8 research outputs found
Recommended from our members
Control Strategies for Two Player Games
Computer games have been around for almost as long as computers. Most of these games, however, have been designed in a rather ad hoc manner because many of their basic components have never been adequately defined. In this paper some deficiencies in the standard model of computer games, the minimax model, are pointed out and the issues that a general theory must address are outlined. Most of the discussion is done in the context of control strategies, or sets of criteria for move selection. A survey of control strategies brings together results from two fields: implementations of real games and theoretical predictions derived on simplified game-trees. The interplay between these results suggests a series of open problems that have arisen during the course of both analytic experimentation and practical experience as the basis for a formal theory
The phenomenon of Decision Oscillation: a new consequence of pathology in Game Trees
Random minimaxing studies the consequences of using a random number for scoring
the leaf nodes of a full width game tree and then computing the best move using the
standard minimax procedure. Experiments in Chess showed that the strength of play
increases as the depth of the lookahead is increased. Previous research by the authors
provided a partial explanation of why random minimaxing can strengthen play by showing
that, when one move dominates another move, then the dominating move is more likely
to be chosen by minimax. This paper examines a special case of determining the move
probability when domination does not occur. Specifically, we show that, under a uniform
branching game tree model, whether the probability that one move is chosen rather than
another depends not only on the branching factors of the moves involved, but also on
whether the number of ply searched is odd or even. This is a new type of game tree
pathology, where the minimax procedure will change its mind as to which move is best,
independently of the true value of the game, and oscillate between moves as the depth of
lookahead alternates between odd and even
Recommended from our members
The Expected-Outcome Model of Two-Player Games
This paper introduces a new, crisp definition of two-player evaluation functions. These functions calculate a node's expected-outcome value. or the probability that a randomly chosen leaf beneath it will represent a win. The utility of these values to game programs will be assessed by a series of experiments that compare the performance of expected-outcome functions with that of some popular, previously studied evaluators. To help demonstrate the domain-independence of these new functions, the experiments will be run on variants of several games, including tic-tac-toe, Othello, and chess. In addition, the paper outlines a. new probabilistic model of game-trees which involves rethinking many long-accepted assumptions in light of the newly defined expected-outcome functions
Análise do uso de formalização de conhecimento heurÃstico no ensino de jogos através do estÃmulo à alternância entre competição e colaboração
Resumo: Neste trabalho de doutoramento, verifica-se a hipótese de que o estÃmulo à formalização de conhecimento heurÃstico de jogo por aprendizes contribui para que estes compreendam melhor, os conceitos trabalhados no processo de aprendizagem. Sendo esta atividade de instrução apoiada por software, e privilegiando a alternância entre a colaboração e competição entre os estudantes. O projeto PROTEX, de apoio computacional ao ensino de xadrez nas escolas brasileiras, apresentado em Direne et al. (2004), descreve um ambiente educacional onde o aprendiz formaliza o seu conhecimento heurÃstico de jogo, e esta representação criada pode ser analisada, comentada, e usada por outros estudantes. E através de jogadores automáticos, a heurÃstica especificada por um indivÃduo pode ser validada, quando esta é utilizada como lógica de escolha de jogadas em uma partida automatizada. Alguns conceitos e ferramentas para este sistema foram anteriormente desenvolvidos por Martineschen et al. (2006), Feitosa et al. (2007) e Bueno et al. (2008), contudo até o presente estudo a eficácia desta abordagem não podia ser atestada. Com o intuito de realizar esta aferição, os seguintes objetivos foram alcançados por esta pesquisa: (1) realizou-se uma análise crÃtica, e uma revisão bibliográfica completa sobre os trabalhos acadêmicos e comerciais relacionados a este tema; (2) expandiu-se o conjunto de conceitos e softwares para permitir a competição artificial entre as especificações feitas; e (3) conduziu-se um estudo empÃrico sobre o uso deste novo ferramental, em um ambiente real de ensino e aprendizagem de xadrez. E a partir da análise dos resultados encontrados, constatou-se que a proposição inicial demonstrou-se válida