A Brief Review of Fixed Points, Hex Game and Hex Theorem

TL;DR

This paper reviews the mathematical foundations of Hex, focusing on fixed point theorems and the Hex Theorem, to explain why a tie is impossible in the game.

Contribution

It provides a concise overview of the equivalence between fixed point theorems and the Hex Theorem, clarifying their role in game theory.

Findings

Hex cannot end in a tie due to topological constraints

Fixed point theorems underpin the Hex Theorem

The equivalence explains the game's inherent properties

Abstract

Understanding the Impossibility of a Tie in Hex via Fixed Point Theorems, the Hex Theorem, and Their Equivalence.