Simple PDF minmax.pdf - Artificial Intelligence Minimax and alpha-beta pruning In which we examine the problems that arise when we try to plan ahead in

Simple PDF minmax.pdf - Artificial Intelligence Minimax and...

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1Artificial IntelligenceMinimax and alpha-beta pruning2In which we examine the problems that arise when we try to plan ahead in a world that includes a hostile agent (other agent planning against us).
23GamesAdversarial search problems and Game theory– Competitive environments in which goals of multiple agents are in conflict (often known as games)Game playing is idealization of worlds in which hostile agents act so as to diminish ones well-being!Games problems are like real world problems JClassic AI games– Deterministic, turn-taking, two-player, perfect information4Classic AI GamesState of game easy to representAgents usually restricted to fairly small number of well-defined actionsNEW: Opponent introduces uncertaintyGames usually too hard to solve directly– ChessBranching factor 35Often go to 50 moves by each playerAbout 35100nodes!Therefore, games are a good domain to study
35AI Game PlayDefine optimal move and need algorithm for finding itIgnoreportions of search tree that make no difference to final choice– “Pruning”6A Game Defined as Search ProblemInitial stateBoard position– Whose move it isOperators(successor function)– Defines legal moves and resulting statesTerminal(goal) test– Determines when game is over (terminal states)Utility (objective, payoff) function– Gives numeric value for the game outcome at terminal statese.g., {win = +1, loss = -1, draw = 0}
47XXXXXXXXXXOXOXOXOXXOXXOXXOXOXOXOXOOXXXOXOXXXOO-10+1OXOXUtilityTerminalPartial search tree for game Tic-Tac-Toe(you are X)8Optimal Strategies:Perfect Decisions in Two-Person GamesTwo players– MAX– MINTurn-taking: MAX moves first, then take turns with MIN moving until game overAt end, points awarded to winning playerOr penalties given to loserCan formulate this gaming structure into a search problem
59An OpponentIf were normal search problem, then MAX (you/agent) need only search for sequence of moves leading to winning stateBut, MIN (the opponent) has inputMAX must use a strategy

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• Fall '16
• Max, Minimax