On Pruning Techniques for Multi-Player Games

Maxn (Luckhardt and Irani, 1986) is the extension of the minimax backup rule to multi-player games. We have shown that only a limited version of alpha-beta pruning, shallow pruning, can be applied to a maxn search tree. We extend this work by calculating the exact bounds needed to use this pruning technique. In addition, we show that branch-and-bound pruning, using a monotonic heuristic, has the same limitations as alpha-beta pruning in a maxn tree. We present a hybrid of these algorithms, alpha-beta branch-and-bound pruning, which combines a monotonic heuristic and backed-up values to prune even more effectively. We also briefly discuss the reduction of a n-player game to a `paranoid' 2-player game. In Sergeant Major, a 3-player card game, we averaged node expansions over 200 height 15 trees. Shallow pruning and branch-and-bound each reduced node expansions by a factor of about 100. Alpha-beta branch-and-bound reduced the expansions by an additional factor of 19. The 2-player re...

• Type: Conference
• Year: 2000
• Where: AAAI
• Authors: Nathan R. Sturtevant, Richard E. Korf
• Keywords: AAAI 2000, Alpha-beta Branch-and-bound Pruning, Alpha-beta Pruning, Branch-and-bound Pruning, Intelligent Agents