Multi-player alpha-beta pruning
Artificial Intelligence
Artificial intelligence: a modern approach
Artificial intelligence: a modern approach
On Pruning Techniques for Multi-Player Games
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Last-branch and speculative pruning algorithms for max
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Incorporating opponent models into adversary search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Robust game play against unknown opponents
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
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Algorithms for pruning game trees generally rely on a game being zero-sum, in the case of alpha-beta pruning, or constant-sum, in the case of multi-player pruning algorithms such as speculative pruning. While existing algorithms can prune non-zero-sum games, pruning is much less effective than in constant-sum games. We introduce the idea of leaf-value tables, which store an enumeration of the possible leaf values in a game tree. Using these tables we are can make perfect decisions about whether or not it is possible to prune a given node in a tree. Leaf-value tables also make it easier to incorporate monotonic heuristics for increased pruning. In the 3-player perfect-information variant of Spades we are able to reduce node expansions by two orders of magnitude over the previous best zero-sum and non-zero-sum pruning techniques.