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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

#31

Post by LesZedCB »

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…

best explanation i've heard is the game has 100 doors.

you choose 1 of 100 possible doors. the host then opens 98 doors, all with nothing behind them. at that point it's much easier to see that you chances improve greatly by switching.

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

#32

Post by almostdeadguy »

gerdesj wrote: post #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…

"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.…

The Monty Hall problem absolutely becomes more obvious when the host's behavior is explicitly documented. And as this article points out, many key aspects of the host's behavior are implausible, which is a large part of what makes it counter-intuitive: https://ima.org.uk/4552/dont-switch-mathematicians-answer-mo...

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

#33

Post by rout39574 »

coldtea wrote: post #30

> That’s a great question, and the answer is a definite no – they are not in conflict. Again, the pressure to think that the past influences future independent events is powerful. Regression to the mean is not a power in the universe that ensures that statistics work out in the end, it is purely a probability. I find TFA's argument about the gambler fallacy not being associated with regression to the mean quite hand…

But "streaks" are irrelevant. Reversion to the mean doesn't tell you things across trials, it tells you things about individual trials.

Try this on: What is the "mean" red-black on the roulette wheel? There isn't one.

The only way you can reasonably expect the past streak to have an impact on the next spin, is if you've concluded the streaks are sufficiently unlikely to cause you to judge the wheel not to be fair.

If it's random, then you have no recourse but to post-hoc description. There is -no- predictive weight.

... And editing your comment to refer to groups of throws is disingenuous. It would have been more honest to modify your case in a reply.

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

#34

Post by thom »

bryanlarsen wrote: post #19
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.

Always happy to see this Motie idiom still in use!

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

#35

Post by almostdeadguy »

yata69420 wrote: post #27
mikenew wrote: post #22

Earlier quoted context omitted.

Maybe I'm just misunderstanding something then? I'm not trying to be dismissive or act like I think I have some special intuition here. It really does just seem straightforward. Imagine the problem this way: The host of a game show presents you with 100 doors, behind one of which is a prize. You pick one, and you know that your odds of having chosen the correct door are 1 in 100. The host, who knows where the prize i…

I'm with you. Usually when it comes up in pop culture, it's not mentioned that the host can't open a door with a prize. That's the only reason it's confusing.

And that they can't open the door chosen by the contestant! Also perhaps more subtly, that Monty picks at random when given the option. The original problem prompt is _highly_ underspecified (and makes assumptions that are counter-intuitive to how a game show host might behave).

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

#36

Post by jodrellblank »

mhb wrote: post #29
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…

Your intuition is wrong and it doesn't matter what the host knows before showing you the door that doesn't have the prize. Here's some explanation: https://betterexplained.com/articles/understanding-the-monty...

How can they reliably show you the door that doesn't have the prize, if they don't know where the prize is? They can't, which means the host must know, which means it must matter what the host knows?

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

#37

Post by bhelkey »

mhb wrote: post #29
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…

Your intuition is wrong and it doesn't matter what the host knows before showing you the door that doesn't have the prize. Here's some explanation: https://betterexplained.com/articles/understanding-the-monty...

> Your intuition is wrong and it doesn't matter what the host knows before showing you the door that doesn't have the prize.

This is not correct and your source doesn't support your point

From your link:

> Monty helps us by “filtering” the bad choices on the other side

Monty knows which door holds the car and which holds the goat

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

#38

Post by bhelkey »

zeroxfe wrote: post #20
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.

> I'm pretty sure you don't actually understand the Monty Hall problem

What did you disagree with? Their understanding of the problem seems pretty solid to me.

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

#39

Post by mhb »

jodrellblank wrote: post #36
mhb wrote: post #29

Earlier quoted context omitted.

Your intuition is wrong and it doesn't matter what the host knows before showing you the door that doesn't have the prize. Here's some explanation: https://betterexplained.com/articles/understanding-the-monty...

How can they reliably show you the door that doesn't have the prize, if they don't know where the prize is? They can't, which means the host must know, which means it must matter what the host knows?

He's not reliably showing it. You're being presented with a situation in which the door shown doesn't have the prize.

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

#40

Post by mhb »

jodrellblank wrote: post #36
mhb wrote: post #29

Earlier quoted context omitted.

Your intuition is wrong and it doesn't matter what the host knows before showing you the door that doesn't have the prize. Here's some explanation: https://betterexplained.com/articles/understanding-the-monty...

How can they reliably show you the door that doesn't have the prize, if they don't know where the prize is? They can't, which means the host must know, which means it must matter what the host knows?

An illuminating example uses a deck of cards. You're trying to get the ace of spades. You pick a card. I don't know anything but I turn over 50 of the 51 remaining cards and they're not the ace of spades. Do you want to switch your pick to the alternative unknown card?
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