Weak Ordering Space Search in Turnbased War Chess Gaming TurnBased War Chess Game (TBW) is the most important part of turnbased 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 Nanxe2x80x99s 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 nonredundant enumeration algorithm in weak order space. Consequently, the completeness and efficiency (zero redundancy of the plans) of the new algorithm are guaranteed.

Using Combinatorial Solutions and Atomic Weights to Play Competitive AI Clobber. Clobber is a twoplayer abstractstrategy game with no element of random chance. Introduced by game theorists Michael H. Albert, J. P. Grossman and Richard Nowakowski in 2001, it has subsequently been extensively studied for its combinatorial properties. Since 2005, it has been a major event in the Computer Olympiad.Although the concept of endgame tables has been introduced for Clobber and a use case suggested, usage of such has been scant in the Computer Olympiad or in the further development of other areas of Combinatorial Game Theory. We remedy this gap in this paper and demonstrate how to implement and use combinatorial solutions and atomic weights in an endgame table to perfect the play of Clobber by AI.We find that with the proper leveraging of endgame tables, it is possible to play perfectly on many Clobber positions of up to 70 pieces (on a 10x10 opening position) within time limits of most tournaments, and the solutions of Clobber on some significantly sized boards are likely reachable in the near future.