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# Adversarial Search - PowerPoint PPT Presentation

Adversarial Search Chapter 6 Section 1 – 4 Games vs. search problems "Unpredictable" opponent  specifying a move for every possible opponent reply Time limits  unlikely to find goal, must approximate Solutions Search problems: a path Games: a strategy But how?

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Presentation Transcript

Chapter 6

Section 1 – 4

Games vs. search problems
• "Unpredictable" opponent  specifying a move for every possible opponent reply
• Time limits  unlikely to find goal, must approximate
• Solutions
• Search problems: a path
• Games: a strategy
• But how?
Minimax
• Perfect play for deterministic games
• Idea: choose move to position with highest minimax value = best achievable payoff against best play
• E.g., 2-ply game:
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
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)
• A simple example of the value of reasoning about which computations are relevant (a form of meta-reasoning)
Resource limits

Suppose we have 100 secs, explore 104 nodes/sec106nodes per move

Standard approach:

• cutoff test:

e.g., depth limit (perhaps add quiescence search)

Explore nonquiescent positions further until quiescence

• evaluation function

= estimated desirability of position

Evaluation functions
• For chess, typically linear weighted sum of features

Eval(s) = w1 f1(s) + w2 f2(s) + … + wn fn(s)

• e.g., w1 = 9 with

f1(s) = (number of white queens) – (number of black queens), etc.

Cutting off search

MinimaxCutoff is identical to MinimaxValue except

• Terminal? is replaced by Cutoff?
• Utility is replaced by Eval

Does it work in practice?

bm = 106, b=35  m=4

4-step lookahead is a hopeless chess player!

• 4-step ≈ human novice
• 8-step ≈ typical PC, human master
• 12-step ≈ Deep Blue, Kasparov