{"title":"An Enhanced Solver for the Game of Amazons","authors":"Jiaxing Song, Martin Müller","doi":"10.1109/TCIAIG.2014.2309077","DOIUrl":null,"url":null,"abstract":"The game of Amazons is a modern board game with simple rules and nice mathematical properties. It has a high computational complexity. In 2001, the starting position on a 5 × 5 board was proven to be a first player win. The enhanced Amazons solver presented here extends previous work in the following five ways: by building more powerful endgame databases, including a new type of databases for so-called blocker territories, by improving the rules for computing bounds on complex game positions, by local search to find tighter local bounds, by using ideas from combinatorial game theory to find wins earlier, and by using a df-pn based solver. Using the improved solver, the starting positions for Amazons on the 4 × 5, 5 × 4, 4 × 6, 5 × 6, and 4 × 7 boards were shown to be first player wins, while 6 × 4 is a second player win. The largest proof, for the 5 × 6 board, is presented in detail.","PeriodicalId":49192,"journal":{"name":"IEEE Transactions on Computational Intelligence and AI in Games","volume":"7 1","pages":"16-27"},"PeriodicalIF":0.0000,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1109/TCIAIG.2014.2309077","citationCount":"7","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.2014.2309077","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Computer Science","Score":null,"Total":0}
引用次数: 7
Abstract
The game of Amazons is a modern board game with simple rules and nice mathematical properties. It has a high computational complexity. In 2001, the starting position on a 5 × 5 board was proven to be a first player win. The enhanced Amazons solver presented here extends previous work in the following five ways: by building more powerful endgame databases, including a new type of databases for so-called blocker territories, by improving the rules for computing bounds on complex game positions, by local search to find tighter local bounds, by using ideas from combinatorial game theory to find wins earlier, and by using a df-pn based solver. Using the improved solver, the starting positions for Amazons on the 4 × 5, 5 × 4, 4 × 6, 5 × 6, and 4 × 7 boards were shown to be first player wins, while 6 × 4 is a second player win. The largest proof, for the 5 × 6 board, is presented in detail.
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.
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