Algorithms in a Nutshell by George T. Heineman

Author:George T. Heineman
Language: eng
Format: epub
Publisher: O'Reilly Media
Published: 2016-03-08T16:00:00+00:00

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Individual comparisons show the dramatic improvement of AlphaBeta; some of these cases explain why AlphaBeta is so powerful. For the game state shown in Figure 7-11, AlphaBeta explores only 450 game states (instead of 8,232 for Minimax, a 94.5% reduction) to determine that player X should select the center square, after which a win is assured.

Figure 7-11. Sample tic-tac-toe board after two plays

However, the only way to achieve such deep reductions is if the available moves are ordered such that the best move appears first. Because our tic-tac-toe solution does not order moves in this fashion, some anomalies will result. For example, given the same board state rotated 180 degrees (Figure 7-12), AlphaBeta will explore 960 game states (an 88.3% reduction) because it expands the game tree using a different ordering of valid moves. For this reason, search algorithms often reorder moves using a static evaluation function to reduce the size of the game tree.

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