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I thought this question was put to rest 15 years ago by Marilyn Vos Savant -- google "Marilyn Vos Savant 3 door problem", or look at
http://barryispuzzled.com/zmonty.htm
What WAS interesting is that several professors of mathematics at leading universities disagreed with her, and publicly stated so (after politely being advised not to), the pissing contest was raised to a level where Marilyn posted their letters WITH names and affiliation. MIT finally stepped in and confirmed Marilyns calculations.
SheetWise
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It stuns me that people doubted her. Years ago when I first ran into this problem I didn't want to believe that switching was optimal. Simulations weren't good enough, because I wanted to understand why it worked.
I made a little diagram of the possible outcomes, and it became obvious in minutes what the truth was.
This coming from a guy who almost failed his senior math class in high school. This statement is misleading, because the only reason I got poor marks was because I didn't turn in any homework, but it makes my point seem cooler so I'm leaving it in.
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I remember when the Marilyn Vos Savant column came out - I used to read them back in school. I wasn't convinced of the answer at first, especially after seeing so many conflicting replies. So I wrote a simple computer program to simulate it - and I didn't even need to run it to understand. Just in writing the program, it became clear that there were 3 possible cases (prize behind door a,b, or c) and that in 2 of the cases, you need to switch to win the prize. I was then befuddled as to why math PhDs were writing in to argue the point.
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Yeah, that's what happened to me. As I was writing the program, I realized that to check if the switch was correct, I only had to write pickedDoor != prizeDoor