# bab4d - Search Techniques: Minimax Two-ply minimax and one...

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Search Techniques: Minimax Ch04C / 1 Two-ply minimax and one of two possible MAX second moves of tic-tac-toe from Nilsson (1971).

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Search Techniques: Minimax Ch04C / 2 Two-ply minimax applied to X’s move near the end of the game of tic-tac-toe from Nilsson (1971).
Search Techniques: Minimax Ch04C / 3 Minimax procedure is impractical because the game tree for any interesting games is extremely large. If there are a minimum of b options for each player on each turn and the minimum number of moves required to end in a win or a draw is d , then the procedure wil take time proportional to b d .

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Search Techniques: Alpha-Beta Pruning Ch04C / 4 Alpha-Beta Pruning Minimax procedure requires two-pass analysis of the search space: If we know half-way through a calculation that it will succeed or fail, then there is no point doing the rest of it. For example 1, in programming language if (A > 10 or B < 0) or if(A > 10 and B < 0) statement 1; statement 2; If we have an idea that is surely bad, do not take time to see how truly awful it is. First to descend to the ply depth and there apply the heuristic Second to propagate values back up the tree. Minimax pursues all branches in the space, including many that could be ignored or pruned by a more intelligent algorithm. If first condition is succeed (A > 10 - true) there is no need to bother trying the second condition. For example 2, in programming language if (A > 10 or B < 0) // no point continuing if the first condition statement 1; // is fails (A > 10 – false)
Search Techniques: Alpha-Beta Pruning Ch04C / 5 The idea is called alpha-beta principle which uses two parameters, traditionally called alpha and beta, to keep track expectations. In the special context of games, the alpha-beta principle dictates that, whenever we discover a fact about a given node, we should check what we know about the ancestor nodes. It may be that the best that we can hope for at the parent node can be revised or determined exactly. It may be that no further work is sensible below the parent node.

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## This note was uploaded on 10/23/2011 for the course ENCS ENCS5 taught by Professor Abdelsalam during the Spring '10 term at Birzeit University.

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bab4d - Search Techniques: Minimax Two-ply minimax and one...

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