Three players enter a room and a red or blue hat is placed on each person's head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players' hats but not his own.

No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical $3 million prize if at least one player guesses correctly and no players guess incorrectly. What strategy should they use to maximize their chances of success?

(From - http://www.princeton.edu/~sjmiller/riddles/riddles.html)

(In reply to Probability by TomM)

the chances of fliping a coin 4 times and all 4 times being heads is 1/16. so if i flip a coin 3 times and each time comes up heads, the fourth flip has a 1/16 probobility of being heads right? NOPE! its still 1/2, so the optimal chance of winning is 50/50 not 25/75 as stated in the solution :)

Posted by James on 2002-12-15 15:05:03