A presentation of On Hats and Other Covers

A team of n players enters a game room, and each player is fitted with a hat, which is either red or green. A player can see the other players’ hat colors, but hot his own. Each player is then asked to make a declarations, which must be one of the statements “my hat is red,” “my hat is green,” or “I pass.” All the players must declare simultaneously, and no communication is allowed between them during the game. they are permitted, however to hold a strategy coordination meeting before the game starts. The team wins if at least one player declares his hat color correctly and no player declares an incorrect color . . . the goal of the team is to devise a strategy that maximizes the winning probability.