Algorithms for games
Springer-Verlag, 1988 - Computers - 197 pages
""Algorithms for Games"" aims to provide a concrete example of the programming of a two-person game with complete information, and to demonstrate some of the methods of solutions; to show the reader that it is profitable not to fear a search, but rather to undertake it in a rational fashion, make a proper estimate of the dimensions of the "catastrophe," and use all suitable means to keep it down to a reasonable size. The book is dedicated to the study of methods for limiting the extent of a search. The game programming problem is very well suited to the study of the search problem, and in general for multi-step solution processes. With this in mind, the book focuses on the programming of games as the best means of developing the ideas and methods presented. While many of the examples are related to chess, only an elementary knowledge of the game is needed.
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Algorithms for Games and Probability Theory
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5-subtree A°-threat algorithm axiom backward step base position A0 Bd(C best move Black position blank move branches A1 chess programs choose colB color opposite Computer Chess consider construct corresponding critical branch defined endgames evaluation function f(A Figure fin(B fin(C forced game formula forward step fragments game programming game tree 21 improving move inadmissible influence predicate influence relation influences the branch methods minimax model game model scores move belongs moves leading node non-terminal position noughts-and-crosses null-rank squares number of moves number of positions opponent original game 21 parameters Pawn piece player poor moves position fin(5 positions of rank probabilistic proof pruned tree random variables recursion refutation move region of convergence rules satisfied sc(A search depth search tree Shannon model shortening the search subtree 21 Suppose terminal positions theorem threat transfer of scores true score values virtual moves White and Black White Black White position winning moves