383-Fall11-Lec8 - 1 CMPSCI 383 September 29, 2011...

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Unformatted text preview: 1 CMPSCI 383 September 29, 2011 Adversarial Search 2 Why are games interesting to AI? Simple to represent and reason about Must consider the moves of an adversary Time constraints Russell & Norvig say: Games, like the real world, therefore require the ability to make some decision even when calculating the optimal decision is infeasible. Metareasoning: reasoning about reasoning 3 Searched up to 30 billion positions per move; sometimes reaching a depth of 40 plies. 1997 4 Dr. Marion Tinsley Chinook 1990, 1994 5 6 7 8 Todays lecture Introduce search in adversarial environments Key concepts Game tree Min and Max players Minimax value Methods for searching realistic game trees Alpha-beta pruning Approximate evaluation functions Games with chance elements 9 CSP terminology This data structure is defined by the initial game state and the legal moves for each player This is the value of a node for a given player, assuming that both players play optimally to the end of the game. This is a level of the search tree defined by a move by a single player What is a Game tree What is the minimax value What is a Ply 10 Game tree (2=player, deterministic, turns) 11 Minimax algorithm Perfect play for deterministic games Idea select moves with highest minimax value . That is, select the best achievable payoff against best play by your opponent 12 Minimax algorithm 13 Properties of minimax Complete? Yes (if tree is finite) Optimal? Yes (against optimal opponent) Time complexity O(b m ) Space complexity O(bm) (depth-first) but for chess, b 35, m 100 Exact solution is completely infeasible 14 Adversarial search terminology This method can eliminate large portions of the game tree from consideration, thus speeding up search. This expression returns an estimate of the expected utility of the game for a given position What is Alpha-beta pruning What is an Evaluation function 15 How does pruning work? 16 Using DFS, can we prune this tree? Using DFS, can we prune this tree?...
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383-Fall11-Lec8 - 1 CMPSCI 383 September 29, 2011...

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