Quixo Is Solved

TL;DR

This paper presents the first complete analysis of the game Quixo, demonstrating it is a draw with optimized algorithms and data structures, and explores smaller variants and interesting game states.

Contribution

It introduces novel techniques and efficient algorithms to solve Quixo, a previously unanalyzed game, establishing its outcome as a draw.

Findings

Quixo is a draw game on a 5x5 board

Efficient algorithms enable solving within reasonable resources

Analysis of smaller boards reveals interesting states

Abstract

Quixo is a two-player game played on a 5$\times$5 grid where the players try to align five identical symbols. Specifics of the game require the usage of novel techniques. Using a combination of value iteration and backward induction, we propose the first complete analysis of the game. We describe memory-efficient data structures and algorithmic optimizations that make the game solvable within reasonable time and space constraints. Our main conclusion is that Quixo is a Draw game. The paper also contains the analysis of smaller boards and presents some interesting states extracted from our computations.