Bo-Nian Chen

Chinese Dark Chess

Chinese dark chess is a popular and easy-to-learn game in Asia. The characteristic of possible revealing of unknown pieces makes it different from Chinese chess or Western chess. Players with luck may win a game by chance. Thus, there is a probabilistic behavior that a player has to consider. Computer Chinese dark chess problems can be divided into three phases: 1) the opening game, 2) the middle game, and 3) the endgame. Revealing pieces reasonably and effectively is the main issue in the opening game. In the middle game, the choice of revealing pieces or moving pieces becomes the critical issue. Designing a good evaluation function is also important both in the middle game and endgame. In an advantageous endgame, how to capture all opponent’s pieces to win the game is also a hard problem. Search-based methods, such as αβ pruning, are only suitable in the positions where revealing actions do not influence the results. However, according to our experiments, programs that reveal pieces reasonably and effectively have better playing strength. In this paper, we introduce the game Chinese dark chess and give some research topics about this game. We also discuss some strategies for considering the revealing actions in this paper.

Equivalence Classes in Chinese Dark Chess Endgames

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.

Aggregating consistent endgame knowledge in Chinese Chess

We often incorporate endgame heuristics as part of the evaluation function for Chinese Chess programs. In order to aggregate endgame knowledge effectively, we propose a Chinese Chess endgame knowledge-based system to construct a large set of consistent endgame heuristics, called endgame knowledge base, which is used in our program, Contemplation. The knowledge-based system consists of the acquisition module, the inference module, the inquiry module and the verification module. This system implements our graph model that has the functionality of maintaining consistency and improving its correctness. The experimental results on self-play test show that the playing strength of Contemplation has a distinct enhancement with this knowledge base.

Conflict resolution of chinese chess endgame knowledge base

Endgame heuristics are often incorperated as part of the evaluation function used in Chinese Chess programs. In our program, Contemplation, we have proposed an automatic strategy to construct a large set of endgame heuristics. In this paper, we propose a conflict resolution strategy to eliminate the conflicts among the constructed heuristic databases, which is called endgame knowledge base. In our experiment, the correctness of the obtained constructed endgame knowledge base is sufficiently high for practical usage.

Knowledge Inferencing on Chinese Chess Endgames

Several Chinese chess programs exhibit grandmaster playing skills in the opening and middle game. However, in the endgame phase, the programs only apply ordinal search algorithms; hence, they usually cannot exchange pieces correctly. Some researchers use retrograde algorithms to solve endgames with a limited number of attack pieces, but this approach is often not practical in a real tournament. In a grandmaster game, the players typically perform a sequence of material exchanges between the middle game and the endgame, so computer programs can be useful. However, there are about 185 million possible combinations of material in Chinese chess, and many hard endgames are inconclusive even to human masters. To resolve this problem, we propose a novel strategy that applies a knowledge-inferencing algorithm on a sufficiently small database to determine whether endgames with a certain combination of material are advantageous to a player. Our experimental results show that the performance of the algorithm is good and reliable. Therefore, building a large knowledge database of material combinations is recommended.

Advanced Meta-knowledge for Chinese Chess Endgame Knowledge Bases

The proper evaluation of a possible transition from the middle game to the endgame is an important research issue. We constructed an endgame knowledge base that consists of a large set of endgame heuristics that supports the evaluation. Moreover, a general graph model is proposed to resolve conflicts between two competing material combinations. However, it turned out to be difficult to find such competing material combinations. We need better meta-knowledge rules to find more potential conflicts. In this article, we propose five meta-knowledge rules for Chinese chess. Two examples of meta-knowledge rules are piece exchanges and pawn exchanges. The meta-knowledge rules are inducted from real games played by masters. The heuristics so found are endowed with confidence factors to show their chances of being correct. Using this method, 20% of a previous constructed body of endgame knowledge, consisting of 124, 747 material combinations, was found to be erroneous. About 82.13% of these heuristic errors are auto-corrected using our algorithm. By using the corrected knowledge base, the strength of our game-playing program, CONTEMPLATION, is clearly improved according to self-play tests.

Multilevel Inference in Chinese Chess Endgame Knowledge Bases

In Chinese chess, retrograde analysis can be used to solve complex elementary (i.e., fundamental) endgames and to provide perfect play. However, there are still many practical endgames pending to be analysed due to problems related to the complex playing rules. Of course, there is heuristic endgame knowledge for the evaluation functions. This knowledge is often applied to the complex endgames or the real endgames to improve the playing strength. One crucial problem is to choose relatively advantageous endgames by selecting appropriate piece exchanges. For this problem, we designed a Chinese chess endgame knowledge-based system with a large set of endgame heuristics, called an endgame knowledge base. We use this knowledge base in our program, CONTEMPLATION. To maintain the quality of the constructed knowledge base, it is important to detect and resolve conflicts between the heuristics. A conflict-resolution method enables Chinese chess experts to correct erroneous entries by using knowledge about two endgames that differ by precisely one piece. The problem involves detecting potential errors so that a human expert can easily revise and improve the reliability of the knowledge base. In this article, we introduce two major enhancements to the above method. First, we propose a general graph model to handle the heuristics when the endgames involved are differing in more than one piece. Second, we add a confidence-factor parameter to encode the probability that a heuristic may be true. Such heuristics are often used in real games when pieces are exchanged. The resulting graph model is effective in maintaining the consistency of predefined meta-knowledge, and thus improves the overall quality significantly. The results of the experiments on self-play tests demonstrate that the derived knowledge base improves the playing strength of CONTEMPLATION.

Integration of Chinese Chess Endgame Knowledge Bases

We often incorporate endgame heuristics as part of the evaluation function for CHINESE CHESS programs. We propose a semi-automatic strategy to construct a large set of endgame heuristics, which is called endgame knowledge base, which is used in our program, Contemplation. We also handle the conflict problem in large amount of knowledge. By applying the semi-automatic construction and modification process, we can obtain a consistent endgame knowledge base. Finally, we discuss about our method to achieve high correctness for practical usage.

An Intelligent Tutoring System of Chinese Chess

Computer Chinese chess is an application of artificial intelligence. The playing strength of many Chinese chess programs is at the level of human masters or grandmasters. However, it is not easy for a human player to learn Chinese chess skills from these strong programs because their outputs are no more than moves and score values. It is necessary for a student to understand why he or she loses the game and to receive feedback after practice. In this paper, we propose an intelligent tutoring system for learning Chinese chess. The system interacts with students by playing games with them and gives comments and suggestions to them during a game without any human intervention. After some iterations of practice, our system reports their learning achievements by analyzing their game records.

Knowledge abstraction in Chinese chess endgame databases

Retrograde analysis is a well known approach to construct endgame databases. However, the size of the endgame databases are too large to be loaded into the main memory of a computer during tournaments. In this paper, a novel knowledge abstraction strategy is proposed to compress endgame databases. The goal is to obtain succinct knowledge for practical endgames. A specialized goal-oriented search method is described and applied on the important endgame KRKNMM. The method of combining a search algorithm with a small size of knowledge is used to handle endgame positions up to a limited depth, but with a high degree of correctness.