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quiz2_2010

# quiz2_2010 - 6.034 Quiz 2 20 October 2010 Name email Circle...

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6.034 Quiz 2 20 October 2010 Name email

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Problem 1: Games (50 points) Part A: Minimax (10 points) A1: Perform Minimax (5 points) Perform the minimax algorithm, without alpha-beta, on this tree. Write the minimax value at each node . A2: Rotate the Tree (5 points) Using the minimax calcluations from part A1, without performing any alpha-beta calculation, rotate the children of each node in the above tree at every level to ensure maximum alpha-beta pruning . 2
Part B: Alpha Beta (30 points) While playing a game, you find yourself in the situation indicated by the following tree. Because this tree is difficult to read, the the tree has been broken into two subtrees, shown on the next two pages. Do all your work on those subtrees, not the tree shown above. The tree above is merely meant to show how the two subtrees connect. Note that the root node AA is shown in both halves. B1 The Game Tree (7 points) You are provided with static values at all the nodes. In this part of the problem, you are to ignore the static values at intermediate notes. You are to use only the values on the leaf nodes. Perform the alpha-beta algorithm on the graph tree on the next two pages. 1) Use the boxes to help you perform your alpha-beta calculations as needed. 2) Draw an 'X' through any branch that is blocked from further consideration by an alpha-beta calculation. 3) Assume no progressive deepening 3

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B2 Evaluations (20 points) How many nodes were statically evaluated and which were they? # Evals __________ Nodes: _________________________________________________ B3 Move (3 points) What move is chosen as the best? What node in the deepest level is the maximizing player trying to move towards? AA-->__________ Moving Toward: __________ 6
Part C: Progressive Deepening (10 points) Assume you have the same setup as in Part B , except this time, you have an 5-second time-limit for each move. Each static evaluation takes 1 second . Assume there is no time associated with building the alpha-beta tree and no time associated with performing the alpha beta search. You are to use progressive deepening and alpha-beta together.

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quiz2_2010 - 6.034 Quiz 2 20 October 2010 Name email Circle...

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