CS10 : The Beauty and Joy of Computing
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1 CS10 : The Beauty and Joy of Computing Lecture #16 : Computational Game Theory UC Berkeley EECS Summer Instructor Ben Chun CHECKERS SOLVED! 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!
2 Computational Game Theory History Definitions Game Theory What Games We Mean Win, Lose, Tie, Draw Weakly / Strongly Solving Gamesman Dan s Undergraduate R&D Group Demo!! Future UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (2)
3 Computer Science A UCB view CS research areas: Artificial Intelligence Biosystems & Computational Biology Computer Architecture & Engineering Database Management Systems Graphics Human-Computer Interaction Operating Systems & Networking Programming Systems Scientific Computing Security Theory UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (3)
4 en.wikipedia.org/wiki/the_turk The Turk (1770) A Hoax! Built by Wolfgang von Kempelen to impress the Empress Could play a strong game of Chess thanks to Master inside Toured Europe Defeated Benjamin Franklin & Napoleon! Burned in an 1854 fire Chessboard saved The Mechanical Turk (1770) UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (4)
5 en.wikipedia.org/wiki/claude_shannon Claude Shannon s Paper (1950) Father of Information Theory Digital computer and digital circuit design theory Defined fundamental limits on compressing/storing data Wrote Programming a Computer for Playing Chess paper in (1950) All chess programs today have his theories at their core His estimate of # of Chess positions called Shannon # Now proved < ~ Claude Shannon ( ) UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (5)
6 en.wikipedia.org/wiki/deep_blue_(chess_computer) Deep Blue vs Garry Kasparov (1997) Kasparov World Champ 1996 Tournament Deep Blue First game DB wins a classic! But DB loses 3 and draws 2 to lose the 6-game match 4-2 In 1997 Deep Blue upgraded, renamed Deeper Blue 1997 Tournament Deeper Blue GK wins game 1 GK resigns game 2 even though it was draw! DB & GK draw games 3-5 Game 6 : (May 11 th ) Kasparov blunders move 7, loses in 19 moves. Loses tournament 3 ½ - 2 ½ GK accuses DB of cheating. No rematch. Defining moment in AI history IBM s Deep Blue vs Garry Kasparov UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (6)
7 What is Game Theory? Combinatorial Sprague and Grundy s 1939 Mathematics and Games Board games Nim, Domineering, dots and boxes Film: Last Year in Marienbad Complete info, alternating moves Goal: Last move Computational R. C. Bell s 1988 Board and Table Games from many Civilizations Board games Tic-Tac-Toe, Chess, Connect 4, Othello Film : Searching for Bobby Fischer Complete info, alternating moves Goal: Varies Economic von Neumann and Morgenstern s 1944 Theory of Games and Economic Behavior Matrix games Prisoner s dilemma, auctions Film : A Beautiful Mind (about John Nash) Incomplete info, simultaneous moves Goal: Maximize payoff UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (7)
8 What Board Games do you mean? No chance, such as dice or shuffled cards Both players have complete information No hidden information, as in Stratego or Magic Two players (Left & Right) usually alternate moves Repeat & skip moves ok Simultaneous moves not ok The game can end in a pattern, capture, by the absence of moves, or UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (8)
9 What s in a Strong Solution For every position Assuming alternating play Value (for player whose turn it is) Winning ( losing child) Losing (All children winning) Tieing (! losing child, but tieing child) Drawing (can t force a win or be forced to lose) Remoteness How long before game ends? W..." W W W T..." W W W L T L..." W W W D D..." W W W W W UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (9)
10 GamesCrafters A groups that strongly solves abstract strategy games and puzzles 70 games / puzzles in our system Allows perfect play against an opponent Ability to do a postgame analysis UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (10)
11 What did you mean strongly solve? Wargames (1983) UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (11)
12 Thanks to Jonathan U Alberta for this slide Weakly Solving A Game (Checkers) Master: main line of play to consider Workers: positions to search Endgame databases (solved) Log of Search Space Size UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (12)
13 Strong Solving Example: 1,2,,10 Rules (on your turn): Running total = 0 Rules (on your turn): Add 1 or 2 to running total Goal Be the FIRST to get to 10 Example Ana: 2 to make it 2 Bob: 1 to make it 3 Ana: 2 to make it 5 Bob: 2 to make it 7 photo Ana: 1 to make it 8 Bob: 2 to make it 10 I WIN! 7 ducks (out of 10) UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (13)
14 Example: Tic-Tac-Toe Rules (on your turn): Place your X or O in an empty slot on 3x3 board Goal If your make 3-in-a-row first in any row / column / diag, win Else if board is full with no 3-in-row, tie Misére is tricky 3-in-row LOSES Pair up and play now, then swap who goes 1st Values Visualization for Tic-Tac-Toe UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (14)
15 Tic-Tac-Toe Answer Visualized! Recursive Values Visualization Image Misére Tic-tac-toe Outer rim is position Inner levels moves Legend Lose Tie Win Misére Tic-Tac-Toe 2-ply Answer UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (15)
16 GamesCrafters.berkeley.edu GamesCrafters (revisited) Undergraduate Computational Game Theory Research Group 300 students since 2001 We 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 (16)
17 Connect 4 Solved, Online! Just finished a solve of Connect 4!! It took 30 Machines x 8 Cores x 1 weeks Win for the first player (go in the middle!) 3,5 = tie 1,2,6,7 = lose Come play online! UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (17)
18 Gamescrafters.berkeley.edu! Future Board 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 ply One by one, we re going to solve them and/or beat humans We ll never solve some E.g., hardest game : Go Strongly solving (GamesCrafters) We visit EVERY position, and know value of EVERY position E.g., Connect 4 Weakly solving (Univ Alberta) Go s search space ~ 3361 We prove game s value by only visiting SOME positions, so we only know value of SOME positions E.g., Checkers UC Berkeley CS10 The Beauty and Joy of Computing : Computational Game Theory (18)
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