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quiz2_2009 - 6.034 Quiz 2 Name EMail Circle your TA and...

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6.034 Quiz 2 October 21, 2009 Name EMail Circle your TA and recitation time, if any, so that we can more easily enter your score in our records and return your quiz to you promptly. TAs Erica Cooper Matthew Peairs Charles Watts Mark Seifter Yuan Shen Jeremy Smith Olga Wichrowska Thu Time Instructor 11-12 Gregory Marton 12-1 Gregory Marton 1-2 Bob Berwick 2-3 Bob Berwick 3-4 Bob Berwick Fri Time Instructor 1-2 Randall Davis 2-3 Randall Davis 3-4 Randall Davis Problem number Maximum Score Grader 1 50 2 50 Total 100 There are 11 pages in this quiz, including this one. In addition, tear-off sheets are provided at the end with duplicate drawings and data. As always, open book, open notes, open just about everything. 1
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Problem 1:Games (50 points) For your reference in working this problem, pseudo code for the standard version of minimax with alpha beta is given on the tear off sheet at the end. Part A: Working with a maximally pruned tree (25 points) For the following min-max tree, cross out those leaf nodes for which alpha-beta search would not do static evaluations in the best case possible (minimum number of static evaluations, maximum pruning of nodes to be statically evaluated). MAX MIN MAX MIN Part A1 Now, list the leaf nodes at which alpha-beta would do static evaluations in the best case possible. 2
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Part A2 What is the final value returned by the alpha beta search in the best case possible for the given tree? Express your answer as the simplest function of the static values of the leaf nodes (e.g. take n to be the static value at the leaf node labeled n). Your function may contain operations such as max and min . Part A3 What constraints ensure best case possible (minimum static evaluation) for the given tree? State your constraints as inequalities on the static values of the leaf nodes. Part A4 Suppose your static evaluation function, S ( node), is modified as follows: S'( node) = 42 x S ( node) + 1000. (If S(node) = 1, S'(node) = 1042) Would your answer for Part A1 be the same for all possible S(node) values?
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