Adversarial Search
Game playing
 Multi-agent
competitive environment
 The most common games are deterministic, turntaking, 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 X
X
X O O
X O X
O X
O
X O X
O O X
X X O
+1
-1
0
 Two
players, max and min
 Loop:



Max put X
Min put O
Until one play takes 3 contiguous space or all spaces are filled
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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
[4,
4 +∞]
max
min
4
[-∞, 3]
[-∞, 3]
max
(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 explored
Randomized order works reasonably well
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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
HW1 due next Monday,
Exam 1 on next Monday
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