We generalize Ebert's Hat Problem for three persons and three colors. All players guess simultaneously the color of their own hat observing only the hat colors of the other players. It is also allowed for each player to pass: no color is guessed. The team wins if at least one player guesses his or her hat color correct and none of the players has an incorrect guess. This paper studies Ebert's hat problem, where the probabilities of the colors may be different (asymmetric case). Our goal is to maximize the probability of winning the game and to describe winning strategies. In this paper we use the notion of an adequate set. The construction of adequate sets is independent of underlying probabilities and we can use this fact in the analysis of the asymmetric case. Another point of interest is the fact that computational complexity using adequate sets is much less than using standard methods.

翻译：我们将艾伯特帽子问题推广到三人三色的情形。所有玩家同时根据观察到的其他玩家帽子颜色来猜测自己帽子的颜色，同时允许每位玩家选择“放弃”（不进行猜测）。团队获胜的条件是至少有一名玩家正确猜中自己帽子的颜色，且没有任何玩家猜错。本文研究艾伯特帽子问题，其中各颜色概率可能不同（非对称情形）。我们的目标是最大化游戏获胜概率并描述获胜策略。本文引入了“充分集”的概念，充分集的构造独立于底层概率分布，这一特性可用于分析非对称情形。另一个值得关注的点是，使用充分集的计算复杂度远低于标准方法。