Author Topic: Regression toward the mean  (Read 8725 times)

Sputnik

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Regression toward the mean
« on: November 07, 2014, 10:53:49 AM »
 
Quote
So waiting for triggers, and all the rest of it, makes no difference to mathematical probabilities pertaining to various patterns etc.

Quoted from Wikipedia:

"Regression toward the mean simply says that, following an extreme random event, the next random event is likely to be less extreme. In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and variant law of averages). Similarly, the law of large numbers states that in the long term, the average will tend towards the expected value, but makes no statement about individual trials. For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10, while the law of large numbers states that in the long term, this event will likely average out, and the average fraction of heads will tend to 1/2. By contrast, the gambler's fallacy incorrectly assumes that the coin is now "due" for a run of tails, to balance out."

« Last Edit: November 07, 2014, 12:18:38 PM by Sputnik »


 

kav

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Re: Regression toward the mean
« Reply #1 on: November 07, 2014, 01:12:46 PM »
Hi guys,

Nice topic!
Let me look like a fool, but I have a (logical) objection, especially considering Wikipedia's quote about regression towards the mean.
To me this seems like saying that at the end we will arrive at a city that is west but we may probably achieve that by going east.
Random walks are not 100% random if we know the final (long run) destination.
Yes, I know all about gambler's fallacy. But just think about the example above outside ready-made buzzwords.
It is indeed possible to arrive at a city that is located west of you by going east, but in total you must walk more miles to the west than you walked east.

Further "heretic" reading:
The big Lie
A dialog between Math professor vs Gambler
« Last Edit: November 07, 2014, 05:26:20 PM by kav »
 

Sputnik

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Re: Regression toward the mean
« Reply #2 on: November 07, 2014, 03:36:02 PM »

 Well it is simple to see the truth about that statment.
 I am pretty sure Mike could code it.

We all know that the trails is independeant (a 50/50 siutution) and all patterns has the same probability.
This means that you can pick any 10 random outcomes and compare them with 10 future outcomes.
Then using the benchmark O for "oppisite" and S for "same" and observe the results.

Simple as that.
 

Mike

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Re: Regression toward the mean
« Reply #3 on: November 07, 2014, 04:30:48 PM »
Sputnik,

Regression to mean is a true phenomenon, no doubt, but I think it can easily be misinterpreted. What it does not say is that you can get an advantage by waiting for an extreme event and then betting for it to regress. As you point out, it would be easy enough to put this to the test (coding it) by using some extreme events as your trigger to bet, then seeing whether the next x spins yielded any better result than simply betting in a random manner. I assume that's what  you meant?

@ Kav,

Interesting dialogue between R.D. Ellison and Prof. Snell. Thanks.
 

kav

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Re: Regression toward the mean
« Reply #4 on: November 07, 2014, 05:47:29 PM »
Thanks Mike,

A couple years ago, I requested anyone to test this claim:
If in 50 consecutive spins an Even Cance appeared only 12 times or less, in the next 50 spins that Even Chance will dominate more often than not.
Then Bayes had programmed this little tool I attach for testing the regression.
Please note that the tool uses a RNG and not actual spins. I'm not sure if the import real spin data feature works.
Please use it and share your finding.

Quote
The numbers are adjusted by the sliders. The trigger value is what the program looks for (number of wins) in the first sample. So in the screenshot the number of wins is 12 in the last 50 spins (1st sample). The program then starts from the first spin in the sequence of 250,000 spins and advances by 1 spin at a time checking each 50 spin sequence for 12 wins OR LESS. When it finds such a sequence, it jumps to the next sequence of spins the length of which is given by the number you input for the 2nd sample (again, 50 in the screenshot).

When you've entered these 3 numbers, hit GO! and WAIT.  ;)

After a few minutes, the list will fill with numbers. The numbers on the left are the trigger values (so they will be the trigger value or LESS), and the numbers in the right column are how many WINS you got betting the entire 2nd sample sequence. So if for example this number is 28 (and the 2nd sample value was 50), it means you would have made 3 units profits when betting the spins which followed the sample which contained the underrepresented side.
 

Sputnik

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Re: Regression toward the mean
« Reply #5 on: November 07, 2014, 08:53:15 PM »
IMPORTANT NOTE AND DETAIL

Do you know how regression towards the mean look like (correction) ?

Lets say we have 10 reds and regard that as rare and extreme event.
A window of 10 trails.

Then after that we will compare the next 10 trails to observe if there is any regression present.
Let say i get 3 more reds and 1 black.
Then that is not regression towards the mean or correction.

This only mean that the reds stop growing stronger, there is no correction present.
From this moment you can get more reds and then there is no regression.

You need at least two blacks to say you got a tiny event of regression towards the mean.
A indication that the reds oppisite effect become true.

Same with STD.
If i get a window with 16 events hitting 3.0 STD - for example 14 singles contra 2 series.
(There is as many singles as there is series).

Then regression towards the mean can look and come in different ways.
Lets take it from the beginning.

If i have 14 singles and 2 series and have 3.0 STD as benchmark (regarding as rare and extreme window of events).
Then if i get two series, then the STD of 3.0 stop growing and indicate a small draw-down, but i dont have regression twoards the mean until i have three series in a row.
(same as 10 reds and 1 black and you need two before you can start talking about correction)
You need a fictive win before you know the correction are present.

Then is also another state that we have to ask if it is part of correction, regression towards the mean.
If we get one serie and one single alternating after 3.0 STD, then the window of events hovering around the bell curves top at 3.0 without getting weaker or stronger and stay at that level (zero point).
I regard this state as part of regression towards the mean or as pure correction.
(same with 10 reds and then black and red alternating).

So we have to look at tiny waves or regression and medium wave of regression and large waves of regression.

How do you capture regression towards the mean (tendency)

If you start to play after a rare event stop growing, then you are chasing for events and play with  the same style as using any kind of selection.
If you are going to play to catch regression towards the mean, you might only play when regression towards the mean is present, has happen.
This mean that all tiny indications should be triggers and that means you have a tendency towards regression towards the mean, correction.

The march or algorhtim to attack after tendency of regressio toward the mean.

Lets say i have a small indication of tendency or regression.
If i lose my first bet, then what?
Do i start over for a new tendeny or do i attack before that with other indictation as correction alredy has been present.

That is the question.

For example if i want to catch larger series.
Then lets say a serie of three is a indication of tendency towards regression.
I lose, then i might want to attack next time when series of two shows to catch tiny, medium, larger waves of regression.
« Last Edit: November 07, 2014, 09:11:44 PM by Sputnik »
 

kav

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Re: Regression toward the mean
« Reply #6 on: November 07, 2014, 10:08:58 PM »
Nice post.

IMO the simple answer would be to keep your attack and even make it stronger as the deviation increases.
My suggestion would be something like Oscar's Grind . From the "well known systems" this one, in my opinion, is the best in taking advantage of a regression movement.
 

Real

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Re: Regression toward the mean
« Reply #7 on: November 09, 2014, 04:08:08 AM »
Wow, there are so many things wrong within this thread that I don't know just where to begin.

 

kav

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Re: Regression toward the mean
« Reply #8 on: November 09, 2014, 08:21:23 AM »
Wow, there are so many things wrong within this thread that I don't know just where to begin.

Hi Real,
Yes, they probably are. I'm sure that if you believe that roulette can not be beaten with any other way except with visual ballistics or some sort of "Advantage Play" we all look like fools to you, trying to approach something that isn't even there. Like someone who doesn't believe in UFOs in a UFO forum. Still, I think there are many ways you could offer knowledge and be constructive to the discussions, without repeating endlessly your (possibly correct) views about the house edge and gambler's fallacy etc.
I'm certainly open to your contributions. Not just open, more than that, I urge you to share your knowledge and experience. Not your disbelief. I'm sure we all can learn a thing or two from you.
 

Mike

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Re: Regression toward the mean
« Reply #9 on: November 09, 2014, 09:16:34 AM »
Regression to the mean does not somehow mean that spins are not independent under some circumstances, so if you have observed an extreme event it does not make it any more likely that the next event will be less extreme. That is, there is no cause and effect operating. The next event, regardless of what has happened previously is unlikely to be extreme only because all extreme events are relatively unlikely, by definition, and that is the only thing that regression to the mean says.

So it is a fallacy, just as much as the gambler's fallacy, to use some extreme event as a trigger, believing that the following event will be less extreme than the first. No computer simulation is necessary to show that using a trigger in this way won't work. Ten reds in the next 10 spins is no more or less likely given that in the previous ten spins there were also ten reds, or ten blacks, or anything in between.

If you look for extreme events in a larger number of spins, say 100 or 200, these will occur as frequently as the normal or binomial distribution says they will, again regardless of what has gone before. So in 100 spins you will get between 45 and 55 reds in 68% of sessions, between 40 and 60 reds in 95% , and between 35 and 65 reds in 99.7%.
« Last Edit: November 09, 2014, 09:24:15 AM by Mike »
 

Mike

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Re: Regression toward the mean
« Reply #10 on: November 09, 2014, 09:42:15 AM »
If you're going to look at past results and learn something from them, it is more logical to bet with the flow, rather than against it. I'm not saying that this will somehow give you a  winning system, but if there is some bias in the way that outcomes are being generated, it will be reflected in the outcomes, naturally. Of course, this makes much more sense when considering the inside bets and sectors of the wheel, rather than the outside bets..
 

kav

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Re: Regression toward the mean
« Reply #11 on: November 09, 2014, 10:29:34 AM »
Mike,
I understand what you wrote. And it is "mathematically correct" (as in "politically correct"). However one wonders, what DOES regression to the mean means. If nothing changes after a strong deviation, if it is business as usual, I don't see the need for a new term. Why take something normal and call it "regression to the mean"?
Believe me I know well the "official explanation". That regression to the mean is a phenomenon, that results from sample increase and not from result differentiation.
However, think again my simplistic geometric example above. Think visually.  There's more to it than... nothing. With a roulette spins sample we are taking a direction. With the following samples (spins) we walk further. If we vaguely know the destination we will end up to, we can make some guesses about the road.

A very rough sketch to help you understand my way of thinking:


There's another physics theory that IMO supports my approach: The Ergodic Hypothesis
A stochastic process is said to be ergodic if its statistical properties (such as its mean and variance) can be deduced from a single, sufficiently long sample (realization) of the process. The reasoning behind this is that any sample from the process must represent the average statistical properties of the entire process, so that regardless what sample you choose, it represents the whole process, and not just that section of the process. A process that changes erratically at an inconsistent rate is not said to be ergodic. Roulette is an ergodic system.
More on this on a future article on www.roulette30.com
« Last Edit: November 09, 2014, 10:36:26 AM by kav »
 

Real

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Re: Regression toward the mean
« Reply #12 on: November 09, 2014, 11:48:26 PM »
"If a number has appeared 2131 times less than chance would have dictated after 100,000 spins, then it is on target to be still 2131 short of expectation after 1,000,000 spins, or any other huge number of future spins. Fate doesn't dictate that it will regress to the norm in terms of absolute count, only in percentage terms. eg, in your example, instead of appearing 1/38th of the time, or 2.631578947368421%, it instead came out 500/100,000 = 0.5%: It's 2.131578947368421% short, which is way out.But if after 1,000,000 spins it is still 2131 appearances short, then it will have appeared (1,000,000/38 - 2131) = 24184 times: It will have appeared 2.418478947368421% of the time. At 2.418478947368421% It will be closer to the expected 2.63158% and so can be said to be regressing to the mean.Now lets say we spin 1,000,000,000,000 times starting out 2131 appearances short and ending at 2131 short. It would then have appeared (1,000,000,000,000/38 -2131) times = 26315787342 times or 2.6315787342% : It has pretty much regressed almost exactly to the expected appearance frequency, but it is still numerically just as far away.Purely and simply, regressing to the mean does not mean any short term variation gets cancelled out, only that it becomes statistically insignificant in percentage terms.Oh, and just to be controversial 400/infinity = 0 EXACTLY. Not close to, but exactly: That's the nature of infinity." -Wizardofvegas forum

In the end, regression toward the mean appears to happen because the sum of all spins yet to happen dwarf the number of spins that you have collected.

What is described early in the thread is simply part of the gambler's fallacy.

-Real
« Last Edit: November 10, 2014, 11:57:12 AM by kav »
 

Mike

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Re: Regression toward the mean
« Reply #13 on: November 10, 2014, 08:11:15 AM »
"Purely and simply, regressing to the mean does not mean any short term variation gets cancelled out, only that it becomes statistically insignificant in percentage terms.


No, that's not correct. Regression to the mean does not mean that - he's talking about the law of large numbers here; that the ratio will approach the mean as you take more samples. Regression to the mean says that if an extreme event occurs, the next event will not be so extreme, it doesn't lump together the two events and say that the combined event will be closer to the mean than the first, although that is a consequence.

If the first event is 10 reds in 50 spins, and the next 50 spins produces 20 reds, then the ratio of reds is 0.2 in the first event and 0.3 for the combined events (20 + 10)/(50 + 50), but it is 0.4 for the 2nd event taken alone.
 

kav

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Re: Regression toward the mean
« Reply #14 on: November 10, 2014, 12:03:37 PM »
Hi Real,

If you read my post carefully you will see that I know very well all the arguments. I wrote:
Quote
That regression to the mean is a phenomenon, that results from sample increase and not from result differentiation.

Believe me if I disagree with your or anyone's interpretation, at least it is not due to ignorance.

Furthermore Mike makes a very good point about the (subtle?) difference between the "law of large numbers" and "regression to the mean".