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Unformatted text preview: nodes intermediate and final values for , , and v . v : Nau: Game Theory 4 Updated 10/5/11 v : 1 1 1 1 1 1 1 1 Homework 4.4. At each node x of the tree shown below, let v ( x ) be x s minimax value. Suppose Max uses an evaluation function e ( x ) that returns v ( x ) with probability 0.9, and v ( x ) with probability 0.1. At the root node, what is Maxs probability of choosing the best move if Max searches (a) to depth 1? (b) to depth 2? (c) to depth 3? Nau: Game Theory 5 Updated 10/5/11 Homework 4.5. Let x and y be Pgame boards of size 2 2 (hence it is Mins move at both x and y). Suppose that e(x) = e(y) = 1/2, where e is the evaluation function that counts the fraction of 1 squares in the board. (a) What is the probability that x is a forced win for Max? Explain why. (b) Suppose Max is trying to choose whether to move to x or to y. What is the probability that Max is at a critical node?...
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 Fall '11
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