This document discusses alpha-beta pruning, an algorithm used to prune branches in decision trees during game tree search. It uses alpha and beta values to discard branches that cannot possibly change the outcome. The algorithm is demonstrated on a sample decision tree for a game with nodes A, B, C, and D showing how alpha (the best value for maximizing player) and beta (the best value for minimizing player) are updated during the search to prune branches until a terminal node is reached.

1. 17
ADVERSARIAL SEARCH
ALPHA-BETA PRUNING

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ALPHA-BETA PRUNING.
A
B D
C
MAX
MIN
3 8
12 6
4
2 14 5 2
3 2 2
3
a1
a2
b1
b2
b3 c1
c2
c3 d1
d2
d3
Terminal

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ALPHA-BETA PRUNING.
A
B
MAX
MIN
3 8
12
[-∞,3]
[-∞, ∞]
α= The value of the best (highest value)
choice we have found so far at any choice
point along the path for MAX.
β= The value of the best (lowest value)
choice we have found so far at any choice
point along the path for MIN.
If α > β Prune
Terminal

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ALPHA-BETA PRUNING.
A
B D
C
MAX
MIN
3 8
12 6
4
2 14 5 2
[3,3]
[3, ∞]
[-∞,2]
[-∞,14]

5. Subscribe
ALPHA-BETA PRUNING.
A
B D
C
MAX
MIN
3 8
12 6
4
2 14 5 2
[3,3]
[3, 3]
[-∞,2]
[2,2]
Terminal

6. Example
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A
D E F G
B
C
2 3 -5
6 -3
MAX
MAX
MIN
Terminal
Complexity
Best Case: O(bd/2 )
Worst Case: O(bd )
=
3
β=min<3
=max>6
β=3
=max>3
=-3
β=min<-3
=
3

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Reference:
Artificial Intelligence
A Modern Approach Third Edition
Peter Norvig and Stuart J. Russell
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