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URL:  https://boards.fool.com/iand-i-dont-care-what-the-math-says-i-think-30398371.aspx

Subject:  Re: 5 Statistics Problems To Change Your View Date:  11/25/2012  3:02 PM
Author:  jpasc Number:  409548 of 567774

[i]And I don't care what the math says, I think it's 50-50 for Monte Hall. How does the door know if this is "the same game" or a new one with only two doors to chose from? Monte may know, but he's not doing the choosing. Door=roulette wheel. No institutional memory. Every spin is independent of whatever came before. [/i]

The answer is definitely 2/3 to switch. The problem is with the article in that it left out what I think is the most important piece of information when describing the Monty Hall problem:

The position of the prize does not change after the empty door is revealed.

Once you make a choice, the prize is either behind the door you choose (1/3 chance) or one of the doors you didn't choose (2/3 chance). One of the doors you didn't choose now gets opened revealing nothing, but if the prize stays behind the same door then the chance you picked the door with the prize the first time is still only 1/3 and the chance that you didn't pick door with the prize (one of which is now open) is still 2/3, so you should switch to the unopened door that you did not pick the first time.

If the prize got randomly assigned again once the wrong door was revealed then the odds would change to 1/2-1/2. If it stays in the same place, the original probabilities of 1/3-2/3 remain.
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