Solving 8×8 Domineering

Abstract

So far the game of Domineering has mainly been investigated by combinatorial-games researchers. Yet, it is a genuine two-player zero-sum game with perfect information, of which the general formulation is a topic of AI research. In that domain, many techniques have been developed for two-person games, especially for chess. In this article we show that one such technique, i.e., transposition tables, is fit for solving standard Domineering (i.e., on an 8×8 board). The game turns out to be a win for the player first to move. This result coincides with a result obtained independently by Morita Kazuro. Moreover, the technique of transposition tables is also applied to differently sized $\text{m×n}$ boards, $\text{m}$ ranging from 2 to 8, and $\text{n}$ from $\text{m}$ to 9. The results are given in tabular form. Finally, some conclusions on replacement schemes are drawn. In an appendix an analysis of four tournament games is provided.