New PDF release: Expected Outcome Model of Two Player Games

By Bruce Abramson

ISBN-10: 0273033344

ISBN-13: 9780273033349

The Expected-Outcome version of Two-Player video games bargains with the expected-outcome version of two-player video games, within which the relative benefit of game-tree nodes, instead of board positions, is taken into account. the anomaly of static evaluate and the issues it generates within the seek approach are tested and the improvement of a domain-independent static evaluator is described.

Comprised of 8 chapters, this publication starts with an summary of the explanation for the mathematical research of video games, by means of a dialogue on a few prior man made intelligence (AI) study efforts on game-trees. the subsequent part opens with the definition of a nodes expected-outcome worth because the anticipated worth of the leaves underneath it. The expected-outcome version is printed, paying specific recognition to the expected-outcome price of a game-tree node. This version used to be applied on a few small types of tic-tac-toe and Othello. The ebook additionally offers effects that supply powerful aid for either the validity of the expected-outcome version and the rationality of its underlying assumptions.

This monograph is meant for experts in AI and computing device technological know-how.

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Expected-outcome, as a statistical measure of distribution means, is governed by the law of large numbers, which states t h a t as t h e size of a population grows, t h e observed m e a n approaches t h e distribution's actual mean at a rate linear in t h e population size [21]. In the case of (d, 6, / ) - t r e e s , this means t h a t as t h e trees get deeper, expected-outcome values (observed means) become increasingly accurate measures of / ' s theoretical mean. Since the size of t h e leaf population is given by 6 d , t h e r a t e of increased accuracy is exponential in d.

In other words, if the value at the Ξι,-quantile of F is 1, Td{v) wm< converge to 1; if it is 0, convergence will be to 0. The only instance in which the value of the root may be either 0 or 1, then, is when the value at the appropriate quantile is in some neighborhood around Ξ&. On an S-curve, this may involve a significant portion of the curve. In a step function, however, the "neighborhood" is a point; unless p is set at exactly that point, it will either be above or below the relevant threshold.

When neither player can move, the one with the most discs is declared the winner. (For more detailed descriptions, see [22] [28] [48]). These games contributed four small variants for study, although only two of them, 3-by-3 tic-tac-toe and 4-by-4 Othello, actually have game-trees that are small enough to generate entirely. The other two, 4-by-4 tic-tac-toe and 6-by-6 Othello, were chosen because they are small enough for large portions of their trees to be examined, yet large enough to offer more interesting testbeds than their smaller cousins.

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Expected Outcome Model of Two Player Games by Bruce Abramson

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