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games_probs

# games_probs - MIT EECS 6.034 Articial Intelligence(Fall...

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MIT EECS 6.034: Artificial Intelligence (Fall 2006) Instructor: Luis E. Ortiz Practice Problems on Search in Games Original date: October 8, 2005; Last revised: October 22, 2006 For all the problems in this document, Minimax refers to the minimax algorithm, while Alpha- Beta refers to minimax with alpha-beta pruning. 1. Consider the following game tree. MAX V K W P Q R S T L E F G H J U C B A D I M N O 9 1 2 7 5 3 1 5 9 2 6 8 3 9 MAX MIN MAX MIN Assume that the children of each node are evaluated from left to right. (a) Use the Minimax to compute the value of each node in the game tree. (b) List the nodes that are evaluated by Alpha-Beta . (c) Redraw the game tree such that Alpha-Beta performs the minimum number of evalu- ations (i.e., the best case for Alpha-Beta ). How many nodes are evaluated by Alpha- Beta in the resulting game tree? (d) Redraw the game tree such that Alpha-Beta performs the maximum number of eval- uations (i.e., the worst case for Alpha-Beta ). How many nodes are evaluated by Alpha-Beta in the resulting game tree?

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games_probs - MIT EECS 6.034 Articial Intelligence(Fall...

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