Author Topic: The Gambler's Fallacy  (Read 1869 times)

Bayes

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The Gambler's Fallacy
« on: May 15, 2016, 09:48:18 AM »
I know it's been done to death, but it's kind of obligatory.

http://www.roulettician.com/articles/article3.html

Feel free to comment or disagree with anything you think is misleading or just wrong.  :)
« Last Edit: May 15, 2016, 02:20:58 PM by Bayes »


 
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Reyth

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Re: The Gambler's Fallacy
« Reply #1 on: May 15, 2016, 07:36:45 PM »
Don't have time right now to do charts and statistical examples (I have done so many times elsewhere) but there is more to the statistical picture than just numbers of blacks and reds and there IS a statistical force (or "rubber band" as you say) that governs wheel outcomes.

It is evidenced by the objective successive diminishing of streaks (this applies to streaks of reds and black) and the minimum appearances of groups of numbers (this applies to ratios of outcomes).

Since the occurrences of both these phenomena can be proven to tend toward certain limits (practically speaking), its not a fallacy to apply them to roulette play BUT to argue that an event that has a 1 in 1Q chance of occurring is as statistically relevant as an event that has a 1 in 37 chance is the true fallacy. 

Of course we know that every spin of the wheel in and of itself has a 1 in 37 chance of producing a particular number and it would be wrong to deny it but its just as wrong to deny the significance of successive diminishing streaks and the minimum appearances of groups of numbers WHICH ARE JUST AS VALIDLY TRUE.  It is fallacious not to acknowledge both together.

To restate this as Harry J has so eloquently done:

The odds of producing a single number is in a single spin is 1/37 which is NOT THE SAME as the odds of producing that number after 400 consecutive spins where the number has not hit [(1/37)*(1/37)*...out to 400...(1/37)].  The same principle applies to minimum occurrences of groups of numbers where the number of spins is weighed against the number of occurrences and a practical minimum can be expected (65 of an EC in 200 spins is a commonly understood, if not exactly precise, example).

A STREAK OF 1/37 REPEATED SUCCESSIVELY IS STATISTICALLY RELEVANT BECAUSE EACH SUCCESSIVE ELEMENT OCCURS LESS AND LESS OFTEN UNTIL I SIMPLY CANNOT DEMONSTRATE ANY ADDITIONAL OCCURRENCES -- I SIMPLY DON'T HAVE THE TIME NOR CPU RESOURCES.

To ignore statistical relevancy is to live in a world of fantasy and is the true fallacy.  To somehow claim objectivity while ignoring statistical relevancy and use this argument to discourage progress in a field of endeavor is intellectually criminal; at the very least, the veracity of the motives driving such actions are suspect.
« Last Edit: May 15, 2016, 08:22:55 PM by Reyth »
 
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scepticus

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Re: The Gambler's Fallacy
« Reply #2 on: May 15, 2016, 08:35:10 PM »
and.. if  choosing one number  has a 1 in 37 chance of winning in each and every spin  why is it that  the chance of choosing the winning  number  in each of  two spins has a  only a 1 in 1369 chance ? Doesn’t more than one spin change the odds of  a sequence as opposed to one spin  ?

and.. just how does an “ infinite expectation” become classed  as a “ certainty” ? The “ infinite expectation” is a big problem for anyone who wants to use maths to decide what to do in the real world - as opposed to  indulging in hypotheses !
 
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Reyth

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Re: The Gambler's Fallacy
« Reply #3 on: May 15, 2016, 08:49:24 PM »
The “ infinite expectation” is a big problem for anyone who wants to use maths to decide what to do in the real world!

LOL.

Just go back to bed, its too dangerous to get up, the roof will cave in...eventually!
« Last Edit: May 15, 2016, 08:51:36 PM by Reyth »
 

Bayes

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Re: The Gambler's Fallacy
« Reply #4 on: May 15, 2016, 09:33:15 PM »
@ scep,

Quote
and.. if  choosing one number  has a 1 in 37 chance of winning in each and every spin  why is it that  the chance of choosing the winning  number  in each of  two spins has a  only a 1 in 1369 chance ? Doesn’t more than one spin change the odds of  a sequence as opposed to one spin  ?

If the chance of 2 chosen numbers is 1 in 1369 it shows that the spins are independent.

Quote
and.. just how does an “ infinite expectation” become classed  as a “ certainty” ? The “ infinite expectation” is a big problem for anyone who wants to use maths to decide what to do in the real world - as opposed to  indulging in hypotheses !

"infinite expectation" is just mathematician speak. I've shown in the Long Run article that outcomes converge well before infinity.

@ Reyth,

Must confess I'm not sure how to interpret your post. I'm not denying that successive streaks diminish, only that you can't say that given a streak has just happened, the chance of the next outcome has changed because of it. The only way you can say that and not be contradicting yourself is to say that the wheel isn't fair.
 

scepticus

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Re: The Gambler's Fallacy
« Reply #5 on: May 15, 2016, 10:03:51 PM »
" If the chance of 2 chosen numbers is 1 in 1369 it shows that the spins are independent.”
The point I was making, Bayes, is that each and every spin has a 1in 37 chance .Method players don’t rely on 1 chance but 1 win in a chosen sequence. .The chance of one number winning in each and
every spin is still 1 in 37. The 1 in 1369 assumes the bettor  wins on both spins.

"infinite expectation" is just mathematician speak. I've shown in the Long Run article that outcomes converge well before infinity.

Exactly my point, It is just mathematicians’ speak - irrelevant in the real world. All it means is that the bettor is at a disadvantage on each and every spin and so is unlikely to win over an extended period.
Outcomes may converge  before infinity but the question  facing gamblers  is “  Can we make use of this information ?”   Frankly, I doubt it.
 

Ringmaster

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Re: The Gambler's Fallacy
« Reply #6 on: May 15, 2016, 10:32:44 PM »
Talk is cheap, argument, well, constructive or desstructive, depending on your POV, but the one unifying factor is that we all are learning navigation techniques to apply to roulette.
My biggest breakthrough, that provided me with major and most consistent wins, came after I learnt how to generate truly random targets, during play, so data shmarta, testing smesting, just show me the money! -R.
 
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Reyth

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Re: The Gambler's Fallacy
« Reply #7 on: May 15, 2016, 11:38:35 PM »
Must confess I'm not sure how to interpret your post. I'm not denying that successive streaks diminish, only that you can't say that given a streak has just happened, the chance of the next outcome has changed because of it.

Ok, its really simple.  The odds of 4 repeats of a single number is 1 in 1.87M, right?  I mean you agree here, obviously, its undeniable. 

So (regardless of payout) are you trying to say that if I bet the other 36 numbers from the first spin that I don't have a 1 in 1.87M chance of losing on the 4th spin after 3 repeats in a row?  Which is it?

I don't need to change anything.  I just need to accept the objective facts the way they actually are; ALL OF THEM.

Quote
The only way you can say that and not be contradicting yourself is to say that the wheel isn't fair.

There is no contradiction in my mind at all.  The odds of an individual spin remain at 1/37 AND streaks produced by those odds diminish and minimum occurrences of groups of numbers will consistently tend towards a practical target.

On a separate note, its not that the wheel isn't fair its that variance can be quite extensive at times and preparing for and dealing with that is simply put, very difficult.
« Last Edit: May 15, 2016, 11:45:05 PM by Reyth »
 

Sheridan44

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Re: The Gambler's Fallacy
« Reply #8 on: May 16, 2016, 01:33:55 AM »
Equilibrium is theoretical, reality is its shadow effect.
 

Ringmaster

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Re: The Gambler's Fallacy
« Reply #9 on: May 16, 2016, 02:22:12 AM »
Without equilibrium, the Earth would not orbit the Sun, Gravity would not balance the Vacuum of Space, Centrifugal Force would not exist, and Roulette would be quite difficult to play, and that's Reality!!!
 
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scepticus

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Re: The Gambler's Fallacy
« Reply #10 on: May 16, 2016, 02:34:40 AM »
Without equilibrium, the Earth would not orbit the Sun, Gravity would not balance the Vacuum of Space, Centrifugal Force would not exist, and Roulette would be quite difficult to play, and that's Reality!!!

Depends on what you mean by equilibrium Ringmaster.
What do YOU mean by equilibrium ?
 

Bayes

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Re: The Gambler's Fallacy
« Reply #11 on: May 16, 2016, 08:13:30 AM »

So (regardless of payout) are you trying to say that if I bet the other 36 numbers from the first spin that I don't have a 1 in 1.87M chance of losing on the 4th spin after 3 repeats in a row? 

That's exactly what I'm saying. Where did the odds of 1 in 1.87M come from? Answer: from multiplying the separate probabilities of each single hit which is 1/37.

1.87 x 106 = 1 / (1/37)4

Quote
There is no contradiction in my mind at all.  The odds of an individual spin remain at 1/37 AND streaks produced by those odds diminish and minimum occurrences of groups of numbers will consistently tend towards a practical target.

Yes, there's no contradiction in that. But if I understand you correctly you're taking an extra leap and concluding that after a streak the chance of the next single outcome has increased. That would mean that outcomes aren't independent.
« Last Edit: May 16, 2016, 08:38:00 AM by Bayes »
 

Reyth

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Re: The Gambler's Fallacy
« Reply #12 on: May 16, 2016, 09:52:38 AM »

Quote from: Reyth
I bet the other 36 numbers from the first spin...

Like Dobble has said, serious gamblers don't speak about and bet on individual spins but groups of spins.  I have not denied the chances of a single spin and am very clear on the fact that it is 1/37 which means each spin is independent AND affected by the force of equal distribution -- BOTH apply to each spin.

Its not a contradiction, it is just reality which I have no need to deny.
« Last Edit: May 16, 2016, 12:42:28 PM by Reyth »
 

kav

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Re: The Gambler's Fallacy
« Reply #13 on: May 27, 2016, 08:02:59 PM »
Hello Bayes,

I like very much your way of writing. You offer much needed knowledge to the roulette players. I believe that your site marries roulette with math and statistics in the best possible way. Congrats.

Now in your very well written article I spotted a small mistake. In the past we have discussed again about this and you agreed to my position. You write:

The belief that the difference between reds and blacks gets closer to zero as you get more spins is completely wrong. In fact, the reverse is true: as the number of spins increase, the difference between the numbers of reds and blacks tends to increase.

This not exactly true. As much as it is possible that the difference (in absolute numbers) increase, it is possible that the difference (in absolute numbers) decrease. Otherwise we are not talking about a fair wheel. We could just bet on the trend and win.

I understand that you want to make the distinction between ratios and proportion on one side and difference and absolute numbers on the other side. And I agree on this. But I believe you were carried away in order to explain the difference.

Now on the real issue of gambler's fallacy.
I can not and have never explained my position in full detail. I may do so in due time. For now please allow me to just throw some fancy terms without much explanation. The roulette wheel is definitely an ergodic system. This means that according to Poincaré recurrence theorem : after a sufficiently long but finite time, it will return to a state very close to the initial state.
In simple terms this means that what goes up must go down.
Anyway I just want to point to the concept of ergodicity and not actually debate gambler's fallacy here. (The Concept of Probability in Statistical Physics )
« Last Edit: May 28, 2016, 08:39:34 AM by kav »
 
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Jesper

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Re: The Gambler's Fallacy
« Reply #14 on: May 28, 2016, 12:10:32 AM »
We can easy see the number of streaks of four reds are half of the numbers of three. So after three it is still about 50% it will continue to four or change.  So 12 reds in a row will not indicate next spins odds will change.

In a very large number of spins the proportion equals, I just not know how to really make use of it. The only time I think I do it is when I suppose a number is unlikely to be absent more than 600 times. Which can be used on a penny table with a good spreed.

I have done trials setting the autospins on 1000 spins and run it for a lot of times. As  long I do not lose much or win I have done it for days, and I have seen the colors or other EC will not be forced to even out in numbers. Red can be dominant for 100000 spins, and even if the proposition decrease, it is still dominant in numbers. I do not know how long it will take for the other chance to be sure catching up, as I never did a so long run I have seen it every time. In practice it will only work on a NoZero as the opposite  and zero will  be dominant nearly sure after much less number of spins than 100000. I have seen numbers being hot for days.

As in a long run it is zillions of combinations, we see a run of 1000 spins once in our life, it would be an very rare situation if any gambler saw an exactly same raw of 1000 numbers twice. Just think about the chessboard problem, we are talking figures here.
 
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