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We generalize Ebert's Hat Problem for three persons and three colors. Allplayers guess simultaneously the color of their own hat observing only the hatcolors of the other players. It is also allowed for each player to pass: nocolor is guessed. The team wins if at least one player guesses his or her hatcolor correct and none of the players has an incorrect guess. This paperstudies Ebert's hat problem, where the probabilities of the colors may bedifferent (asymmetric case). Our goal is to maximize the probability of winningthe game and to describe winning strategies. In this paper we use the notion ofan adequate set. The construction of adequate sets is independent of underlyingprobabilities and we can use this fact in the analysis of the asymmetric case.Another point of interest is the fact that computational complexity usingadequate sets is much less than using standard methods.

Ebert's asymmetric three person three color Hat Game