Download e-book for kindle: Expected Outcome Model of Two Player Games by Bruce Abramson

By Bruce Abramson

ISBN-10: 0273033344

ISBN-13: 9780273033349

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

Comprised of 8 chapters, this publication starts with an outline of the explanation for the mathematical learn of video games, by way of a dialogue on a few earlier synthetic 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 was once applied on a few small types of tic-tac-toe and Othello. The publication additionally offers effects that supply robust 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 laptop technological know-how.

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Extra resources for Expected Outcome Model of Two Player Games

Example text

To effectively study the victory margins, a random variable that represents the disc differential, T> — (weighted-squares' score) — (sampler's score), must be defined. Assuming that V is distributed approximately normally, standard tests regarding the means of normal distributions can be used to answer some questions about the functions' relative strengths. First, using the disc-differential criterion, does the weaker sampler still appear equivalent to weighted-squares? 69, respectively, what is the probability that the true value μν = 0?

Many interesting results have been derived on (d, 6, /)-trees and board splitting games, but of particular relevance to expected-outcome are the minimax convergence [37] and last player [31] theorems. According to these theorems, the minimax value of the root of a (d, 6, /)-tree is essentially (with probability approaching one) determined as soon as the parameters of the tree are set. In a tree with leaf values restricted to WIN and LOSS, for example, there is a threshold value, denoted by Ξ&, such that if WIN leaves were generated with probability greater than Ξ&, the tree's minimax value is almost certain to be a WIN.

B) If pi < (1 — Ξ&), then as d —> oo, Td{pi) = Fdfa) = · · · = Fd{Vb) = 0. Since all of the moves are LOSSes, they are all equally "optimal". Recall t h a t Td(p) is defined as the percentage of all d e p t h d trees whose leaves are assigned a 1 with probability p t h a t result in a forced win for M A X . According to (a) and (b), then, for any ρχ φ Ξ^, t h e percentage of forced-win trees approaches either 0 or 1 as d grows to oo. ,mi > be (d,6,/)-trees Expected-Outcome with identical branching factors and depths, and binomially distributed leaf values with expected-outcome values of pi > p2 > · · · > p&, respectively, where all roots converge.

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Expected Outcome Model of Two Player Games by Bruce Abramson


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