Generalized Three and Four Person Hat Game

TL;DR

This paper analyzes generalized multi-player hat games with varying probabilities, introducing a probability-independent method to construct winning strategies that maximize success chances.

Contribution

It develops a probability-independent approach using adequate sets to find optimal strategies for three and four-player hat games with unequal color probabilities.

Findings

Constructed winning strategies for 3 and 4 players with different color probabilities.

Demonstrated that adequate sets are independent of underlying probabilities.

Provided a framework for analyzing similar multi-player, multi-color hat problems.

Abstract

This paper studies Ebert's hat problem for three and 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 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.