The Secret of Selective Game Tree Search, When Using Random-Error Evaluations
Game tree search deals with the problems that arise, when computers play two-person-zero-sum-games such as chess, checkers, othello etc. The greatest success of game tree search so far, was the victory of the chess machine ‘Deep Blue’ vs. G. Kasparov, the best human chess player in the world at that time. In spite of the enormous popularity of computer chess and in spite of the successes of game tree search in game playing programs, we do not know much about a useful theoretical background that could explain the usefulness of (selective) search in adversary games.
We introduce a combinatorial model, which allows us to model errors of a heuristic evaluation function, with the help of coin tosses. As a result, we can show that searching in a game tree will be ‘useful’ if, and only if, there are at least two leaf-disjoint strategies which prove the root value. In addition, we show that the number of leaf-disjoint strategies, contained in a game tree, determines the order of the quality of a heuristic minimax value. The model is integrated into the context of average-case analyses.
- I. Althöfer. Root evaluation errors: How they arise and propagate. ICCA Journal, 11(3):55–63, 1988.
- C. Donninger. Null move and deep search. ICCA Journal, 16(3):137–143, 1993.
- R. Feldmann. Fail high reductions. Advances in Computer Chess 8 (ed. J. van den Herik), 1996.
- H. Kaindl and A. Scheucher. The reason for the benefits of minmax search. In Proc. of the 11 th IJCAI, pages 322–327, Detroit, MI, 1989.
- D.E. Knuth and R.W. Moore. An analysis of alpha-beta pruning. Artificial Intelligence, 6(4):293–326, 1975. CrossRef
- U. Lorenz. Controlled Conspiracy-2 Search. Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS), (H. Reichel, S. Tison eds), Springer LNCS, pages 466–478, 2000.
- U. Lorenz. P. ConNers wins the 10th Grandmaster Tournament in Lippstadt. ICCA Journal, 23(3):188–192, 2000.
- U. Lorenz. Parallel controlled conspiracy number search. Proceedings of the 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), ACM Press, pages 320–321, 2001.
- D.A. McAllester. Conspiracy Numbers for Min-Max searching. Artificial Intelligence, 35(1):287–310, 1988. CrossRef
- D.S. Nau. Quality of Decision versus depth of search on game trees. PhD thesis, Duke University, Durham, NC, 1979.
- J. Pearl. On the nature of pathology in game searching. Artificial Intelligence, 20(4):427–453, 1983. CrossRef
- J. Pearl. Heuristics — Intelligent Search Strategies for Computer Problem Solving. Addison-Wesley Publishing Co., Reading, MA, 1984.
- J. Schaeffer. Conspiracy numbers. Artificial Intelligence, 43(1):67–84, 1990. CrossRef
- J. Schaeffer and A. Plaat. Kasparov versus Deep Blue: The Rematch. ICCA Journal, 20(2):95–125, 1997.
- The Secret of Selective Game Tree Search, When Using Random-Error Evaluations
- Book Title
- STACS 2002
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- 19th Annual Symposium on Theoretical Aspects of Computer Science Antibes - Juan les Pins, France, March 14–16, 2002 Proceedings
- pp 203-214
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Springer-Verlag Berlin Heidelberg
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