Introduction to Artificial Intelligence

CS 438 Spring 2008• Today

– AIMA, Ch. 6– More Adversarial

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• Next Tuesday– AIMA, Ch. 13– Reasoning with

Uncertainty

SOE Open House

• Schedule

• EB 2029

• Activity– Man vs Machine Reversi– Class folder

• Open House

Assignment 3: Game Playing

• It Tourney Time!

Minimax Recap

α-β pruning• Strategy

– Any path that is being expanded that is clearly worse than any known path can be abandoned early.

Why is it called α-β?

• α is the value of the best (i.e., highest-value) choice found so far at any choice point along the path for max

• If v is worse than α, max will avoid it prune that branch

• Define β similarly for min

–•

α-β pruning

• α (alpha): Best choice for max• β (beta): Best choice for min

if maxChoice >= β then prune

if minChoice <= α then prune

α-β pruning example

α-β pruning example

if maxChoice >= β then prune

if minChoice <= α then prune

α-β pruning example

if maxChoice >= β then prune

if minChoice <= α then prune

α-β pruning example

if maxChoice >= β then prune

if minChoice <= α then prune

α-β pruning example

if α >= β then prune

if β <= α then prune

The α-β algorithm

The α-β algorithm

How many states can be avoided?

• It depends on the order states are generated in– If the best moves for each player are

generated first then significant pruning can occur

– If the worst moves are generated first then NO pruning can occur