bjornssonm01a - Preprint of paper: Theoretical Computer...

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Unformatted text preview: Preprint of paper: Theoretical Computer Science, vol. 252(1-2), 177–196. Multi-Cut αβ-Pruning in Game-Tree Search Yngvi Bj¨ornsson and Tony Marsland University of Alberta, Department of Computing Science, Edmonton AB, Canada T6G 2H1 { yngvi,tony } @cs.ualberta.ca Abstract. The efficiency of the αβ-algorithm as a minimax search pro- cedure can be attributed to its effective pruning at so-called cut-nodes; ideally only one move is examined there to establish the minimax value. This paper explores the benefits of investing additional search effort at cut-nodes by also expanding some of the remaining moves. Our results show a strong correlation between the number of promising move alterna- tives at cut-nodes and a new principal variation emerging. Furthermore, a new forward-pruning method is introduced that uses this additional information to ignore potentially futile subtrees. We also provide exper- imental results with the new pruning method in the domain of chess. 1 Introduction The αβ-algorithm is the most popular method for searching game-trees in such adversary board games as chess, checkers and Othello. It is much more efficient than a plain brute-force minimax search because it allows a large portion of the game-tree to be pruned, while still backing up the correct game-tree value. How- ever, the number of nodes visited by the algorithm still increases exponentially with increasing search depth. This obviously limits the scope of the search, since game-playing programs must meet external time-constraints: often having only a few minutes to make a decision. In general, the quality of play improves the further the program looks ahead 1 . Over the years, the αβ-algorithm has been enhanced in various ways and more efficient variants have been introduced. For example, although the basic algorithm explores all continuations to some fixed depth, in practice it is no longer used that way. Instead, various heuristics allow variations in the distance to the search horizon (often called the search depth or search tree height), so that some move sequences can be explored more deeply than others. “Interest- ing” continuations are expanded beyond the nominal depth, while others are terminated prematurely. The latter case is referred to as forward-pruning , and involves some risk of overlooking a good continuation. The rationale behind the 1 Some artificial games have been constructed where the opposite is true; when backing up a minimax value the decision quality actually decreases with increasing search depth. This phenomenon has been studied thoroughly and is referred to as pathology in game-tree search [10]. However, such pathology is not seen in chess or the other games we are investigating. approach is that the time saved by pruning non-promising lines is better spent searching others more deeply, in an attempt to increase the overall decision qual- ity....
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This note was uploaded on 10/23/2011 for the course ENCS ENCS5 taught by Professor Abdelsalam during the Spring '10 term at Birzeit University.

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bjornssonm01a - Preprint of paper: Theoretical Computer...

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