Algorithms in a Nutshell 2E by George T. Heineman Gary Pollice and Stanley Selkow

Author:George T. Heineman, Gary Pollice, and Stanley Selkow
Language: eng
Format: mobi
Tags: COMPUTERS / Programming / Algorithms
ISBN: 9781491912959
Publisher: O’Reilly Media
Published: 2015-07-28T04:00:00+00:00

2

549,936

47,508

91%

±6.8%

3

549,864

112,086

80%

±10.2%

Individual comparisons show the dramatic improvement of AlphaBeta and some of these cases explain why AlphaBeta is so powerful. On the game state shown in Figure 7-11, AlphaBeta explores only 47 game states (instead of 8,232 for Minimax, a 99.4% 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.

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