Solving Breakthrough for the 6 × 6 Board

Abstract

Breakthrough is a well-known abstract board game played regularly at the Computer Games Olympiad. Despite the straightforward gameplay mechanics of the game, determining optimal play strategies poses significant challenges. We have (weakly) solved a variant of the game played on the $6\times 6$ board, representing the largest board instance of the game solved to date. The game is a win for the first player. We apply a hybrid approach of computing endgame tablebases, defining game-specific race patterns, using a family of parallelizable proof-number-based solvers, and training a neural-network-based heuristic job scheduler to construct a solution tree and proof of the game’s game-theoretic value. This approach allowed us to not only solve the $6\times 6$ game variant, but also lays the foundation for solving the game’s larger board-size variants.