AlphaZero for a Non-Deterministic Game

The AlphaZero algorithm, developed by DeepMind, achieved superhuman levels of play in the games of chess, shogi, and Go, by learning without domain-specific knowledge except game rules. This paper investigates whether the algorithm can also learn theoretical values and optimal plays for non-deterministic games. Since the theoretical values of such games are expected win rates, not a simple win, loss, or draw, it is worthy investigating the ability of the AlphaZero algorithm to approximate expected win rates of positions. This paper also studies how the algorithm is influenced by a set of hyper-parameters. The tested non-deterministic game is a reduced and solved version of Chinese dark chess (CDC), called 2×4 CDC. The experiments show that the AlphaZero algorithm converges nearly to the theoretical values and the optimal plays in many of the settings of the hyper-parameters. To our knowledge, this is the first research paper that applies the AlphaZero algorithm to non-deterministic games.