lecture4 ch5

Artificial Intelligence: A Modern Approach

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1 ICS-171:Lecture 4: 1 Lecture 4: Game Playing and Search ICS 171, Summer 2000 ICS-171:Lecture 4: 2 Outline Computer programs which play 2-player games game-playing as search with the complication of an opponent General principles of game-playing and search evaluation functions, minimax principle alpha-beta-pruning, heuristic techniques Status of Game-Playing Systems in chess, checkers, backgammon, Othello, etc, computers routinely defeat leading world players Applications? think of “nature” as an opponent: economics, medicine, etc
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2 ICS-171:Lecture 4: 3 Chess Rating Scale 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 1966 1971 1976 1981 1986 1991 1997 Ratings Garry Kasparov (current World Champion ) Deep Blue Deep Thought ICS-171:Lecture 4: 4 Game-Playing and AI Game-playing is a good problem for AI research: all the information is available i.e., human and computer have equal information game-playing is non-trivial need to display “human-like” intelligence some games (such as chess) are very complex requires decision-making within a time-limit more realistic than other search problems games are played in a controlled environment can do experiments, repeat games, etc: good for evaluating research systems can compare humans and computers directly can evaluate percentage of wins/losses to quantify performance
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3 ICS-171:Lecture 4: 5 Search and Game Playing Consider a board game e.g., chess, checkers, tic-tac-toe configuration of the board = unique arrangement of “pieces” each possible configuration = state in search space Statement of Game as a Search Problem States = board configurations Operators = legal moves Initial State = current configuration Terminal State (Goal ) = winning configuration ICS-171:Lecture 4: 6 Game Tree Representation New aspect to search problem there’s an opponent we cannot control how can we handle this? S Computer Moves Opponent Moves Computer Moves G Possible Goal State lower in Tree (winning situation for computer)
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4 ICS-171:Lecture 4: 7 Complexity of Game Playing Imagine we could predict the opponent’s moves given each computer move How complex would search be in this case? worst case, it will be O(b d ) – Chess: b ~ 35 (average branching factor) d ~ 100 (depth of game tree for typical game) • b d ~ 35 100 ~10 154 nodes!! (“only” about 10 40 legal states) – Tic-Tac-Toe ~5 legal moves, total of 9 moves • 5 9 = 1,953,125 9! = 362,880 (Computer goes first) 8! = 40,320 (Computer goes second) well-known games can produce enormous search trees ICS-171:Lecture 4: 8 Utility Functions Utility Function: defined for each terminal state in a game assigns a numeric value for each terminal state these numbers represent how “valuable” the state is for the computer positive for winning negative for losing zero for a draw Typical values from -infinity (lost) to +infinity (won) or [-1, +1].
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5 ICS-171:Lecture 4: 9 Greedy Search with Utilities A greedy search strategy using utility functions
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