Weak Ordering Space Search in Turn-based War Chess Gaming

Turn-Based War Chess Game (TBW) is the most important part of turn-based strategy game, and the research on its AI is hard but has a great significant impact not only on video games but also on applied mathematics. This paper is aimed at eliminating order independent redundancy plans in Nan’s enumeration methods. First, we propose the Weak Order Correlation theory, whose necessary and sufficient condition are deduced theoretical. Then, using this theory and its conditions, we design the non-redundant enumeration algorithm in weak order space. Consequently, the completeness and efficiency (zero redundancy of the plans) of the new algorithm are guaranteed.