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A Minimax Algorithm Better than Alpha-Beta? No and Yes
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- Author(s) / Creator(s)
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Technical report TR95-15. This paper has three main contributions to our understanding of fixed-depth minimax search: (A) A new formulation for Stockman's SSS* algorithm, based on Alpha-Beta, is presented. It solves all the perceived drawbacks of SSS, finally transforming it into a practical algorithm. In effect, we show that SSS = Alpha-Beta + transposition tables. The crucial step is the realization that transposition tables contain so-called solution trees, structures that are used in best-first search algorithms like SSS. Having created a practical version, we present performance measurements with tournament game-playing programs for three different minimax games, yielding results that contradict a number of publications. (B) Based on the insights gained in our attempts at understanding SSS, we present a framework that facilitates the construction of several best-first fixed-depth game-tree search algorithms, known and new. The framework is based on depth-first null-window Alpha-Beta search, enhanced with storage to allow for the refining of previous search results. It focuses attention on the essential differences between algorithms. (C) We present a new instance of the framework, MTD(f). It is well-suited for use with iterative deepening, and performs better than algorithms that are currently used in most state-of-the-art game-playing programs. We provide experimental evidence to explain why MTD(f) performs better than the other fixed-depth minimax algorithms. | TRID-ID TR95-15
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- Date created
- 1995
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- Subjects / Keywords
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- Type of Item
- Report
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- License
- Attribution 3.0 International