannot possibly be correct. Which is more likely? a repeat in a long sequence of spins or a short sequence?. The longer the sequence, the more likely a repeat. My calculation for 8 spins is the same as the Wiz's except he is assuming an American wheel which accounts for the slightly different result.
After spin #1: 1  36/37 x 35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.55682 or 55.68% chance of at least one repeat in 8 spins.
But after the next spin, we have to calculate afresh because past spins are not uncertain (they have a probability of 100%). The calculation is the same as above (and the Wiz's), but now because the sequence is shorter (6 spins left out of the original 8) we start from 35/37 and not 36/37.
The chance of NO repeats in the next SIX spins is:
35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37
So the chance of AT LEAST ONE repeat in the next SIX spins is:
After spin #2: 1  35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.54451.
And so on for the remaining calculations. By the time you get to spin 7, there is only one spin left from the original 8. The chance that it will NOT be one of the previous 7 is 30/37 (there are 30 ways to be wrong) so the chance that it WILL be is 1  30/37 = 7/37.
The important thing to realize is that once successive spins from the original 8 spin sequence have passed, they are not included in the subsequent calculations.
Actually, that's not quite right. They ARE included, but for spins already observed the probabilities are 1 (100%). You could make this explicit though:
After spin #1: 1  36/37 x 35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.55682
After spin #2: 1  1 x 35/37 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.54451
After spin #3: 1  1 x 1 x 34/37 x 33/37 x 32/37 x 31/37 x 30/37 = 0.51848
After spin #4: 1  1 x 1 x 1 x 33/37 x 32/37 x 31/37 x 30/37 = 0.47599
After spin #5: 1  1 x 1 x 1 x 1 x 32/37 x 31/37 x 30/37 = 0.41247
After spin #6: 1  1 x 1 x 1 x 1 x 1 x 31/37 x 30/37 = 0.32067
After spin #7: 1  1 x 1 x 1 x 1 x 1 x 1 x 30/37 = 0.18919

I think you have got it wrong , Mike.
Admitting that the more spins the greater chance of a repeat you argue that the first of the 8 has a better chance than than the last of the 8 so contradict your own argument .
The wiz shows that the chance of a repeat OVER A SEQUENCE of 8 is 53% WITH WHICH YOU AGREE !So, if there IS a better chance of a repeat over 8 and you argue that the MORE numbers the BETTER the chance then you must accept that virtual betting IS TO BE RECOMMENDED ! Demolishing your previous argument that virtual betting is nonsense.
I am arguing that if a repeat over a sequence of 8 means anything it means that it applies to ALL series of 8 past  present and future so your SELECTIVE long series of 8 only reflects some of the 47% so claim that 47% has a better chance than 53 % !
I could give a long series of 8 which shows that each and every one shows a repeat !
Am I the one that is wrong here ?
btw Mike 'you have been USING past numbers to make your point so heed your own advice !

The answer to this riddle is a matter of viewpoint.
Mike is correct in that the chance of a match decreases when the remaining numbers to fill the group decrease, but that isn't the question. The question is what is the chance of a single match in a group of 8. They both agree that the answer to the question is over 50%.
Mike maintains that as the remaining numbers decrease so do the cances that a match will occur.
Scep argues that if the answer is correct the fact that the early numbers fail to match increases the chance that a match will occur.
I have no doubt that a mathematician would agree with Mike, but I know that many serious players, including myself, base their play on Scep's arguement !
From Mike's viewpoint there are 8 posible results depening on IF or Where the match occurs. From Scep's viewpoint there are only two. The match will or will not occur.
One final point that is often forgotten in these debates. MATHS DOES NOT, OR EVER CAN, CONTROL CHANCE.
Regards,
Harry

Harry
Just how do you conclude that mathematicians would agree with Mike on this particular point when the wiz and most of us even Real  agrees that in one spin the chance of a repeat is 2.7% ? Are you seriously agreeing with him that betting ONE number has a better chance of being the repeat of the FIRST number than the following 6 numbers ?
Whatever it is he is calculating I don't think it is the same problem as wiz is calculating .
I agree with your other points and have said so on a number of occasions it is often a matter of perception and all hypothesis are subject to variance . Variance IS public enemy number one !!

Harry,
One final point that is often forgotten in these debates. MATHS DOES NOT, OR EVER CAN, CONTROL CHANCE.
Of course not, and it doesn't pretend to. The notion of being able to control chance is a contradiction in terms. Math can only describe a model of reality, it cannot actually BE reality, but the model of roulette is a good one, given certain basic assumptions.
Virtual bets can only "work" if outcomes are not independent. The classic virtual bet scenario of waiting for 10 reds in a row before betting black WOULD be effective if each red number in the sequence was blocked every time it hit. So suppose each of the 10 reds was a different number, say 7, 12, 9, 34, 3, 16,18, 36,23, 1. If each of these numbers was blocked as they hit, so that on subsequent spins the ball could not land on them, this would mean that there were only 8 red numbers "available" by the time you got to the 10th spin, so the chance of black would not be 18/37, but 18/27 (66%). But of course numbers are not blocked on successive spins  the chance of each number hitting remains the same (assuming an unbiased wheel), therefore virtual betting does not have any merit.
Probability theory can only predict outcomes to the extent that the model corresponds to reality. scep's model does NOT correspond to reality, (ie. all outcomes ARE available from spin to spin  which he implicitly denies, or overlooks), which is why the empirical data does not match the predictions given by it.
The logic is the same no matter how "clever" the bet selection is, so it applies equally to the birthday problem system.
It's not a matter of viewpoint. Either virtual betting gives you a mathematical advantage or it doesn't. There is no argument, whether logical, mathematical, or empirical which shows that it does give you an advantage. If you think there is, please present it. The only "argument" I've seen so far is the belief that it does.

Mike
My nine block idea of Double Dozen or Parlayed Dozens DOES give " proof " that virtual spins are useful and I have offered to show it to you LIVE ! You are too blinkered to see it.
My Homepage makes it clear that " Ideas are given  Not Guarantees ". What it contains are ideas for
Dozens and Columns The Nine Blocks
Even Chances  4 Gives 3 ( misnamed )
Doubles Streets/ Sixlines  The Dice Theory
and the Birthday Method for Straights/ En Plein
All are subject to criticism. What have YOU given us here that we didn't already know ?
They are IDEAS Mike for others to leave or take and run with.
You accept that it is valid to transfer the Birthday Problem to Roulette but cannot accept what I think is a logical inference. That IF the Advantage of birthdays does not kick in until the 23rd visitor then it can be argued that the Advantage of the 8 in roulette kicks in until the 8th GIVEN that the prior spins in the 8 did not show a repeat. If the prior 22 do not show a repeat in birthdays why then should the 23rd ? So it IS a difference of opinion, Mike.
What you persistently fail to understand is that we have heard all your arguments time and time again so you are most definitely here to "teach " us. ONE number has the same chance as 7 ? !
Your failure to tell us YOUR approach demonstrates that you are AFRAID to do so because you
know that it is speculation  nothing more .Parroting " Physics " does not impress us here Mike .
Take on board the words of Albert Einstein
" So far as the laws of mathematics refer to reality they are not certain and so far as they are certain they do not refer to reality " .
Your certainty , Mike , is misplaced.

scepticus,
More waffle in an effort to distract from the main point. The topic of this thread is "A Common Error in Probability", not the merits or otherwise of AP. You've made it abundantly clear that you won't accept that your ideas are flawed, even though I have provided empirical results (independently verified by Reyth) demonstrating that they are. It's up to readers to decide what to believe. Reality always has the last word, even if you refuse to face it.
I'm done. Good luck.

Now you are both jumping on me.
@Scep,
I hold by what I said. A mathematician would give you the same answer as Mike. The equation wouldn't balance otherwise. Like you i don't believe that maths can be applied directly to chance, because chance revels in unbalanced equations.
@Mike,
As I said it's a matter of viewpoint. The math view is that there are 5 separate chances each having odds of 18/37. The punter links them together and claims he has a 94.25% chance of getting one right. Americans say Tom ay to, Brits say tomahto.
As to virtual bets the arguement is not so clearcut. After 2 reds have been spun. Math says that as 2 the reds are past there are only 3 chances ie 85% of there being 1 black in 5 spins. The punter says no the fact that 2 reds have passed doesn't alter the fact that there is a 94% chance of there being 1 black. The count becomes more critical as it procedes. After 4 reds have been spun math says there is only 48% chance that there will be 1 black The punter holds to 95% because the bet has not yet lost. He claims that the 95% chance of seeing 1 black remains the same if 2 or even 4 reds have already been spun. The already completed spins are classed as VIRTUAL or IMAGINARY bets. As they have cost nothing the punter feels that they give him an advantage.
Once again it is a matter of viewpoint. The math says that each red that is spun REDUCES the chance of there being a black. The punter says the 95% holds true until the bet is lost. Therefor each red that is spun INCREASES the chance that the next spin will be black.
There is no certainty in either case. So literally, YER PAYS YER MONEY AND YER TAKES YER CHOICE.
I JUST LIKE THE PUNTERS ODDS BETTER THAN THE CASINOS.
Harry

Harry,
Forget about the math, forget even about logic. You're in favor of testing, but why bother if it's all a matter of "viewpoint". If your viewpoint trumps and overrides empirical testing, what's the point of it?
You're saying that both the mathematician and the gambler are correct, but if you actually do some testing and simply count how many times black comes up after 4 or 5 reds it won't be any different than if you hadn't waited for the 4 or 5 reds, and yet you say the 95% and 50% probabilities are somehow "optional" (depending on whether you're a mathematician or a gambler).
This is what I mean about "Alice in Wonderland". It's simply an attack on rationality and common sense.

Mike,
My viewpoint is based on my research, not the other way around. We have been taught from youth that maths overides everything and is always right. I don't dispute your maths. I am merey pointing out there is no certainty here. Maths is no longer absolute. This is particularly true in the short term where most roulette players operate. Those who don't tend to be losers.
I have explained my views in the other thread, I see little point in repeating them here. Lets agree to difer without constantly attacking each other. It doesn't help us or those who are trying to understand the game.
Harry

I think it is clear that my view on Probability is different from Harry's an Mikes and PROBABLY the majority of members. I agree that is pointless to continue this " conversation ". So I shall finish my contribution with my reasoning.
I am using " Conditional Probability " Harry and Mike don't.
Conditional Probability considers the probability of an" event "GIVEN that something has ALREADY occurred. In the Birthday Problem 22 people NEED to be already in the room
without two of THEM not sharing a birthday before the 23rd tilts the balance to 53%.These are
not any old 22 numbers but 22 numbers with NO REPEAT .
Transferring the same reasoning to roulette IS valid  unless you also claim that the Birthday Problem calculation is invalid.

I think this thread is a great example how we can agree to disagree, in a civilized and mature manner, with all points of view clearly presented.
Congrats!

I hope this will clear some misconceptions about probability in roulette.
A system player (one who knows what he's doing), does not and should not try to fight the less than favorable odds built into the game. That's the wrong way of approaching the game.
A system player's goal is to engage in a series of bets where the desired result is to end up with more money than the amount he invested on his bets. And that applies to every subsession (per trigger), and as well as the entire session for the day.
In doing so, the system player is in fact using probabilities, but not the ones that are built into the game. These are the probabilities that are the result of extensive research and observation. Always in conjunction with money values that can change at will at any time. The goal is not to win more times than to lose. The goal is to end up with an amount greater than the amount invested in bets.
And the only statistical information the system player needs from roulette are the payouts.
They determine the length of the series of bets and the amounts needed to carry out the bets that will suit the goal.
So when you look for systems that win, always keep in mind that you have to change your approach.
It is the empirical probabilities that count, coupled with carefully selected money amounts, that would result in a positive cash flow. It's all about positive cash flow. That's the meaning of winning in roulette.
Instead of being buried under the weight of the game's probabilities, find your own.
When you do your home work, you will come up with probabilities that apply in a range of bets, where a positive cash flow is most likely to occur. And with varying money amounts and virtual bets, you will find that is not that hard to beat roulette after all.
So forget about the probabilities built into the game (all you need is the payouts), and concentrate on your own research results, that combined with specific money amounts result in a positive cash flow.

I think this thread is a great example how we can agree to disagree, in a civilized and mature manner, with all points of view clearly presented.
Congrats!
Diplomatic as ever , kav !

I largely agree palestis . Probability is only a guide to forecasting an uncertain future .The gambler's aim is to win more money than he loses so the best "Empirical Evidence " is his Profit and Loss account .The " Long Run " argument is a red herring  we will never reach it.
AND it is the STRATEGY that makes the difference !

palestis,
What's the difference between probabilities "built into" the game and those which are obtained by empirical research? why can you ignore the former but the latter can give you meaningful data?

I am using " Conditional Probability " Harry and Mike don't.
Conditional Probability considers the probability of an" event "GIVEN that something has ALREADY occurred.
All probabilities are essentially conditional. There is no "absolute" probability of anything, it's always conditioned on some information.
Here are two conditional probabilities:
1). What's the probability that a red will hit, given that it is also an even number?
2) What's the probability that red will hit, given that it has already hit 10 times in a row?
For 1), the subset of possible numbers is restricted, because it is given that even will hit, so the red numbers must be one of the even numbers.
In the case of 2), what is given does not restrict the chance of red hitting, so the probability is the same as if red had NOT just hit 10 times in a row.

palestis,
What's the difference between probabilities "built into" the game and those which are obtained by empirical research? why can you ignore the former but the latter can give you meaningful data?
Hi Mike,
The probabilities "built in" are those that are available on the layout, and can be called. They are all based on a single spin, are favourable to the 'House' even when a progression is involved.
The probabilities we obtain by empirical research fall outside the single spin single result concept that is the casino norm. The concepts of 'Virtual'(imaginary) bets and bets spread over several spins and several targets cannot be made on the layout and basically remain in the punters mind until they unfold and progress.
Like AP we use our research to bend the rules without breaking them !
Harry

The probabilities we obtain by empirical research fall outside the single spin single result concept that is the casino norm. The concepts of 'Virtual'(imaginary) bets and bets spread over several spins and several targets cannot be made on the layout and basically remain in the punters mind until they unfold and progress.
Harry,
I have asked this question to Palaistis before and he gave me his answer.
I'd like to ask you the same:
Do you see a difference between "virtual bets" and "past spins".
How can you explain the difference between these two scenarios, when my predetermined bet is Black:
 I virtual bet Black 3 times and lose
 I go to a table where Red has come 3 times

I am using " Conditional Probability " Harry and Mike don't.
Conditional Probability considers the probability of an" event "GIVEN that something has ALREADY occurred.
All probabilities are essentially conditional. There is no "absolute" probability of anything, it's always conditioned on some information.
Here are two conditional probabilities:
1). What's the probability that a red will hit, given that it is also an even number?
2) What's the probability that red will hit, given that it has already hit 10 times in a row?
For 1), the subset of possible numbers is restricted, because it is given that even will hit, so the red numbers must be one of the even numbers.
In the case of 2), what is given does not restrict the chance of red hitting, so the probability is the same as if red had NOT just hit 10 times in a row.
You claim that
"All probabilities are essentially conditional. There is no "absolute" probability of anything, it's always conditioned on some information. "
That is what I have been arguing , Mike ! It is YOU that has declared " absolutes " .We " absolutely " MUST lose " in the Long Run " for example.
What YOU have to answer is why you accept that a series of 8 numbers has a 53% chance of of a repeat yet deny it in practice. The 53% chance applies to ALL series of 8 with NO exceptions . Yet you make an exception with no reasoning except the " received wisdom" .

The answer to this riddle is a matter of viewpoint.
Mike is correct in that the chance of a match decreases when the remaining numbers to fill the group decrease, but that isn't the question. The question is what is the chance of a single match in a group of 8. They both agree that the answer to the question is over 50%.
Mike maintains that as the remaining numbers decrease so do the cances that a match will occur.
Scep argues that if the answer is correct the fact that the early numbers fail to match increases the chance that a match will occur.
I have no doubt that a mathematician would agree with Mike, but I know that many serious players, including myself, base their play on Scep's arguement !
From Mike's viewpoint there are 8 posible results depening on IF or Where the match occurs. From Scep's viewpoint there are only two. The match will or will not occur.
One final point that is often forgotten in these debates. MATHS DOES NOT, OR EVER CAN, CONTROL CHANCE.
Regards,
Harry
I still " don't get it "Harry so please enlighten me . What was Mike calculating ?

I am using " Conditional Probability " Harry and Mike don't.
Conditional Probability considers the probability of an" event "GIVEN that something has ALREADY occurred.
All probabilities are essentially conditional. There is no "absolute" probability of anything, it's always conditioned on some information.
Here are two conditional probabilities:
1). What's the probability that a red will hit, given that it is also an even number?
2) What's the probability that red will hit, given that it has already hit 10 times in a row?
For 1), the subset of possible numbers is restricted, because it is given that even will hit, so the red numbers must be one of the even numbers.
In the case of 2), what is given does not restrict the chance of red hitting, so the probability is the same as if red had NOT just hit 10 times in a row.
You misunderstand " Conditional Probabilities " Mike .
They take into consideration " Events "that have passed and your first question doesn't qualify .That particular question illustrates your ignorance. How do you KNOW that the number WILL be even ? Are you psychic ?
Your second question does, though , as it speaks of the past.
Ignoring the zero the answer is Over one spin the EXPECTATION is 50/50 but if Expectations were realised there would be no gambling.What IS certain is that Red will appear it is only a matter of WHEN and some of the members here have said that they win using a STRATEGY.
I don't bet that way .As most members here know  I don't view things as most do  but why should i be the one that is necessarily wrong because I view things differently ?

palestis,
What's the difference between probabilities "built into" the game and those which are obtained by empirical research? why can you ignore the former but the latter can give you meaningful data?
The roulette's job is to spin continuously one number at a time. And there are standard probabilities associated with each number coming up. And also with groups of numbers, like dozens, DS's, QUADs, etc.
If a player bets constantly (and most of roulette players do, as I rarely see any players skipping spins), the obvious result will be a loss at some point in time. Not only because of the HE but also because of the rapid depletion of the bank roll. The casino has infinite bank roll. The player has limited bank roll.
An astute system player is a player who choses to bet only when conditions are seemingly in his favor. The length and amount of his bets, is predetermined, all along having the freedom to stop and walk away. MANY SMALL SESSIONS DO NOT ADD UP TO A LONG RUN SESSION if the player comes back another time another day. .
Because THE ASTUTE PLAYER IS VERY SELECTIVE WHEN HE WILL BET. As he only choses special conditions to bet , rather than betting left and right all the time. The roulette is not selective. It has to spin nonstop.
To answer you question about empirical probabilities all I have to do is bring a familiar example.
The probability of 5 black in a row is [18/37]^5. And we see it happening often. 5 black, 5 red, 5 odd etc. You and your similarly thinking colleagues, claim that after 5 blacks have come up, what happens next is a new situation unaffected by those 5 already spun blacks.
This is that you and the gaming experts have been saying all along.
Therefore after 5 black, the probability of another set of 5 blacks should be the same. [18/37]^5.
Isn't that what you are claiming? (the wheel has no memory).
Then how do you explain the fact that although it's easy to see 5 of SOMETHING in a row,
seeing another 5 after that is very rare?
I can go thru a list of a daily results table and see many times 5 of something in a row.
If that doesn't affect what happens next, then y do I have such a hard time seeing another 5? (to make a total of 10 in a row).
Is the [18/37]^5 more powerful for the first 5, and then it loses its strength for next [18/37]^5?.
It shouldn't be. [18/37]^5 is [18/37]^5 and should always be the same.
You may say that it falls under the [18/37]^10 if you expect to see another 5. That is y I don't see it too often.
BUT YOU SAY THE FIRST 5 DON'T COUNT, BECAUSE THEY ARE PAST SPINS AND DON'T AFFECT THE NEXT RESULTS.
Do you see my point?
The fact that I don't see another 5 black after already 5 spun blacks, is called "empirical observation". and there is a probability associated with at least a red coming up in the next 5 spins, THAT HAS NOTHING TO DO WITH THE GAME'S BUILT IN PROBABILITY OF [18/37]^5.
At that point I have a choice to play red for the next 5 spins, or use 2 virtual losses (which in effect would mean 7 black in a row), and bet only 3 spins.
If I win the first 2 I wasted my time. Not my money.
Then I will patiently wait for another 5 of something and do the same after that.
That is being selective means.
In effect, with patience, I squeeze the breath out of the roulette so hard, to the point that she has no other choice but to spin what I will bet.

[That is what I have been arguing , Mike ! It is YOU that has declared " absolutes " .We " absolutely " MUST lose " in the Long Run " for example.
Yes, you must absolutely lose in the long run GIVEN certain assumptions (that the payouts are unfair, outcomes are independent, the wheel is unbiased, you are playing the GAME and not the device, etc).
What YOU have to answer is why you accept that a series of 8 numbers has a 53% chance of of a repeat yet deny it in practice. The 53% chance applies to ALL series of 8 with NO exceptions . Yet you make an exception with no reasoning except the " received wisdom" .
scepticus, I've already answered this many times in the last halfdozen pages. I think you're so muddled you don't even understand the problem sufficiently to state it coherently. To put it yet another way, the series of 8 numbers should be taken "collectively" (as a group) and not "distributively" (each number in the group). the 53% applies collectively, to the whole series as a series. Probability is not "conserved" as each number comes up so that the 53% is transferred from each number to the next. You think it is, which is why you believe that having seen 7 numbers with no repeats, the 53% must apply the 8th and final number.
Apart from the logical and mathematical arguments I've given, both Reyth and I have demonstrated using computer simulation that this is false. Also, do you realize what an incredible edge you would have if the chance of any one of the 7 numbers hitting in one spin was 53%? If this was the case, the casinos would have gone out of business years ago.
Here's the calculation. You're betting 7 numbers so the return on a win is +35 u for the winning number minus 6 u from the losing numbers, so the profit is +29 u, and (according to you) the chance of a win is 53%. This means that you will lose 7 units 100%  53% = 47% of the time.
the EV (expected value) is then [+29 x 0.53  7 x 0.47] / 7 = 1.726, an edge in your favor of 72.6%!

You misunderstand " Conditional Probabilities " Mike .
They take into consideration " Events "that have passed and your first question doesn't qualify .That particular question illustrates your ignorance. How do you KNOW that the number WILL be even ? Are you psychic ?
Your second question does, though , as it speaks of the past.
No scepticus, it's you who misunderstands. Conditional probability doesn't apply only to events that have passed, if just means that IF some event or state occurs or is true, the probability is modified in the light of this information. So I don't need to KNOW that the number will be even, just that IF it is, the probability of red is different than what it would be if I didn't have that information.
In probability theory (https://en.wikipedia.org/wiki/Probability_theory), a conditional probability measures the probability (https://en.wikipedia.org/wiki/Probability) of an event (https://en.wikipedia.org/wiki/Event_%28probability_theory%29) given that (by assumption, presumption, assertion or evidence) another event has occurred.^{[1]} If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB), or sometimes P_{B}(A). For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person has a cold (https://en.wikipedia.org/wiki/Common_cold), then they are much more likely to be coughing. The conditional probability of coughing given that you have a cold might be a much higher 75%. The concept of conditional probability is one of the most fundamental and one of the most important concepts in probability theory.^{[2]} But conditional probabilities can be quite slippery and require careful interpretation.^{[3]} For example, there need not be a causal or temporal relationship between A and B.
https://en.wikipedia.org/wiki/Conditional_probability

palestis,
An astute system player is a player who choses to bet only when conditions are seemingly in his favor. The length and amount of his bets, is predetermined, all along having the freedom to stop and walk away. MANY SMALL SESSIONS DO NOT ADD UP TO A LONG RUN SESSION if the player comes back another time another day. .
Because THE ASTUTE PLAYER IS VERY SELECTIVE WHEN HE WILL BET. As he only choses special conditions to bet , rather than betting left and right all the time. The roulette is not selective. It has to spin nonstop.
The key word here is "seemingly". Mathematically there is no justification for assuming that the "special conditions" put the odds in your favor. Since there is no mathematical evidence that bet selections of this kind change the odds, the onus is on you to provide some empirical evidence. Would you be up for the challenge?
Whether you have an edge or not It makes no sense to say that many small sessions don't add up to a long run session, but I think I know what you're trying to say.
I don't disagree that short streaks are more common than long streaks, only that ANY PARTICULAR SHORT STREAK DOES NOT INDICATE WHETHER IT WILL CONTINUE ON TO BECOME A LONG STREAK. How can it? After a streak of 5 the probability of another streak of 5 (making a streak of 10) is exactly the same as the first streak, so how can the first streak affect, cause, or indicate the second?.
In order to make a profit you have to increase stakes from spin 6 to 10 (or at least, after spin 6), and the amount you gain from those times when the streak ends before 10 will be lost from the fewer times it ends after 10. If the initial streak of 5 really did indicate that the streak would end before 10 then you could make a profit flatbetting, but you can't, because in the spins 6  10 the first wins are just as likely to occur anywhere in the sequence  they are not MORE likely to occur on spins 6 or 7 (corresponding to a win or break even) just BECAUSE there has already been a streak of 5.

mike
You still think you have proved your case when you haven't.
1) Your " calculations " seem to refer to each succeeding number being a repeat ONLY of the seed number whereas the Wiz's calculations are for ANY two of the 8 repeating .
2 ) The chance of the ONE remaining number being the same as the first in your scenario MUST be 2.7 % and not your 1.89%
3 )You still fail to understand that the chance of a repeat over ANY 8 spins is 53 % and refers to ALL series of 8 so if no repeats have occurred in ANY previous 8 then the last 7 non repeats must have a 53% chance of a repeat . If you accept the Birthday solution then you must accept the Roulette 8 solution . That does not mean that it WILL happen only that it is more likely than not.
4 ) WOW ! What breathtaking arrogance to say that the Wiz's calculations are OK so far as it goes .
SO FAR AS IT GOES !!!!
Well, that puts Mike Shackleford in his place , doesn't it !

Mike
Something that has already happened is "Factual Information" and so is worth more than an
" Assumption " that may or not be true. Your "Assumption" that the next spin WILL be even cannot be true unless it actually happens .Your reasoning here is wooly or it would give the bettor an advantage which you yourself say just cannot be true.
When others here make "Assumptions " based on prior information you trash them but claim ownership yourself ?

1) Your " calculations " seem to refer to each succeeding number being a repeat ONLY of the seed number whereas the Wiz's calculations are for ANY two of the 8 repeating .
You obviously haven't understood the calculations, try reading them again. And the Wiz's calculations are not for any two, but for at least one repeat, which is not the same.
2 ) The chance of the ONE remaining number being the same as the first in your scenario MUST be 2.7 % and not your 1.89%
I have no idea what you're talking about here. The calculation is not for the one remaining number being the same as the first but for the one remaining number being one of the previous 7. And where did I say the chance of one number hitting is 1.89%? you are totally confused.
3 )You still fail to understand that the chance of a repeat over ANY 8 spins is 53 % and refers to ALL series of 8 so if no repeats have occurred in ANY previous 8 then the last 7 non repeats must have a 53% chance of a repeat . If you accept the Birthday solution then you must accept the Roulette 8 solution . That does not mean that it WILL happen only that it is more likely than not.
This is getting very boring. And what do you mean by ALL series of 8? of course you are referring to all series of 8. So what? you're missing the point, again.
4 ) WOW ! What breathtaking arrogance to say that the Wiz's calculations are OK so far as it goes .
SO FAR AS IT GOES !!!!
Well, that puts Mike Shackleford in his place , doesn't it !
My calculations do not contradict the Wiz's. "As far as it goes" refers to the fact that he only showed the calculation for the series of 8, NOT the remaining series as successive spins came up. He was replying to a specific question.
It's a bit rich for you to accuse me of being arrogant when you ignore the "received wisdom" and yet offer no proof or evidence that it is incorrect.

Mike
Something that has already happened is "Factual Information" and so is worth more than an
" Assumption " that may or not be true. Your "Assumption" that the next spin WILL be even cannot be true unless it actually happens .Your reasoning here is wooly or it would give the bettor an advantage which you yourself say just cannot be true.
When others here make "Assumptions " based on prior information you trash them but claim ownership yourself ?
scepticus,
Did you actually read the post where I included a quote and link to the Wikipedia article on conditional probability? Apparently all the textbooks are wrong  again!
Your "Assumption" that the next spin WILL be even cannot be true unless it actually happens
Probability depends on what you know or don't know. IF you have some information which has a bearing on the probability of an event (and you always do, which is why all probability is conditional on information) then of course you should take it into account. Is this really so difficult to understand?

The probabilities we obtain by empirical research fall outside the single spin single result concept that is the casino norm. The concepts of 'Virtual'(imaginary) bets and bets spread over several spins and several targets cannot be made on the layout and basically remain in the punters mind until they unfold and progress.
Harry,
I have asked this question to Palaistis before and he gave me his answer.
I'd like to ask you the same:
Do you see a difference between "virtual bets" and "past spins".
How can you explain the difference between these two scenarios, when my predetermined bet is Black:
 I virtual bet Black 3 times and lose
 I go to a table where Red has come 3 times
Hi Kav,
My appologies for the delay. We have a problem here with power cuts("Lload Shedding"). If the demand for power goes up they simply switch large areas out of the Grid. It comes in 3 sizes. 3 hour blackouts, 6 hour blackouts and "sorry folks we will let you know in a few days when you can swich on again." The 3 hour one often happen every day.
Back to your Question.
The past spins we use are those we used in our research, not those that have occurred in the past few minutes. We look for events that often recur and establish an average. At the same time we look for any signs that might point to the event recurring.
The obvious target being streaks of the various bets available on the layout. This can include any number or combination of numbers. Personally I mainly use 2 criteria, FLOW, being the direction the wheel appears to be taking, and "The Rule of Thirds". I compare what is happening here and now with my experience in the past that has been confirmed by testing. Which will have produced a 'winning range'" ie like a bell graph of results. My research tells me that most of the wins will occur within that range.
Having identified a possible target I must now decide What part of the "range" I am going to bet. Generally to bet it all would expose too much of my bankroll to a possible loss. eg. If I had established a "range" of between 3 and 10 for EC bets, I would need a 7 step progression if I began betting after your 3 reds. This would expose too much of my bankroll to the chance of a loss. I rarely make more than 2 or 3 bets on an EC target. At this point the descision depends a lot on the personality and playing style of the punter. Palestis likes to bet the end of the "range" where a quick win seems more likely. He will often win 10 or more bets before encountering a loss. I prefer to bet into the middle of the "range". This means that I will lose many of my bets. In fact I generally lose more bets than I win. I consider this the cost of doing business. Both of us use so called VIRTUAL bets to reach the sector of the "range " we like to bet. If the virtual bet wins we have lost nothing but an opportunity, and there are plenty of those If a bet is lost we simply wait for a new target. If our "homework" is correct the casino cannot expect to win several times in a row.
I think I have answered both your questions, but I'll deal with them again.
I see 3 reds I would make one or two Virtual bets. The if black hadn't won I would venture 2 or 3 real bets If one of them won or NONE of them won I would stop and wait for a new target. I don't move around, you would get a different answer from Palestis , who does.

My appologies for the delay. We have a problem here with power cuts("Lload Shedding"). If the demand for power goes up they simply switch large areas out of the Grid. It comes in 3 sizes. 3 hour blackouts, 6 hour blackouts and "sorry folks we will let you know in a few days when you can swich on again." The 3 hour one often happen every day.
Harry, where do you live? just curious...
Which will have produced a 'winning range'" ie like a bell graph of results. My research tells me that most of the wins will occur within that range.
Having identified a possible target I must now decide What part of the "range" I am going to bet. Generally to bet it all would expose too much of my bankroll to a possible loss. eg. If I had established a "range" of between 3 and 10 for EC bets, I would need a 7 step progression if I began betting after your 3 reds.
For EC bets 87.5% of wins come in the first 3, with longer streaks being increasingly less likely, so why don't you restrict your betting to 2 or 3 bets early in the streak?

Hi Harry,
Thank you very much for your answer.
Your answer is similar to palestis.
I still do not understand your and palestis reasoning behind the difference of "past spins" and "virtual bets".
The only reasoning I can think of is that you want to include the "lost spins" in your personal permanence.
But the fact that your bets are only virtual makes this a bit debatable if you can include "virtual bet" which you actually have not bet in your personal permanence.
Now this is another very interesting philosophical debate about roulette.
Like I have said many times, there is much more to it than math.

1) Your " calculations " seem to refer to each succeeding number being a repeat ONLY of the seed number whereas the Wiz's calculations are for ANY two of the 8 repeating .
You obviously haven't understood the calculations, try reading them again. And the Wiz's calculations are not for any two, but for at least one repeat, which is not the same.
2 ) The chance of the ONE remaining number being the same as the first in your scenario MUST be 2.7 % and not your 1.89%
I have no idea what you're talking about here. The calculation is not for the one remaining number being the same as the first but for the one remaining number being one of the previous 7. And where did I say the chance of one number hitting is 1.89%? you are totally confused.
3 )You still fail to understand that the chance of a repeat over ANY 8 spins is 53 % and refers to ALL series of 8 so if no repeats have occurred in ANY previous 8 then the last 7 non repeats must have a 53% chance of a repeat . If you accept the Birthday solution then you must accept the Roulette 8 solution . That does not mean that it WILL happen only that it is more likely than not.
This is getting very boring. And what do you mean by ALL series of 8? of course you are referring to all series of 8. So what? you're missing the point, again.
4 ) WOW ! What breathtaking arrogance to say that the Wiz's calculations are OK so far as it goes .
SO FAR AS IT GOES !!!!
Well, that puts Mike Shackleford in his place , doesn't it !
My calculations do not contradict the Wiz's. "As far as it goes" refers to the fact that he only showed the calculation for the series of 8, NOT the remaining series as successive spins came up. He was replying to a specific question.
It's a bit rich for you to accuse me of being arrogant when you ignore the "received wisdom" and yet offer no proof or evidence that it is incorrect.
O.K. Mike I understand your chart now but it does not change my perception of the problem .So far as I can see you and Slacker are making a two pronged attack on my perception.
a ) I cannot use past spins.
b) Even if I did I would be betting only 7 numbers on the last spin if the prior seven spins did not show a repeat. ( The seed plus the following six )
Am I right ? If not please state what your position is )
Let's start afresh here to better clarify our positions.

Hi Harry,
Thank you very much for your answer.
Your answer is similar to palestis.
I still do not understand your and palestis reasoning behind the difference of "past spins" and "virtual bets".
The only reasoning I can think of is that you want to include the "lost spins" in your personal permanence.
But the fact that your bets are only virtual makes this a bit debatable if you can include "virtual bet" which you actually have not bet in your personal permanence.
Now this is another very interesting philosophical debate about roulette.
Like I have said many times, there is much more to it than math.
For some players "recent" past spins and virtual bets are the same, but only if the recent past spins are related to the system. For example if the system is to play the opposite EC, after a certain EC has appeared several times in a row (like RRRR), then this RRRR can be considered as 4 virtual bets (more exactly 4 VIRTUAL LOSSES). Which means that if I was present in that roulette 10 minutes earlier and bet BLACK, I would've lost 4 times in a row. Since the probability to win an EC is close to 50%, and I already lost 4 times in a row, if I place 3 actual bets after this RRRR, I have an increased chance to win, because it's rare for Red to show up 8 times in a row. And that's what has to happen to lose the 3 bet series. 4 already lost (virtually), and 3 actual to make it 7. If black shows up in the 5th , 6th or 7th spin I win. If it doesn't, then I lose just 3 bets. Not 7.
Realistically how often do we see an EC that spun 4 times in a row, to go on for another 4? Not very often.
We might even come across a situation where an EC has come up 8 times in a row. Betting the opposite (real bets), for 3 spins after that, WE BET ON THE PREMISE THAT IT'S EXTREMELY RARE FOR AN EC TO SHOW UP 12 SPINS IN A ROW. And since it has come up 8 spins already, YES THE OPPOSITE IS DUE by a an overwhelming chance in the next 3 spins.
Strict probability junkies will disagree, but reality and long time observation proves otherwise.
And most important of all I said 3 bets and then stop. Some players might go for 4. But that's as far as it should go. If the RED decides to spin 15 times in a row, I will not be destroyed because I will stop after 3 bets. Then I'll wait for another similar trigger.
And those who are in the habit of doing long term research will tell you, that even if it is difficult and rare for roulette to go into extremes, IT IS EVEN MUCH MORE RARE TO REPEAT EXTREMES IN CONSECUTIVE TRIGGERS. That is a fact.
Which means that if I lost these 3 bets now, chances are the next time I see the same conditions (trigger), I will prevail. And by increasing the starting chip value the next time around I will recover the previous loss.
It's a lot better if we keep things simple in the game of roulette. Act on your experience and limit your bets to a recoverable level if a loss should occur.

Hi Harry,
Thank you very much for your answer.
Your answer is similar to palestis.
I still do not understand your and palestis reasoning behind the difference of "past spins" and "virtual bets".
The only reasoning I can think of is that you want to include the "lost spins" in your personal permanence.
But the fact that your bets are only virtual makes this a bit debatable if you can include "virtual bet" which you actually have not bet in your personal permanence.
Now this is another very interesting philosophical debate about roulette.
Like I have said many times, there is much more to it than math.
And here is an example of "virtual bets" that has nothing to do with past spins.
Sometimes I like to bet 12 numbers in groups, like dozen, 3 quads, 2 DS's totally at random, without even looking at what came up before. As if I was betting blindfolded.
I have found thru observations that randomly betting a group like this, I should expect to win (at least for 1 time only), within 8 spins. It could be within the 1st spin or it could be on the 8th spin.
I don't know in advance when I will hit it.
But from empirical experience I know that that "the range" that produces higher percentage of hits is between the 4th and 7th spin. if you try this system thousands of times this is what you will come up with.
Knowing this fact, I will bet randomly this group,
(in the virtual mode) 3 times and aim at losing all 3 times. (virtual loss). Then I will bet with actual money the next 3 or 4 spins and stop, or stop as soon as I win 1 time. Whichever comes first.
If during the first 3 virtual bets I win I start all over again.
I don't worry about "lost winning opportunities", because no matter what you play it could be a winning opportunity.
And to realize all winning opportunities it means that you have to bet ALL THE TIME. No matter what the type of bet is.
Does anybody believe that he can win the game if he never misses a spin?
A gambler wants every winning opportunity he can get his hands on.
A winner only bets in carefully selected situations.

@ Kav,
I had intended to follow up on my last post with some thing very similar to Palestis's post. Unfortunately just after I posted the power was cut for 7 hours. only returning at midnight. Way past my bedtime even if I did have light.
@ Mike,
I live in Germiston, South Africa, one of the towns that make up the "Witwatersrand". A densely populated area the world tends to think of as Johannesburg. My daughter in law took my grand children to Cape Town for the weekend. She suffered through a 3 hour power cut there yesterday morning, only to fly back to a 7 hour cut here.
Back to your roulette question. Palestis's post covered the basic principles that we work to. The "winning range" is not necessarily the area that gets the most hits, but rather the area that produces that bell graph of results. Thus EC spins 1 to 3 tend to produce the expected even rise in results. Spins 4 to 78 are inclined to "spike". While spins 9 omwards produce a steady decline in results. It is that 'SPIKE" we are looking for ! It could occur anywhere in the average graph of results. The 'VIRTUAL" bets are simply waiting spins until the hoped for "spike " is expected to start. Spins before and after the spike are of no interest because they tend to be too even to offer an advantage.
I realise that such a spike would not appear with a mathematical calculation, but I assure you that with EMPIRICAL results it is very clear.
The advantage of this type of play is not the fact that it allows a better percentage of wins.Rather that it allows the punter to restrict his action to a very small number of bets. The real progression being pressing the new trigger on a DIFFERENT TARGET !! The claim , that I have not seen disputed mathematically, is that chance cannot continue to produce results that oppose the average.
For those who believe that maths is in control. I can only point out that the spikes tend to occur more or less equallyon both side of the mean. As we are ONLY interested in the spikes we tend to be "on the money" which ever direction "Regression Towards the Mean" may take.
I hope no one will feel insulted or belitted when I say that Maths and "Personal Permanence" have no meaning when only the spikes are bet. No single loss or series of losses is likely to seriously challenge my bankroll. Because my bets are small and confined I can easily walk away if the FLOW doesn't feel right. Once again that is not likely to happen again and again and again.
Regards,
Harry

Mike
Something that has already happened is "Factual Information" and so is worth more than an
" Assumption " that may or not be true. Your "Assumption" that the next spin WILL be even cannot be true unless it actually happens .Your reasoning here is wooly or it would give the bettor an advantage which you yourself say just cannot be true.
When others here make "Assumptions " based on prior information you trash them but claim ownership yourself ?
Did you actually read the post where I included a quote and link to the Wikipedia article on conditional probability? Apparently all the textbooks are wrong  again!
Your "Assumption" that the next spin WILL be even cannot be true unless it actually happens
Probability depends on what you know or don't know. IF you have some information which has a bearing on the probability of an event (and you always do, which is why all probability is conditional on information) then of course you should take it into account. Is this really so difficult to understand?
Conditional probability
From Wikipedia, the free encyclopedia
[hide]This article has multiple issues. Please help improve it or discuss these issues on the talk page.
This article needs additional citations for verification. (September 2013)
Conditional Probability
www.stat.yale.edu/Courses/199798/101/condprob.htm
The conditional probability of an event B is the probability that the event will occur given the
knowledge that an event A has already occurred. This probability is written P(BA), notation for the probability of B
given A. In the case where events A and B are independent (where event A has no effect on the
probability of event B), the conditional probability of event B given event A is simply the
probability of event B, that is P(B).
Conditional Probability Definition  Investopedia
www.investopedia.com/terms/c/conditional_probability.asp
Probability of an event or outcome based on the occurrence of a previous event or outcome.
Conditional probability is calculated by multiplying the probability of ...
etcetera etcetera  etcetera etc,

scepticus,
The wording in many definitions of conditional probability can suggest that there is a time element, but this is misleading because it's not required that one event occurs BEFORE another in order to satisfy the definition. I'm surprised that a university like Yale has been so sloppy...
In regard to the Wikipedia article:
This article has multiple issues. Please help improve it or discuss these issues on the talk page.
This article needs additional citations for verification.
If you click on the "talk" link and scroll down the page to the "Wrong?" heading (https://en.wikipedia.org/wiki/Talk:Conditional_probability (https://en.wikipedia.org/wiki/Talk:Conditional_probability)) you will see that the original definition was the same as that given in your Yale link:
Conditional probability is the probability of some event A, given that some other event, B, has already occurred
But someone noticed that this made no sense given that the article also says that :
In these definitions, note that there need not be a causal or temporal relation between A and B. A may precede B, or vice versa, or they may happen at the same time.
It's better to keep to the strict mathematical definition, in which there is no reference to time.
P(A  B) = P(A & B) / P(B)
A & B is the event which consists of the outcomes that A and B have in common, that's all.
The Investopedia definition is even worse. Conditional probability is not based on the occurrence of a PREVIOUS event or outcome; the events could be simultaneous.

I argued that, using the Birthday Problem scenario , it was valid to bet the 8th spin when the prior 7 spins showed no repeat. Slacker disagreed and started this thread . Mike then joined in supporting Slacker’s position .Theirs is “ the received wisdom “ which I challenge.
Their mistake is in not realising that I am only betting the last of an 8 numbers series which mathematicians agree have a 53% chance of ANY two in the series being the same. I did not CHOOSE to bet 7 numbers it just so happened that 7 numbers are required when betting the 7th spin of the 8 number sequence .
This can easily be seen if we consider a 10 spin sequence of numbers with the same proviso of at least 2 numbers being the same with a 95% probability that at least two numbers will be the same. This time I need to bet, not 7, but 9 numbers on the last spin if no prior 2 in the sequence are the same  even if I start betting from spin one.
Mike goes further and argues that my last spin bet has less chance than the previous 6 because I have only one bet left .
He misunderstands what the mathematicians are saying here.No one bet has a greater chance than any other in the sequence whether that bet is ONE chip TWO chips or SEVEN chips. All must be considered as one part of a whole, in their totality.
There is a danger here that naïve bettors will accept Mikes’ view that the last bet has less chance than the others and assume that they should only bet the earlier bets of One Chip, Two Chips and Three chips which gives them 3 chances for a total of 6 chips as against betting the seventh spin requiring 7 chips .
It IS difficult to understand why this should be so but so also is the Birthday Problem scenario which Mike accepts.

He misunderstands what the mathematicians are saying here.No one bet has a greater chance than any other in the sequence whether that bet is ONE chip TWO chips or SEVEN chips. All must be considered as one part of a whole, in their totality.
scepticus, this is irrelevant. We are not talking about one bet, but the chance that two or more numbers are the same in a sequence. The chance of this is higher for a longer sequence than for a shorter sequence. What's the chance that in 2 spins both numbers will be the same? is this higher or lower than the chance that two or more numbers will be the same in 10 spins? what about in 100 spins?
More to the point, what is the chance of a number hitting which has already hit? If you're thinking this makes no sense, you'd be right.
And how do you explain the fact that both Reyth and I showed by simulation that the chance that the final number is one of the previous 7 is not 53% but 18.9%?

scepticus,
The wording in many definitions of conditional probability can suggest that there is a time element, but this is misleading because it's not required that one event occurs BEFORE another in order to satisfy the definition. I'm surprised that a university like Yale has been so sloppy...
In regard to the Wikipedia article:
This article has multiple issues. Please help improve it or discuss these issues on the talk page.
This article needs additional citations for verification.
If you click on the "talk" link and scroll down the page to the "Wrong?" heading (https://en.wikipedia.org/wiki/Talk:Conditional_probability (https://en.wikipedia.org/wiki/Talk:Conditional_probability)) you will see that the original definition was the same as that given in your Yale link:
Conditional probability is the probability of some event A, given that some other event, B, has already occurred
But someone noticed that this made no sense given that the article also says that :
In these definitions, note that there need not be a causal or temporal relation between A and B. A may precede B, or vice versa, or they may happen at the same time.
It's better to keep to the strict mathematical definition, in which there is no reference to time.
P(A  B) = P(A & B) / P(B)
A & B is the event which consists of the outcomes that A and B have in common, that's all.
The Investopedia definition is even worse. Conditional probability is not based on the occurrence of a PREVIOUS event or outcome; the events could be simultaneous.
Mike
You asked me to supply you with the sources supporting my argument . This I did. You question the Yale position and counter with What ? Sources who may or may not have qualifications . You CAN NOT be serious. You are required to show verifiable" text books " to support YOUR position just as you asked me to do .
The issue you raised was  GIVEN the next spin was Even what was the probability of it also being Red . I questioned that. You also said that you always have some information on the probability of a future event.What information do you possess that entitles you to claim that the next spin will be even? And if you have such information does that not have a "Time " element  in the past ?

He misunderstands what the mathematicians are saying here.No one bet has a greater chance than any other in the sequence whether that bet is ONE chip TWO chips or SEVEN chips. All must be considered as one part of a whole, in their totality.
scepticus, this is irrelevant. We are not talking about one bet, but the chance that two or more numbers are the same in a sequence. The chance of this is higher for a longer sequence than for a shorter sequence. What's the chance that in 2 spins both numbers will be the same? is this higher or lower than the chance that two or more numbers will be the same in 10 spins? what about in 100 spins?
More to the point, what is the chance of a number hitting which has already hit? If you're thinking this makes no sense, you'd be right.
And how do you explain the fact that both Reyth and I showed by simulation that the chance that the final number is one of the previous 7 is not 53% but 18.9%?
Mike,
You still don't understand what I am arguing.
I AM talking about " the chance that two or more numbers are the same in a sequence " YOUR words.
I AM arguing " the chance of this is higher for a longer sequence than for a shorter sequence "
and that ALL 8 must be considered and each have an equal chance .
It is you and Reyth that claim that the 7th has LESS chance than the shorter sequence of 6  and you are both wrong ! ALL have an EQUAL chance .Your 7 /37 refers only to ONE spin and NOT one spin IN A SEQUENCE .
btw Reyth also pointed out that the source you referred me to says only that "nearly all " and not the certainty you claimed he meant .

Hi Harry,
Thank you very much for your answer.
Your answer is similar to palestis.
I still do not understand your and palestis reasoning behind the difference of "past spins" and "virtual bets".
The only reasoning I can think of is that you want to include the "lost spins" in your personal permanence.
But the fact that your bets are only virtual makes this a bit debatable if you can include "virtual bet" which you actually have not bet in your personal permanence.
Now this is another very interesting philosophical debate about roulette.
Like I have said many times, there is much more to it than math.
Hi Kav,
I am going to add Mikes query to yours. He points out that as the 1st 3 EC bets account for 87.5%of wins why not just bet the first 3 ? This would result in a win of 87.5 per 100 spins. As a 3 step martingale would be needed, the remaining 12.5% would be lost at a cost of 7 each. that's 87.5 loss.
As it happens Mikes figures are wrong. mathematically the 1st 3 spins will only yeild around 85%. He forgot to include the HE !
As an example of both empirical research and virtual betting I offer the following. Over the past few days i have played several sessions using an EC method. The results were.
Total spins 421... Betting opportunities 121. Of these 1st spin won 59, 2nd 30, 3rd 14, 4th 13, 5th 2, 6th 1, 8th 2.
This was slightly unusual because the 1st 3 spins were almost mathematically correct.
I played only 3 spins per bet.
Had I played the 1st 3 I would have lost 23, But I virtually bet the 1st spin( see my post to Kav above)
I was left with 62 actual bets. of these 57 won and 5 lost at a cost of 5 x 7 = 35. giving me a win of 22.
The math probabilities were pretty good in this case but empirical research and virtual bets gave me a win.
To sum up, Empirical research shows where the most action is likely to take place. Virtual Bets gets you there at NO COST. A mathematically losing session is turned into a win !
Harry

Sorry Kav I just realised that I didn't deal with the personal permanece concept.
If I believed that ONLY the spins I bet on were part of my personal permanence. Then I have reached a point where nothing very bad could ever happen. All those long streaks and downturns just pass me by UNBET ! The worse that the house can do is hit me several times with loses one after another. As these loses represent a very small part of my overall bank. I can walk away relatively unharmed. Not even my daily bank would be seriously damaged.
In another thread you make the point, "That witthout risk there can be no profit". This is extremely important. As in any business the risk must be carefully managed. It is pointless trying to outplay the wheel with long progressions. You are simply raising the risk to dangerous levels. The loss, when it comes, wil be devastating
Regards,
Harry

The issue you raised was  GIVEN the next spin was Even what was the probability of it also being Red . I questioned that. You also said that you always have some information on the probability of a future event.What information do you possess that entitles you to claim that the next spin will be even? And if you have such information does that not have a "Time " element  in the past ?
I am not trying to find the probability that the next spin will be even, but some OTHER probability GIVEN that it is. It doesn't matter HOW you know that it is even, you are only concerned with how this information affects the probability you are interested in.
Example two questions in probability
1) what is the probability that the next outcome is red?
2) what is the probability that the next outcome is red, given that it's in the 3rd column?
The answer to 1) is just 18/37.
The answer to 2) can be calculated using the formula (definition) of conditional probability.
P(A  B) = P(A & B) / P(B)
A = the next outcome is red.
B = the next outcome is in the 3rd column.
P(A & B) = 9/37 since there are 9 reds in the 3rd column. P(B) is just 12/37.
So P(A  B) = 9/37 x 37/12 = 9/12.
You don't really need the formula when you understand what conditional probability means, it just means you are restricting the "sample space". In this case you are only interested in the red numbers which are in the 3rd column (not all red numbers), so the sample space has shrunk from 37 to 12, therefore the probability of red given the 3rd column is 9/12.
There is no time element in this; it's not a case of red coming AFTER the 3rd dozen or viceversa, the question is concerned with two attributes of a single number, not two numbers occurring one after the other.
But of course the condition MAY refer to a previous event. eg. what is the probability of red, given that the last outcome was in the 3rd dozen? In this case, the sample space has not changed due to the condition (outcomes are independent), so the chance is just 18/37, the same as it would be without the condition. This is in fact how independence is DEFINED:
if P(A  B) = P(A) then the outcomes are independent. i.e. the probability of A given B is the same as the probability of A.
There are plenty of examples of conditional probability online, including at the Wiz's site.
scepticus, I don't have the time or inclination to write up a complete tutorial on probability, and others have already done a better job of it than I could do. You can't rely on your intuition for this stuff, you need to work through a course and try to solve problems in order to really understand it. Just reading about it isn't good enough either. There are free courses online but I think the best way is just to study a textbook and work through the problems. There is a good basic one here which doesn't assume you know much maths (high school algebra is enough). The answers to half the problems are in the back. You can get a copy from the Book Depository for £3.70 + postage.

The " Time " element I was talking about refers not to the next spin but to your belief that you have " information " prior to the next spin that allows you to claim that the " even " is a given. It is not a " given " but an " assumption".
You do not need to give me your treatise on Probability Theory .What you need to do is give your rebuttal of why you think that my view is wrong regarding the sequence of 8 bets. Failure to do so allows me to say that you are full of bluff and bluster .
This first post here makes the allegation that my use of the spin series is wrong .You concurred so you now need to give your reasons. Your continued evasion to put it concisely in ONE post doesn't impress me or I think  most others in this forum.
As for there being 9 reds in column3 ( and9 Blacks in Column 2 ) THAT is a GIVEN and so is "Information " but information from the past .We still need to interpret it to form a system / method to actually USE it.
I look forward to your treatise on how I have misinterpreted the meaning of the Birthday Problem. Like most other members in the forum I am open to being "educated " .I have rejected your previous attempts and given my reasons. Either you detail your objections or accept that it IS a matter of perception.

the red figures in column 3 are 3/9/12/18/21/27/30/36. I count 8 numbers and not 9. The probability of every pattern is the number of the figures multiplyed by 2.7. The very simple answer is 21.6%.

the red figures in column 3 are 3/9/12/18/21/27/30/36. I count 8 numbers and not 9. The probability of every pattern is the number of the figures multiplyed by 2.7. The very simple answer is 21.6%.
You are right dobbel . I was too busy concentrating on his argument to miss that . He is right , though, if you make ASSUMPTIONS the odds do change correspondingly . I accept this but dispute his assertion that this is a GIVEN . IF ONLY !

@ dobbelsteen, you are right of course, don't know how I counted 9 instead of 8.
scepticus,
What you need to do is give your rebuttal of why you think that my view is wrong regarding the sequence of 8 bets. Failure to do so allows me to say that you are full of bluff and bluster .
And I am allowed to say that, given all the arguments I've presented, plus the empirical evidence, that you are incapable of understanding why your view is wrong.
Regarding conditional probability,
In probability theory (https://en.wikipedia.org/wiki/Probability_theory), a conditional probability measures the probability (https://en.wikipedia.org/wiki/Probability) of an event (https://en.wikipedia.org/wiki/Event_%28probability_theory%29) given that (by assumption, presumption, assertion or evidence) another event has occurred
So it may not be assumption, it could be a fact. If I tell you that the 3rd column has hit, but I don't say which NUMBER has hit, then knowing that there are 8 reds in the column will let you calculate the probability that red has hit. The fact that this doesn't help you with a system is neither here nor there. If you make an assumption then of course you are on shakier ground, but it doesn't invalidate the logic, it just means it's a hypothetical proposition.
On the other hand, you HAVE drawn an illogical conclusion regarding your birthday problem/system. It doesn't matter how long the sequence is, the probability of at least one repeat in the sequence is one probability, the probability of the last spin in the sequence resulting in a repeat GIVEN THAT there have been no repeats so far is quite another. This is a conditional probability, and you KNOW that there have been no repeats so far in the sequence (it's not an assumption), but you fallaciously assume that the probabilities are the same.
According to you, it follows that the longer the sequence, the higher the probability that the final spin will result in a repeat, given that there have been no repeats up to and including the previous spin. Just wait for a long enough sequence without a repeat, and you are almost sure to win. This is pure gambler's fallacy.
Real is correct. Some people will just never get it.

I don't see any point in continuing the discussion. Everything has been said that could be said. It's actually been very useful in highlighting exactly how the gambler's fallacy arises. Most gamblers and roulette players don't have even a superficial grasp of probability, they just think that everything is "uncertain", and that this entitles them to make up their own rules in a subjective way and that these approaches are as valid as any other "view".

Mike, the reason I ask you to put your argument in ONE post is to allow others to consider them without reference to Umpteen other posts with their individual points . So, why don’t you make it easier for others to follow your argument ?
Regarding Conditional Probability . As I pointed out before you have selected the view of wikipedia in preference to other sources which disagree with that view and you even disparage Yale .
Taking Given to mean either a fact OR an assumption can lead to confusion .Taking” Given “to mean an event that has passed and an “Assumption” to mean a guess gives better clarity of thought.
Yes, mike I am arguing that the seventh bet is only one of a “series of 8 “ with an overall 53% chance of success. and Yes, Mike, I am saying that the seventh bet is valid GIVEN that the prior 6 have not shown a repeat. And Yes Mike I do argue that the longer there is no repeat then the greater the chance that it will happen . My idea , though, only encompasses an 8 spin sequence so doesn’t go beyond 8 . Get it ?
I have made it clear that this idea is based on the Birthday Problem .If that is wrong then so am I.
Good luck with proving the Birthday Problem wrong !

scetpicus has presented a strategy for playing roulette in which a player has a positive expected gain per spin in contrary to the popular belief that in the long run the House always has the edge. It is, however, to be noted that one may have to play a large number of spins in order to realize an overall gain.
GREAT scepticus.
I take 40 units (enough for 20 bets ) to a table and leave when I PROFIT  or have a small loss when recovering from a loss of half my stake. I find that I don't have long runs so move from table to table . Hit and Run . For example, on my last visit my results were
(https://forum.roulette30.com/data:image/png;base64,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)(https://forum.roulette30.com/data:image/png;base64,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)8 Tables
spins bets won lost
11 1 14
17 2 10
20 4 2
15 4 2
13 1 14
10 2 10
16 4 2
31 15 6
So 48 chips won
Spins are more than bets because of  ahem  triggers . I am not inclined to give up winnings and , having won at previous tables was losing more than half my stake before recovering to a 6 point loss and decided to stop.I am not inclined to give up all my profits. 48 points profit is acceptable to me.
Am I being selective ? Yes, I am . Sometimes I win less than this  sometimes more occasionally I lose all my 40 units.
What players here want to know is " Will it win for me ? " I do not know  no one knows . ALL I claim is that it wins for me more than I lose.Unlike the AP in this forum I don't claim to know what I don't know.The future is another country . And Gambling is Gambling is Gambling and there is always RISK in gambling.
btw. copy and paste of small spreadsheet did not paste and figures posted
did not align properly. Sorry about that.

scetpicus has presented a strategy for playing roulette in which a player has a positive expected gain per spin contrary to the popular belief that in the long run the House always has the edge. It is, however, to be noted that one may have to play a large number of spins in order to realize an overall gain.
GREAT scepticus.
I think this need paraphrasing. Here's my version, which is more accurate.
scetpicus has presented a strategy for playing roulette in which a player has a negative expected gain per spin in agreement with the popular belief that in the long run the House always has the edge. It is, however, to be noted that one may have to play a small number of spins in order to realize an overall gain.
NOT GREAT scepticus.

scetpicus has presented a strategy for playing roulette in which a player has a positive expected gain per spin contrary to the popular belief that in the long run the House always has the edge. It is, however, to be noted that one may have to play a large number of spins in order to realize an overall gain.
GREAT scepticus.
I think this need paraphrasing. Here's my version, which is more accurate.
scetpicus has presented a strategy for playing roulette in which a player has a negative expected gain per spin in agreement with the popular belief that in the long run the House always has the edge. It is, however, to be noted that one may have to play a small number of spins in order to realize an overall gain.
NOT GREAT scepticus.
Hi Mike,
Sorry I must contradict you here. The HE certainly works on each spin and cannot be ignored, BUT as I showed above a well constructed strategy can temporarily overide the HE with weight of money or a better hit rate. The math answer to this is that the HE will "in the long run" snatch back the advantage. I have no arguement with this ! Which is why I preach short progressions, and that the progressive attack should be spread over several MULTISPIN BETS. EVERY PROGRESSION,THAT IS LONGER THAN 2 OR 3 SPINS, SHOULD HAVE BUILT IN ABORTION POINTS, WHICH ALLOW THE PUNTER TO ABANDON THOSE PROGRESSIONS THAT HE FEELS ARE GOING BAD.
I admit this requires SKILL, EXPERIENCE and a degree of INTUITION that is outside the abilities of most players. That'is where those past numbers come in. Reseach and practice, practice, practice.
Pasteur said " Luck favours the prepared mind." Gary Player the famous South African golfer replide to someone who accused him of being LUCKY. " IT'S A STRANGE THING. THE MORE I PRACTICE THE LUCKIER I GET !"
Regards,
Harry

Harry,
I don't think there's much point in me arguing with you when you're talking in generalities. I disagree with everything you say but in this case I was referring to scepticus' particular system which I have PROVEN does not work, much less has the win rate he claims.
The fact that he has wilfully ignored my proof shows that he is only interested in his agenda, not the truth. There's also no point in arguing with someone like that.
If you care to post the specific details of your system, I will show you that IT doesn't work either.

SIGH !
Mike
Until you prove that the Birthday Problem scenario is wrong you HAVE NOT proven my derivation wrong.
Your common sense deserted you when you claimed to " prove " that the last of seven spins had less chance than the previous six which had ZERO chance of success at that point .
Your naivety about betting roulette is shown when you clearly don't understand that the "stats" I gave do not refer to the 8 number sequence. So far as I am aware I gave no win rate for the 8 number sequence.

Harry,
I don't think there's much point in me arguing with you when you're talking in generalities. I disagree with everything you say but in this case I was referring to scepticus' particular system which I have PROVEN does not work, much less has the win rate he claims.
The fact that he has wilfully ignored my proof shows that he is only interested in his agenda, not the truth. There's also no point in arguing with someone like that.
If you care to post the specific details of your system, I will show you that IT doesn't work either.
Mike,
I have posted 3 systems on the Johnson progression The flaw thread. By all means trash them if you can.
Harry

SIGH !
Mike
Until you prove that the Birthday Problem scenario is wrong you HAVE NOT proven my derivation wrong.
scepticus,
I've proved in multiple ways that your system doesn't work. The one I have in mind is the file I uploaded showing that betting using the trigger of 7 nonrepeats results in a winning percentage of 18.9%, which is 7/37. It was the one you dismissed when Reyth confirmed it over millions of spins because you said it was just one sample, and that the result could be completely different in another sample, thus undermining the very concept of probability, and so would render the birthday problem itself meaningless.

Mike
You and I look at this differently even though we agree that the Birthday Problem can be applied to roulette.
All I am saying is if in ANY 8 of 37 there is a 53% chance of 2 being the same then ANY 2 of that 8 can be that 2. Logic dictates that if there are no repeats in the first 7 then the 8th MUST have a better chance than the prior 6 because THEY have zero chance. Your view that it has LESS chance than the others defies common sense.
Basically, this has nothing to do with roulette but is maths APPLIED to roulette.
You misunderstand my point about Reyths' ( or anyone else's ) million. Tell me Mike  How many variations are there in one million spins of the wheel ? Gazillions ! and yet Reyth's is only ONE of those gazillions and I am expected to accept that one from gazillions is an acceptable sample ?Perhaps when Reyth has given me trillions of samples I may accept that he has a point.
Probability Theory is just that Mike  a theory.Perhaps the best " guess " we have but still speculation however you dress it up. As it's very name implies it does not deal in certainties  only likliehoods .
Get over it Mike.

All I am saying is if in ANY 8 of 37 there is a 53% chance of 2 being the same then ANY 2 of that 8 can be that 2. Logic dictates that if there are no repeats in the first 7 then the 8th MUST have a better chance than the prior 6 because THEY have zero chance. Your view that it has LESS chance than the others defies common sense.
Basically, this has nothing to do with roulette but is maths APPLIED to roulette.
NO. As I have repeatedly told you, as successive spins arise you have to recalculate the chance of at least one repeat for the remaining spins. The 53% applies to 8 spins and 8 spins ONLY.
You misunderstand my point about Reyths' ( or anyone else's ) million. Tell me Mike  How many variations are there in one million spins of the wheel ? Gazillions ! and yet Reyth's is only ONE of those gazillions and I am expected to accept that one from gazillions is an acceptable sample ?Perhaps when Reyth has given me trillions of samples I may accept that he has a point.
scepticus,
Your innumeracy is truly mindboggling. The number of variations is completely irrelevant. Yes, there are a huge number of possible SEQUENCES (meaning the ORDER of the outcomes) in even 100 spins, but so what? It's the PROPORTION of wins versus losses, black versus red, or whatever that is relevant.
What I said still stands. If you needed that many spins to establish a stable probability then probability theory as we know it would be next to useless. Casinos wouldn't be able to operate, much less make a reliable profit.
Not only that, but your objection is a clear case of double standards. You have claimed that you have a system which has won for you more often than not (so much so that you even said the casino might change the rules if it got out LOL). Now how many times have you used it? I'm guessing the number of placed bets is not more than a few 1000. You are happy to claim that the system is probably a winner on this basis, yet a simulation which shows that your birthday system does NOT work over MILLIONS of spins is dismissed by you on the grounds that the sample is too small!
Looks like a case of heads you win, tails I lose. LOL.
Probability Theory is just that Mike  a theory.Perhaps the best " guess " we have but still speculation however you dress it up. As it's very name implies it does not deal in certainties  only likliehoods .
Get over it Mike.
This is a common misconception. The word "theory" does not mean what it means in common usage in a scientific context.
In modern science (https://en.wikipedia.org/wiki/Science), the term "theory" refers to scientific theories (https://en.wikipedia.org/wiki/Scientific_theory), a wellconfirmed type of explanation of nature (https://en.wikipedia.org/wiki/Nature), made in a way consistent (https://en.wikipedia.org/wiki/Consistency) with scientific method (https://en.wikipedia.org/wiki/Scientific_method), and fulfilling the criteria (https://en.wikipedia.org/wiki/Scientific_theory#Characteristics_of_theories) required by modern science (https://en.wikipedia.org/wiki/Modern_science). Such theories are described in such a way that any scientist in the field is in a position to understand and either provide empirical support ("verify (https://en.wikipedia.org/wiki/Proof_%28truth%29)") or empirically contradict ("falsify (https://en.wikipedia.org/wiki/Falsifiability)") it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge,
https://www.youtube.com/watch?v=d80Lf76Ht18 (https://www.youtube.com/watch?v=d80Lf76Ht18)

Well then , substitute Hypothesis for Theory .The answer is still the same.
What I said was that the method I use won more than it lost. IN REAL TIME  not in the airy  fairy Infinite time you claim .
And there ARE gazillions of possibilities in a million spins of the wheel so ONE or even a MILLION millions is still insufficient to be classed as an acceptable sample. You are too stuck up in hypothesis to come into the real world. Mathematicians can only claim that we are LIKELY to lose in INFINITE time. It is utter nonsense to even imagine that any human being will live until infinity. I repeat  anyone who claims that we MUST lose is overstating his or her case.
AS for any 8 number series. Are you really saying that someone who bets from bet one without encountering a repeat has a BETTER chance than someone who has come late to the party and bets only the 8th ? If the maths is that over the 8 spins the chance of ANY 2 being the same ha a 53 % chance of being successful then that applies to all 8 .look again at the Wiz's calculations  they tell a completely different story to yours.
look again at the Birthday Problem. Strange as it may appear,in a sequence of 22 there is less tha a 50% chance of a repeat while a 23 sequence has a 53% chance so , obviously, the more numbers that appear the better the chance of a repeat .Apply this to roulette and there is a need for 8 rather than 7 = as the WIZ's chart shows . Your chart shows that there is LESS chance as the spins progress which defies comm0n sense. And you claim that MY innumeracy is truly mind boggling ! Extend that 8 spin sequence to a 10 spin sequence and there is an INCREDIBLE 95% chance of a repeat. ! Isn't THAT mind boggling ?
Probability Theory IS useless if it needs an INFINITE number of spins which is why mathematicians need to use a " cutoff point" which can only be an assumption which is beyond your comprehension since you don't know the difference between an" Assumption " and a "Given " .
If there is a 53 % chance of ANY 8 showing a repeat then there it is HIGHLY LIKELY that there will be a profit after a millions spins ASSUMING that a million spins is a sufficient sample. And I have made it clear that I do NOT bet the 8 number bet . I am too impatient to wait for a 7 series to appear.
The Birthday Problem conclusion IS hard to accept . but if it is true then so is my 8th bet as it too, sets a parameter.
The Best of Luck in living to infinity !

Well then , substitute Hypothesis for Theory .The answer is still the same.
No it isn't. Did you actually read the quote or watch the vid?
What I said was that the method I use won more than it lost. IN REAL TIME  not in the airy  fairy Infinite time you claim .
Now you're putting words into my mouth. Where did I ever say that the you need an infinite number of spins? You don't. This is just mathematician speak for "the long run". Rather than put a specific number on the "long run" which might be misleading, they use the mathematical abstraction of infinity. In fact, empirical results show that the theoretical probabilities are approximated quite quickly, in a matter of 100's or 1000's of spins.
If you don't believe me, learn how to code and find out for yourself. Reyth has just started a thread on programming in BASIC.
AS for any 8 number series. Are you really saying that someone who bets from bet one without encountering a repeat has a BETTER chance than someone who has come late to the party and bets only the 8th ? If the maths is that over the 8 spins the chance of ANY 2 being the same ha a 53 % chance of being successful then that applies to all 8 .look again at the Wiz's calculations  they tell a completely different story to yours.
No they don't. It's just that you haven't understood.
look again at the Birthday Problem. Strange as it may appear,in a sequence of 22 there is less tha a 50% chance of a repeat while a 23 sequence has a 53% chance so , obviously, the more numbers that appear the better the chance of a repeat .
Yes, that's exactly what I was saying a few post ago.
Your chart shows that there is LESS chance as the spins progress which defies comm0n sense. And you claim that MY innumeracy is truly mind boggling !
Yes, because once spins have spun, they no longer contribute to the original sequence. You are still stuck in the gambler's fallacy and seem incapable of grasping it. Too bad.
Extend that 8 spin sequence to a 10 spin sequence and there is an INCREDIBLE 95% chance of a repeat. ! Isn't THAT mind boggling ?
It would be if you had a 95% chance of a win when betting on 9 numbers, but you don't. The chance is 9/37.
Probability Theory IS useless if it needs an INFINITE number of spins
I agree, but it doesn't. Again, see for yourself by writing your own programs.
If there is a 53 % chance of ANY 8 showing a repeat then there it is HIGHLY LIKELY that there will be a profit after a millions spins ASSUMING that a million spins is a sufficient sample.
No it isn't. It's highly UNLIKELY that there will be a profit after only a few hundred bets. Having reached the point of no return, the hole will only get deeper as you place more bets.
Learn to code and try it for yourself. It's pointless me doing it for you because you'll just ignore it or come back with some absurd objection.

Mike
1 ) We agreed that it was valid to transfer the Birthday Problem to Roulette.
2 ) We don't agree on the probabilities increasing after each non repeat.You think they decrease while I think they increase. ( The Wiz agrees with me here )( as does Yale on " Given )
We are never going to agree on this Mike so I am going no further.Like Real said on another thread I'll leave it up to the members to decide.