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Tic-tac-toe XOX X XOO 3 u Two players, max and min u Loop: u Max put X u Min put O u Until one play takes 3 contiguous space or all spaces are filled +1 XOX OX O XOX OOX XXO 0
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Adversarial Search
Game playing
Multi-agent competitive environment The most common games are deterministic, turn-
taking, two-player, zero-sum game of perfect information
In AI terminology: deterministic, fully observable, two agents act alternately, the utility values at then end are always equal and opposite
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Tic-tac-toe
X O XX
X O O
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Two players, max and min Loop:
Max put X Min put O Until one play takes 3 contiguous space or all spaces are filled
+1
X O XO XO-1
X O XO O XX X O
0
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Higher values are good for max,but bad for min
MAX assumes that min plays optimally What if MIN does not play optimally?
Is MAX still optimal?
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Another example
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max
min
max
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[4, +∞]
[-∞, 3]
(3)
[-∞, 3]
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Assuming a left-to-right evaluation of the tree, give the most general relation between x, y, z, w, k, l and m that must hold such that the tree in the dotted part would be pruned by alpha-beta pruning
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Move ordering
Best ordering leads to O(bm/2) time complexity
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The perfect order is not known until all child nodes are exploredRandomized order works reasonably well
Summary Deterministic, turn-taking, two-player, zero-sum
game of perfect information Minimax algorithm, optimal for optimal player Not all nodes need to be explored, alpha-beta
pruning
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HW1 due next Monday,Exam 1 on next Monday