Generalized four person hat game

Abstract

This paper studies Ebert's hat problem with four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning strategies We use the new concept of an adequate set. The construction of adequate sets is independent of underlying probabilities and we can use this fact in the analysis of our general case.Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:2211.09819, arXiv:1612.00276, arXiv:1704.0424