Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence
World-championship-caliber Scrabble
Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence
CG '98 Proceedings of the First International Conference on Computers and Games
Complexity, appeal and challenges of combinatorial games
Theoretical Computer Science - Algorithmic combinatorial game theory
Locally informed global search for sums of combinatorial games
CG'04 Proceedings of the 4th international conference on Computers and Games
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Many games are naturally described as a sum of games, e.g., nim and the endgame of Go. Let G ,...,G represent n games. Then a move in the sum G + ...+G consists of picking a component game G and making a move in G .. This thesis analyzes play in a sum of games from three different perspectives: computational complexity, approximate solutions, and optimal search algorithms. Lockwood Morris proves that the problem of determining the optimal strategy in a sum of games is PSPACE-complete. This thesis proves that the problem is PSPACE-complete even when the component games are so simple that they can be represented as depth two trees. Hanner shows that the value of a sum of games can be approximated to within the maximum temperature of the component games. This thesis presents a clear and concise proof of Hanner''s bounds. This thesis also improves upon Hanner''s result. It shows that the value of a sum of games can be approximated to within the second highest temperature. This thesis describes how Berliner''s B* search algorithm can be effectively combined with the approximate solutions to speed up the search for an optimal solution.