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