Asymmetric Five Person Hat Game

TL;DR

This paper investigates an asymmetric version of the five-player Ebert's Hat Problem with unequal color probabilities, deriving optimal strategies and maximum winning probabilities using adequate sets.

Contribution

It introduces a novel approach employing adequate sets to solve the asymmetric five-player hat game, improving understanding of optimal strategies under unequal probabilities.

Findings

Maximal winning probabilities are explicitly calculated.

Optimal strategies are characterized using adequate sets.

The approach extends previous symmetric cases to asymmetry.

Abstract

This paper studies asymmetric Ebert's Hat Problem with five players where the probability of the colors may be unequal. We obtain maximal winning probabilities and optimal winning strategies using the concept of adequate sets.