Combinatorial Game Values of Chilled Domineering

• Main Authors: HUANG, YU-WEN, 黃郁雯
• Other Authors: 吳毅成
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/14119082252945305221

碩士 === 國立交通大學 === 多媒體工程研究所 === 100 === Combinatorial Game theory uses mathematical theory to study computer games. The theory describes a game position with a game tree and makes a specific value stand for the result of a game. This game value helps us to analyze the advantage of both players and find the optimum moves. Combinatorial game theory can be applied to Domineering. By studying the game with combinatorial game theory, we know many results of different Domineering game positions. Chilled Domineering is a game invented by Kao et al. in 2010. The rule of chilled domineering is different from domineering and its complexity is higher than domineering. They analyzed all the 3x3 positions of chilled domineering and provided a linear formula to simplify and calculate the position value. The main purpose of this research is to implement a program to analyze Chilled Domineering, generate all 4x4 positions, and calculate the values. Moreover, the research analyzes and categorizes these values and tries to find a way to determine the winner of the position.