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CS10 The Beauty and Joy of Computing Lecture #22 : Computational Game Theory 2011-04-18. UC Berkeley EECS Lecturer SOE Dan Garcia. - PowerPoint PPT Presentation

CS61C - Lecture 13

CS10The Beauty and Joy of Computing

Lecture #22 : Computational Game Theory

2011-04-18Checkers 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, Spring 2011HistoryDefinitionsGame 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011CS 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011A 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011The 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 #Now proved < 2155 ~ 1046.7

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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011Kasparov World Champ1996 Tournament Deep BlueFirst 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 Tournament Deeper BlueGK 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011Economicvon 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 20117No 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 20118Whats 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 20119

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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011What did you mean strongly solve?

Wargames (1983)UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011Peer InstructionEvery year computer power (speed, storage) is growing exponentially, so eventually theyll be able to strongly solve the worlds board games.

Im happy when a game is strongly solved. 12a) FFb) FTc) TFd) TT

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011Weakly Solving A Game (Checkers)

Endgame databases(solved)Master:main line ofplay to considerWorkers: positions to searchLog of Search Space SizeThanks to Jonathan Schaeffer @ U Alberta for this slideUC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011Strong 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 201114Example: 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, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 201115Tic-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, Spring 201116GamesCraftersGamesCrafters.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, Spring 201117Connect 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 = loseCome play online!

UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011Board games are exponential So 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 : GoStrongly solving (GamesCrafters)We visit EVERY position, and know value of EVERY positionE.g., Connect 4Weakly solving (Univ Alberta)We prove games value by only visiting SOME positions, so we only know value of SOME positionsE.g., Checkers

FutureGos search space ~ 336117408965065903192790718823807056436794660272495026354119482811870680105167618464984116279288988714938612096988816320780613754987181355093129514803369660572893075468180597603Gamescrafters.berkeley.eduUC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 2011UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (#)Garcia, Spring 201119