SP10 cs188 lecture 7 -- expectimax search (2PP) (1)

# SP10 cs188 lecture 7 -- expectimax search (2PP) (1) - CS...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 7: Minimax and Alpha-Beta Search 2/9/2010 Pieter Abbeel – UC Berkeley Many slides adapted from Dan Klein 1 Simple two-player game example 2 8 2 5 6 max min

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2 Tic-tac-toe Game Tree 3 Deterministic Games s Many possible formalizations, one is: s States: S (start at s 0 ) s Players: P={1. ..N} (usually take turns) s Actions: A (may depend on player / state) s Transition Function: SxA S s Terminal Test: S {t,f} s Terminal Utilities: SxP R s Solution for a player is a policy: S A 4
3 Deterministic Single-Player? s Deterministic, single player, perfect information: s Know the rules s Know what actions do s Know when you win s E.g. Freecell, 8-Puzzle, Rubik’s cube s … it’s just search! s Slight reinterpretation: s Each node stores a value : the best outcome it can reach s This is the maximal outcome of its children (the max value ) s Note that we don’t have path sums as before (utilities at end) s After search, can pick move that leads to best node win lose lose 5 Deterministic Two-Player s E.g. tic-tac-toe, chess, checkers s Zero-sum games s One player maximizes result s The other minimizes result

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## This note was uploaded on 03/01/2010 for the course COMPUTER S 188 taught by Professor Abbel during the Spring '10 term at Berkeley.

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SP10 cs188 lecture 7 -- expectimax search (2PP) (1) - CS...

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