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Posted by NickMcG on 23/9/2009, 2:15 am, in reply to "Re: Yes. You got it!!"
Ah! Gameboomers. I must go back there. Haven't visited for months. Seems to have disappeared off "My favorites" list.
Here is another interesting little part to this one.
Suppose there is a third player, Charlie.
To win, Alice, Bob and Charlie need to find the car, the key and the goat respectively.
If Charlie opens door 2 first. If it's the goat, they win, if its a car he switches to door 1, if it's a key he switches to door 3. You will find that if you run through all six permutaions that Charlie is succesful on the same 4 permutaions as Bob and Alice. i.e. the team probability of winning is still 2/3. Pretty amazing.
The reason this works has to do with Permutation Cycle lengths and requires absolutely no deductive reasoning on the part of the players (other than coming up with the prearranged strategy).
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