Turn-Based War Chess Model and Its Search Algorithm per Turn

Abstract

War chess gaming has so far received insufficient attention but is a significant component of turn-based strategy games (TBS) and is studied in this paper. First, a common game model is proposed through various existing war chess types. Based on the model, we propose a theory frame involving combinational optimization on the one hand and game tree search on the other hand. We also discuss a key problem, namely, that the number of the branching factors of each turn in the game tree is huge. Then, we propose two algorithms for searching in one turn to solve the problem: (1) enumeration by order; (2) enumeration by recursion. The main difference between these two is the permutation method used: the former uses the dictionary sequence method, while the latter uses the recursive permutation method. Finally, we prove that both of these algorithms are optimal, and we analyze the difference between their efficiencies. An important factor is the total time taken for the unit to expand until it achieves its reachable position. The factor, which is the total number of expansions that each unit makes in its reachable position, is set. The conclusion proposed is in terms of this factor: Enumeration by recursion is better than enumeration by order in all situations.