Solving Abalone on Small Boards

TL;DR

This paper presents the strong and weak solutions of simplified Abalone variants on small hexagonal boards, providing insights into game strategies and computational approaches for high-branching-factor games.

Contribution

It is the first to strongly solve a 2x2x2 Abalone variant and weakly solve a 2x2x3 variant, advancing understanding of game-solving techniques for complex board games.

Findings

Strong solution for 2x2x2 Abalone variant

Weak solution for 2x2x3 Abalone variant

Insights into solving high-branching-factor games

Abstract

Abalone is a 2-player board game with perfect information. The game is played on a 5x5x5 hexagonal grid and ends when a player pushes 6 of their opponents' pieces off the board. Abalone is similar to games like chess and Go in that all three games have high branching factors, making it difficult for a computer to determine the outcome of a game. However, solving smaller, simplified versions of Abalone can offer insight into how to play the full-size game optimally. In this paper, we strongly solve a variation of Abalone played on a 2x2x2 hexagonal board. We also weakly solve an Abalone variation on a 2x2x3 hexagonal board.