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Gambler’s Fallacy and the Regression to the Mean

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Re: Gambler’s Fallacy and the Regression to the Mean

#11

Post by jldugger »

roenxi wrote: post #4
jldugger wrote: post #3

Earlier quoted context omitted.

> Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration Are they actually equally likely though? Perhaps there comes a point where one must consider if observed outcomes match with assumed probabilities. Or are you just having arguments about whether the unfavored outcome is 'overdue.'

Funnily enough, I might have been thinking of the exact opposite of the Gambler's fallacy. My mistake, sorry. But it still seems related to me and I'll explain what I was thinking anyway: For reference: https://www.omnicalculator.com/statistics/coin-flip-probabil... There is a 20% chance that in 7 coin flips there will be >5 heads. By symmetry, 40% chance that there are >=5 heads or >=5 tails. If you look at a series…

well, i'd frame that conversation in terms of confidence intervals. with only 7 trials you are not very confident a>b.

Re: Gambler’s Fallacy and the Regression to the Mean

#12

Post by contravariant »

roenxi wrote: post #2

It is very annoying in business. Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration. It takes a certain level of courage, charisma and stubbornness to argue that there is no evidence that 2nd best is just as good as best when there is a measurable difference between two options. This is a big contributor to why markets perform so well in my…

> This is a big contributor to why markets perform so well in my humble opinion. People who see past the gambler's fallacy to the actual odds of things working get rewarded, and the people who assume the current leader must be doing something different and better than the competition get punished.

The problem with markets is that rewarding the people who can predict the market correctly isn't a particularly useful end result. What you wanted to happen is for the people who are best able to predict the market to determine the 'fair' price, but that's usually only guaranteed as a steady state which fails as soon as a market is even remotely volatile.

Re: Gambler’s Fallacy and the Regression to the Mean

#13

Post by HWR_14 »

mikenew wrote: post #6

So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…

> you change your choice your odds of winning go up from 1/3 to 2/3 which to me makes intuitive sense

Well, my guess is that's because you've fixed your intuitions either by prior exposure to the problem or education. Certainly I think it's intuitive - now. The point is most people's intuitions think it changes from 1/3 to 1/2, regardless of whether you switch or not.

But hey, maybe Bayesian inference is intuitive to you without any math education.

Meanwhile, when this was published in 1990 and thousands of people (10% with PhDs) wrote into the magazine that it was an error. So some people have a very strong contrary intuition.

Re: Gambler’s Fallacy and the Regression to the Mean

#14

Post by gerdesj »

mikenew wrote: post #6

So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…

"which to me makes intuitive sense"

Your intuition is either very good or complete bollocks, or at least worryingly odd 8)

Monty Hall is a really clever problem and worth studying in some depth. Whenever I've encountered it, the rules are always given without ambiguity. Even so, it is very hard to get to the bottom of the probabilities. You can reason your way through it and possibly get to the right answer, unaided. In which case you are far brighter than the followers of a maths column that introduced this problem back in the day. Ah, let's get to the canonical source of knowledge: https://en.wikipedia.org/wiki/Monty_Hall_problem (para 1)

Years (>30) ago I ran a sort of Monte Carlo simulation on this thing. It took a while to encode the rules in GWBASIC and luckily I had a copy of Peitgen's (both Beauty and Science of Fractals) and I was able to get roughly or reasonably random numbers to do the simulation by following his algorithm for generating them! After a while of running on my 286 I got a result. Then I spent a few hours fixing bugs. It took a few more iterations until I got an answer that looked right or at least was between 0 and 1 and didn't end up in syntax error 8)

Dr Ian Stewart gives a great description of the problem in one of his books too.

Re: Gambler’s Fallacy and the Regression to the Mean

#15

Post by HWR_14 »

roenxi wrote: post #4
jldugger wrote: post #3

Earlier quoted context omitted.

> Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration Are they actually equally likely though? Perhaps there comes a point where one must consider if observed outcomes match with assumed probabilities. Or are you just having arguments about whether the unfavored outcome is 'overdue.'

Funnily enough, I might have been thinking of the exact opposite of the Gambler's fallacy. My mistake, sorry. But it still seems related to me and I'll explain what I was thinking anyway: For reference: https://www.omnicalculator.com/statistics/coin-flip-probabil... There is a 20% chance that in 7 coin flips there will be >5 heads. By symmetry, 40% chance that there are >=5 heads or >=5 tails. If you look at a series…

I found you text very confusing, and then figured out your typo.

> There is a 20% chance that in 7 coin flips there will be >5 heads. By symmetry, 40% chance that there are >=5 heads or >=5 tails.

Your first example should say >=5 heads. (Also, your site says almost 23%, making it just over 45% for either via symmetry)

Re: Gambler’s Fallacy and the Regression to the Mean

#16

Post by [deleted] »

mikenew wrote: post #6

So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…

[deleted]

Re: Gambler’s Fallacy and the Regression to the Mean

#18

Post by gexla »

> Yet the illusion of streaks or certain outcomes being “due” is powerful, and such thinking is almost ubiquitous among gamblers. It derives from our tendency toward pattern recognition (apophenia), seeing illusory patterns in random noise.

And yet, pattern recognition is also what you would draw on to see that this is an illusion? Maybe you just need to know the way the game works rather than guessing?

Then continues droning on about patterns.

No mention of volatility or what "regression to the mean" actually looks like (the casino's house edge.)

I get the sense the person who wrote this never gambles. For a much better explanation, find writing from poker players. Also excellent on this subject is Nassim Taleb.

I recommend everyone put up some tuition (losses at the table) to learn poker at a low stakes table. The game will teach you a ton about life.

Re: Gambler’s Fallacy and the Regression to the Mean

#19

Post by bryanlarsen »

chx wrote: post #5

> “I know that the fact that the roulette wheel has come up red 10 times in a row tells me NOTHING about spin #11. On the other hand, I know that over time, there will be just as many black spins as red spins, so at least intuitively, a black spin seems at least a little more likely to come up next in order to push that ratio back towards 50/50. Are these two principles actually in tension with each other? If not, ho…

On the gripping hand, coming up red 10 times in a row is evidence that the odds of red and black aren't even.

Re: Gambler’s Fallacy and the Regression to the Mean

#20

Post by zeroxfe »

mikenew wrote: post #6

So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…

Wow... okay, I'm pretty sure you don't actually understand the Monty Hall problem.
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