{"title":"中国黑棋残局中的等价类","authors":"Jr-Chang Chen, Ting-Yu Lin, Bo-Nian Chen, T. Hsu","doi":"10.1109/TCIAIG.2014.2317832","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49192,"journal":{"name":"IEEE Transactions on Computational Intelligence and AI in Games","volume":"7 1","pages":"109-122"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1109/TCIAIG.2014.2317832","citationCount":"17","resultStr":"{\"title\":\"Equivalence Classes in Chinese Dark Chess Endgames\",\"authors\":\"Jr-Chang Chen, Ting-Yu Lin, Bo-Nian Chen, T. Hsu\",\"doi\":\"10.1109/TCIAIG.2014.2317832\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":49192,\"journal\":{\"name\":\"IEEE Transactions on Computational Intelligence and AI in Games\",\"volume\":\"7 1\",\"pages\":\"109-122\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1109/TCIAIG.2014.2317832\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Computational Intelligence and AI in Games\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TCIAIG.2014.2317832\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Computer Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Computational Intelligence and AI in Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TCIAIG.2014.2317832","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Computer Science","Score":null,"Total":0}
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.
期刊介绍:
Cessation. The IEEE Transactions on Computational Intelligence and AI in Games (T-CIAIG) publishes archival journal quality original papers in computational intelligence and related areas in artificial intelligence applied to games, including but not limited to videogames, mathematical games, human–computer interactions in games, and games involving physical objects. Emphasis is placed on the use of these methods to improve performance in and understanding of the dynamics of games, as well as gaining insight into the properties of the methods as applied to games. It also includes using games as a platform for building intelligent embedded agents for the real world. Papers connecting games to all areas of computational intelligence and traditional AI are considered.