The Levine hat game asks $n$ players, each with an infinite random stack of black or white hats on their head, to predict the location of a black hat on their own head seeing only the hats on everyone else's heads. They are allowed a strategy session before the game, but no further communication. The players win if and only if all predictions are correct. In addition to giving an overview of the game, we discuss the $n = 2$ case in considerable detail (including a conjecture for an optimal strategy) and prove that the optimal success probability, $V_n$, in the $n$-player game is a strictly decreasing function of $n$.

翻译：列文帽游戏要求玩家花一美元,每个玩家头上都有无限的黑帽子或白帽子,以预测自己头上的黑帽子位置,只看到别人头上的帽子。 他们可以在比赛之前有一个策略会议, 但没有进一步的交流。 玩家赢了, 如果而且只有所有的预测都是正确的。 除了对游戏进行概述外, 我们非常详细地讨论美元=2美元的案子( 包括最佳策略的猜测), 并证明美元玩家游戏中最优的成功概率( $V_n美元) 严格地说来是美元越来越少的功能 。