1. CS 460 Spring 2011
Lecture 4

2. Overview Review Adversarial Search / Game Playing
(chap 5 3rd ed, chap 6 2nd ed)

3. Review Evaluation of strategies Informed Search Local Search
Completeness, time & space complexity, optimality
Informed Search
Best First
Greedy Best First
Heuristics: A*
Admissible, Consistent
Relaxed problems
Dominance
Local Search
Hill climbing / gradient ascent
Simulated annealing
K-beam
Genetic algorithms

4. Game playing /Adversarial search

7. Game tree (2-player, deterministic, turns)

9. Minimax

10. Properties of minimax Complete? Yes (if tree is finite)
Optimal? Yes (against an optimal opponent)
Time complexity? O(bm)
Space complexity? O(bm) (depth-first exploration)
For chess, b ≈ 35, m ≈100 for "reasonable" games  exact solution completely infeasible
Do we need to explore every path?

11. α-β pruning example

12. α-β pruning example

13. α-β pruning example

14. α-β pruning example

15. α-β pruning example

16. Properties of α-β Pruning does not affect final result
Good move ordering improves effectiveness of pruning
With "perfect ordering," time complexity = O(bm/2)
 doubles solvable depth of search
A simple example of the value of reasoning about which computations are relevant (a form of metareasoning)
Unfortunately, 35**50 is still an impossible number of searches

17. 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

18. Alpha-beta algorithm