1Foundations of Artificial IntelligenceAdversarial SearchCS472 – Fall 2007Thorsten JoachimsGame PlayingAn AI Favorite•structured task•clear definition of success and failure•does not require large amounts of knowledge (at first glance)•focus on games of perfect informationGame PlayingInitial Stateis the initial board/positionSuccessor Functiondefines the set of legal moves from any positionTerminal Testdetermines when the game is overUtility Functiongives a numeric outcome for the gameGame Playing as SearchxPartial Search Tree for Tic-Tac-Toexxxxxxxxxxxoooooooooo ooo ooxxxxxxxxxxxxx xxxxxxo…………………MIN(O)MAX(X)MIN(O)TERMINALUTILITYMAX(X)0+1-1Simplified Minimax Algorithm1.Expand the entire tree below the root.2.Evaluate the terminal nodes as wins for the minimizer or maximizer (i.e. utility). 3.Select an unlabeled node, n, all of whose children have been assigned values. If there is no such node, we're done ---return the value assigned to the root.4.If nis a minimizer move, assign it a value that is the minimum of the values of its children. If nis a maximizermove, assign it a value that is the maximum of the values of its children. Return to Step 3.
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