Asymmetric Hat Game with three players and three colors

TL;DR

This paper extends the analysis of the Hat Game to asymmetric probabilities with three players and colors, providing exact winning probabilities and optimal strategies for all cases.

Contribution

It offers the first comprehensive solution for asymmetric probabilities in the three-player, three-color Hat Game, filling a key gap in existing research.

Findings

Derived winning probabilities for all asymmetric cases.

Identified optimal strategies for each probability configuration.

Extended understanding beyond the symmetric case.

Abstract

Winning probabilities of The Hat Game (Ebert's Hat Problem) with three players and three colors are only known in the symmetric case: all probabilities of the colors are equal. This paper solves the asymmetric case: probabilities may be different. We find winning probabilies and optimal strategies in all cases.