By Bruce Abramson
The Expected-Outcome version of Two-Player video games offers with the expected-outcome version of two-player video games, during which the relative benefit of game-tree nodes, instead of board positions, is taken into account. the paradox of static assessment 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 off with an summary of the explanation for the mathematical learn of video games, through a dialogue on a few earlier synthetic intelligence (AI) examine efforts on game-trees. the following part opens with the definition of a nodes expected-outcome price because the anticipated price of the leaves underneath it. The expected-outcome version is printed, paying specific cognizance to the expected-outcome price of a game-tree node. This version used to be applied on a few small models of tic-tac-toe and Othello. The ebook additionally offers effects that provide powerful help 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 technology.
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Extra resources for Expected Outcome Model of Two Player Games
Sample text
M& be an optimal ordering of (d,6,/)-trees with identical branching factors and depths, and normal leaf distributions specified by means μι,μ 2 , · · · , μ&, and standard deviations σ1? σ 2 , · · ·, σ^, respectively. If VM<, M,· : (i < j ) =* (μ; - μ,) > z s »(*j - σ;), then linid-^oo Pr[expected-outcome will make optimal moves] = 1. Proof: Any two evaluators, such as expected-outcome and Ξί,-outcome, will agree over a set of moves if and only if they agree on a choice between any two elements of the set.
Instead, satisfactory solutions are sought. Without making any pretense of optimality, then, expected-outcome functions can be applied to real games to determine their merit. Since the ultimate criterion by which an evaluator is judged is its performance in actual competition, three sets of experiments were run to verify both the rationality of the random-play assumption and the strength of the expected-outcome model in realgame settings. The first set generated some small complete game-trees, calculated the exact numbers of WINs, LOSSes, and DRAWs beneath every position, and compared the completely informed expected-outcome function with a well-known game-specific evalu ator.
This is not completely unexpected — evaluation functions that choose among game-trees based on their respective leaf-value distributions cannot discriminate effectively among trees designed with identical parameters because the same value will be assigned to each option. As the trees grow, the discriminating power of expected-outcome diminishes to the point where all decisions are made by a (secondary) tie-breaking rule. This difficulty suggests that fair board splitting games are not a useful vehicle for introducing the possibility of error in the context of the decision quality of expected-outcome and motivates the need for a somewhat different approach.