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URL:  https://boards.fool.com/the-game-just-changed-it-is-now-a-new-game-2-30398134.aspx

Subject:  Re: 5 Statistics Problems To Change Your View Date:  11/25/2012  11:33 AM
Author:  AdvocatusDiaboli Number:  409517 of 567566

The game just changed. It is now a new game, 2 doors, pick one, the odds are 50/50. Change, don't change...it does not change the odds. The only way this is not true is if Monty Hall knows which is the right door and you can game his psychology in which door he shows you. Otherwise, you are in a new game, 2 doors, equal odds.

You're wrong.
It's NOT a new game.
Think of it this way:
You initially pick A. The chance that the car is behind A is 1/3. The chance that it is behind B or C is 2/3.
So if you could pick BOTH B and C instead of A, would you do it? Of course.
And that is, essentially, what you do if you switch after being shown that B or C don't have the prize.
Because we knew already that one of them didn't have the prize, but that collectively they have a 2/3 chance.
Looking from the beginning of the bet, if you switch, you will get the prize in case EITHER B or C had it.



I think you're right about the stones, though. It's a bad example for Simpson's paradox. A really bad one.
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