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# ch05 - Games vs search problems"Unpredictable opponent...

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Adversarial Search Chapter 5 Chapter 5 1 Outline Games Perfect play – minimax decisions α β pruning Resource limits and approximate evaluation Games of chance Games of imperfect information Chapter 5 2 Games vs. search problems “Unpredictable” opponent solution is a strategy specifying a move for every possible opponent reply Time limits unlikely to find goal, must approximate Plan of attack: Computer considers possible lines of play (Babbage, 1846) Algorithm for perfect play (Zermelo, 1912; Von Neumann, 1944) Finite horizon, approximate evaluation (Zuse, 1945; Wiener, 1948; Shannon, 1950) First chess program (Turing, 1951) Machine learning to improve evaluation accuracy (Samuel, 1952–57) Pruning to allow deeper search (McCarthy, 1956) Chapter 5 3 Types of games deterministic chance perfect information imperfect information chess, checkers, go, othello backgammon monopoly bridge, poker, scrabble nuclear war battleships, blind tictactoe Chapter 5 4

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Game tree (2-player, deterministic, turns) X X X X X X X X X MAX (X) MIN (O) X X O O O X O O O O O O O MAX (X) X O X O X O X X X X X X X MIN (O) X O X X O X X O X . . . . . . . . . . . . . . . . . . . . . TERMINAL X X -1 0 +1 Utility Chapter 5 5 Minimax Perfect play for deterministic, perfect-information games Idea: choose move to position with highest minimax value = best achievable payoff against best play E.g., 2-ply game: MAX 3 12 8 6 4 2 14 5 2 MIN 3 A 1 A 3 A 2 A 13 A 12 A 11 A 21 A 23 A 22 A 33 A 32 A 31 3 2 2 Chapter 5 6 Minimax algorithm function Minimax-Decision ( state ) returns an action inputs : state , current state in game return the a in Actions ( state ) maximizing Min-Value ( Result ( a , state )) function Max-Value ( state ) returns a utility value if Terminal-Test ( state ) then return Utility ( state ) v ←-∞ for a, s in Successors ( state ) do v Max ( v , Min-Value ( s )) return v function Min-Value ( state ) returns a utility value if Terminal-Test ( state ) then return Utility ( state ) v ←∞ for a, s in Successors ( state ) do v Min ( v , Max-Value ( s )) return v Chapter 5 7 Properties of minimax Complete ??
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