Algorithms in a Nutshell [PDF]

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Algorithms in a Nutshell – Book

To measure the benefit of AlphaBeta over NegMax, we compare the size of their respective game trees. This task is complicated because AlphaBeta will show its most impressive savings if the opponent’s best move is evaluated first whenever AlphaBeta executes. When there is a fixed number b of moves at each game state, the total number of potential game states to search in a d-ply AlphaBeta is on the order of b d .

If the moves are ordered by decreasing favorability (i.e., the best move first), we still have to evaluate all b children for the initiating player (because we are to choose his best move); however, in the best case, we need to evaluate only the first move by the opponent. Note in Figure 7-9 that, because of move order, the prune occurs after several moves have been evaluated, so the move ordering for that game tree is not optimal.