Three Hats

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.
The same game can be played with any number of players. The general problem
is to find a strategy for the group that maximizes its chances of winning
the prize.
One obvious strategy for the players, for instance, would be for one player
to always guess "red" while the other players pass. This would give the
group a 50 percent chance of winning the prize. Can the group do better?
Submitted  4/15/2001 10:02:38 PM
Hint   Answer