This article describes the current state of computer Chinese chess (Xiang Qi). For two reasons, Chinese-chess programming is important in the field of Artificial Intelligence. First, Chinese chess is one of the most popular and oldest board games worldwide; currently the strength of a Chinesechess program can be compared to that of human players. Second, the complexity of Chinese chess is between that of chess and Go. We assume that after DEEP BLUE's victory over Kasparov in 1997, Chinese chess will be the next popular chess-like board game at which a program will defeat a human top player. In the article we introduce some techniques for developing Chinese-chess programs. In the Computer Olympiads of 2001 and 2002, the programs ELP and SHIGA were the top Chinese-chess programs. Although these two programs roughly have the same strength, they were developed following completely different techniques, as described in the article. The improvements of the best Chinese-chess programs over the last twenty years suggest that a human top player will be defeated before 2010. 1. Chinese chess is a two-player, zero-sum game with complete information. Chinese-chess expert knowledge started to be developed some 800 years ago. Nowadays, the world has many excellent human players. Yet, already now, the strength of the best Chinese-chess programs can be compared to that of human players notwithstanding the fact that the game is considered rather complex. Table 1 shows the state-space complexity and the game-tree complexity of chess, Chinese chess, Shogi, and Go. The state-space complexity of Western chess and Chinese chess was estimated by Allis (1994). The game-tree complexity of Chinese chess is based on a branching factor of 38 and an average game length of 95 plies (Hsu, 1990). The complexity of two other games has been estimated: by Bouzy and Cazenave (2001) for Go and by Iida, Sakuta, and Rollason (2002) for Shogi. The complexity of Chinese chess is between that of Western chess and Shogi. Game State-space complexity Game-tree complexity Chess 50 123 Chinese chess 48 150 Shogi 71 226 Go 160 400 Table 1: State-space complexity and game-tree complexity given by the power of 10.
Chinese Dark Chess, a nondeterministic two-player game, has not been studied thoroughly. State-of-the-art programs focus on using search algorithms to explore the probability behavior of flipping unrevealed pieces in the opening and the midgame phases. There has been comparatively little research on opening books and endgame databases, especially endgames with nondeterministic flips. In this paper, we propose an equivalence relation that classifies the complex piece relations between the material combinations of each player, and derive a partition for all such material combinations. The technique can be applied to endgame database compression to reduce the number of endgames that need to be constructed. As a result, the computation time and the size of endgame databases can be reduced substantially. Furthermore, understanding the piece relations facilitates the development of a well-designed evaluation function and enhances the search efficiency. In Chinese Dark Chess, the number of nontrivial material combinations comprised of only revealed pieces is 8 497 176, and the number that contain at least one unrevealed piece is 239 980 775 397. Under the proposed method, the compression rates of the above material combinations reach 28.93% and 42.52%, respectively; if the method is applied to endgames comprised of three to eight pieces, the compression rates reach 5.82% and 5.98%, respectively.
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