Click here to load reader

prev

next

of 18

View

33Download

0

Tags:

Embed Size (px)

DESCRIPTION

CS10 The Beauty and Joy of Computing Lecture #22 : Computational Game Theory 2010 -11- 17. UC Berkeley EECS Lecturer SOE Dan Garcia. - PowerPoint PPT Presentation

CS61C - Lecture 13

CS10The Beauty and Joy of Computing

Lecture #22 : Computational Game Theory

2010-11-17Checkers solved in 2007!A 19-year project led by Prof Jonathan Schaeffer, he used dozens (sometimes hundreds) of computers and AI to prove it is, in perfect play, a draw! This means that if two Gods were to play, nobody would ever win!UC Berkeley EECSLecturer SOEDan Garciawww.cs.ualberta.ca/~chinook/

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010HistoryDefinitionsGame TheoryWhat Games We MeanWin, Lose, Tie, DrawWeakly / Strongly SolvingGamesmanDans Undergraduate R&D GroupDemo!!FutureComputational Game Theory

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010CS research areas:Artificial IntelligenceBiosystems & Computational BiologyComputer Architecture & EngineeringDatabase Management SystemsGraphicsHuman-Computer InteractionOperating Systems & NetworkingProgramming SystemsScientific ComputingSecurityTheoryComputer Science A UCB view

www.eecs.berkeley.edu/Research/Areas/UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010A Hoax!Built by Wolfgang von Kempelen to impress the EmpressCould play a strong game of ChessThanks to Master insideToured EuropeDefeated Benjamin Franklin & Napoleon!Burned in an 1854 fireChessboard savedThe Turk (1770)The Mechanical Turk (1770)

en.wikipedia.org/wiki/The_TurkUC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010The Father of Information TheoryFounded the digital computerDefined fundamental limits on compressing/storing dataWrote Programming a Computer for Playing Chess paper in 1950C. Shannon, Philos. Mag. 41, 256 (1950).All chess programs today have his theories at their coreHis estimate of # of Chess positions called Shannon #

Claude Shannons Paper (1950)en.wikipedia.org/wiki/Claude_Shannon#Shannon.27s_computer_chess_programClaude Shannon (1916-2001)UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010Kasparov World Champ1996 TournamentFirst game DB wins a classic!But DB loses 3 and draws 2 to lose the 6-game match 4-2In 1997 Deep Blue upgraded, renamed Deeper Blue1997 TournamentGK wins game 1GK resigns game 2even though it was draw!DB & GK draw games 3-5Game 6 : 1997-05-11 (May 11th)Kasparov blunders move 7, loses in 19 moves. Loses tournament 3 - 2 GK accuses DB of cheating. No rematch.Defining moment in AI history

Deep Blue vs Garry Kasparov (1997)en.wikipedia.org/wiki/Deep_Blue_(chess_computer)IBMs Deep Blue vs Garry Kasparov

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010Economicvon Neumann and Morgensterns 1944 Theory of Games and Economic BehaviorMatrix gamesPrisoners dilemma, auctionsFilm : A Beautiful Mind (about John Nash)Incomplete info, simultaneousmovesGoal: Maximize payoff ComputationalR. C. Bells 1988 Board and Table Games from many CivilizationsBoard gamesTic-Tac-Toe, Chess, Connect 4, OthelloFilm : Searching for Bobby FischerComplete info, alternating movesGoal: VariesCombinatorialSprague and Grundys 1939 Mathematics and GamesBoard gamesNim, Domineering, dots and boxesFilm: Last Year in MarienbadComplete info, alternating movesGoal: Last movewww.cs.berkeley.edu/~ddgarcia/eyawtkagtbwataWhat is Game Theory?UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 20107No chance, such as dice or shuffled cardsBoth players have complete informationNo hidden information, as in Stratego & MagicTwo players (Left & Right) usually alternate movesRepeat & skip moves okSimultaneous moves not okThe game can end in a pattern, capture, by the absence of moves, or

What Board Games do you mean?UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 20108Whats in a Strong SolutionFor every positionAssuming alternating playValue (for player whose turn it is) Winning ( losing child) Losing (All children winning) Tieing (! losing child, but tieing child) Drawing (cant force a win or be forced to lose)RemotenessHow long before game ends?WWWW...LLWWW...WTWWW...TDWWWDW...UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 20109

We strongly solve abstract strategy games and puzzles70 games / puzzles in our systemAllows perfect play against an opponentAbility to do a post-game analysisGamesCraftersUC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010What did you mean strongly solve?

Wargames (1983)UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010Weakly Solving A Game (Checkers)

Endgame databases(solved)Master:main line ofplay to considerWorkers: positions to searchLog of Search Space SizeThanks to Jonathan Schaeffer for this slideUC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010Strong Solving Example: 1,2,,10Rules (on your turn):Running total = 0Rules (on your turn):Add 1 or 2 to running totalGoalBe the FIRST to get to 10ExampleAna: 2 to make it 2Bob: 1 to make it 3Ana: 2 to make it 5Bob: 2 to make it 7 photoAna: 1 to make it 8Bob: 2 to make it 10 I WIN!7 ducks (out of 10)

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 201013Example: Tic-Tac-ToeRules (on your turn):Place your X or O in an empty slot on 3x3 boardGoalIf your make 3-in-a-row first in any row / column / diag, winElse if board is full with no 3-in-row, tieMisre is tricky3-in-row LOSESPair up and play now, then swap who goes 1st

Values Visualization for Tic-Tac-ToeUC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 201014Tic-Tac-Toe Answer Visualized!Recursive Values Visualization ImageMisre Tic-tac-toeOuter rim is positionInner levels movesLegendLoseTieWinMisre Tic-Tac-Toe 2-ply AnswerUC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 201015GamesCraftersGamesCrafters.berkeley.eduUndergraduate Computational Game Theory Research Group300 students since 2001We now average 20/semester!They work in teams of 2+Most return, take more senior roles (sub-group team leads)Maximization (bottom-up solve)Oh, DeepaBlue (parallelization)GUI (graphical interface work)Retro (GUI refactoring)Architecture (core)New/ice Games (add / refactor)Documentation (games & code)

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 201016Connect 4 Solved, Online!Weve just finished a solve of Connect 4!!It took 30 Machines x 8 Cores x 1 weeksWin for the first player (go in the middle!)3,5 = tie1,2,6,7 = lose

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010Board games are exponential in natureSo has been the progress of the speed / capacity of computers!Therefore, every few years, we only get to solve one more plyOne by one, were going to solve them and/or beat humansWell never solve someE.g., hardest game : Go

FutureGos search space ~ 336117408965065903192790718823807056436794660272495026354119482811870680105167618464984116279288988714938612096988816320780613754987181355093129514803369660572893075468180597603UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 2010UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Fall 201018