Evaluations - per - move Wins

24 and close to that achieved by. Berliner and McConnell 1] deal with the diiculty in nding optimistic and pessimistic bounds on the real values of game-tree positions. However, their results are not applicable for multi-model search where we look for bounds on the sum of two functions. The sum-bounds for a multi-model search reeect the maximal possible diierence between the subjective evaluations done by the player and its opponent model. In Section 5 we presented practical methods for computing such bounds. The question whether the beneet of modeling outweighs the cost of reduced pruning depends on the domain and on the evaluation function used. In this work we showed an example, in the checkers domain, where the beneet of modeling outweighs the cost of reduced pruning power. The multi-model framework allows the use of arbitrary opponent models. This work points out that pruning is signiicantly reduced for a model which is radically diierent from the player's strategy. However, for zero-sum games, we do not expect the players to evaluate boards in a radically diierent way. In such cases, the pruning power of is signiicant. A uniied theory of heuristic evaluation functions and its application to learning. Table 1: The results obtained by an iterative deepening version of when played against an iterative deepening version of. Both algorithms were allocated the same search resources { leaf evaluations per move. Each row represents a tournament of 1,000 games. The last two columns show the average search depth of the two algorithms. resources per move. We measured the search resources by the number of leaf evaluations available for a move. Table 1 shows the results obtained by , with the player P 1 = (f 1 ; (f 0 ; ?)), against , with the function f 0 , for various values of resource limit (leaf evaluations per move). Each row represents the results of a tournament of 1,000 games. We can see that in all cases searched shallower than due to its reduced pruning power. However, the deeper search of was outweighed by the beneet of modeling. When playing against an player using f 0 , , using the player P 1 = (f 1 ; (f 0 ; ?)), uses the exact opponent function as a model, in contrast to which wrongly uses ?f 0 as an opponent model. As a result, while the player prefers exchange positions, wrongly assumes …