Acknowledgements Portions of this are taken from MIT’s open-courseware http://ocw.mit.edu/http://ocw.mit.edu/ Some items are adapted from Chapter 5 on Games by some professor who adapted it from notes by Charles R. Dyer, University of Wisconsin-Madison
Why Play? Humans play for enjoyment, but computers…? Games of strategy and skill require “intelligence”. We may learn about thinking by learning how to teach computers. Hard but well defined problems, unlike other AI problems like speech, ethics etc. Competition, knowledge-representation, … To provide entertainment, competition and training to humans (that play or program).
Game Theory Von Neumann and Morgenstern analyzed two person zero-sum games, where each person takes a decision simultaneously, and then gets paid according to a payoff matrix. Economic games, can be multi-person, multi- stage. Enemy Strategy AB My Stra tegy X10-10 Y-240
Board Games Two Person Alternating moves Zero Sum Deterministic(not Backgammon or Ludo) Perfect Information (not Bridge, Hearts) Examples Tic-Tac-Toe Checkers Chess Go Reversi (Othello)
History 1949 Claude Shannon paper on Chess 1951 Alan Turing simulation on Checkers 1955 Chess Program using α-β. 1966 MacHack 1990 Belle (harware assist) 2000 Deep Blue (serious hardware)
Top-down Program Repeat Until Done DrawBoard GetPlayerMove CheckLegalMove‘also check if game over MakePlayerMove DrawBoard FindLegalMoves‘also check if game over EvaluateLegalMoves MakeBestMove
Static Position Evaluator Given a position, come up with a “value”. Values are 0…1 or 0…infinity or – infinity…infinity. 0..1 can represent “probability” of my lose/win In chess can count my pieces – enemy pieces. my total piece value – enemy total piece value. Add points for Mobility Add points for Center Control Negative points for exposed king, etc. This is where humans experts excel.
Crude Evaluator You can start off with a crude static evaluator, and a high ply minimax. Russians believed that better would be an excellent but slow static evaluator with lower plies. The extreme strategies are of course a perfect evaluator with 1-ply Or the complete game-tree search with trivial evaluator.
Deep Blue 32 node supercomputer, each with eight special chess processors. 50 – 100 billion moves in 3 mins with a 13-30 ply search
Other Tricks α-β pruning: We do not need to look at every possible move, especially if we have a good candidate. Quiessence: Static evaluate at peaceful situations. Go deeper into fights. Lookup Tables: for opening moves. Special program: for endgames.
Other Games Go is much harder. The best computer is far worse than the best human, even though the rules are very simple Checkers computers are far better than the best humans Tic-Tac-Toe is still a great mystry Othello has a very interesting story.
Rules of the game Start with four squares filled. Move next to opposite colored square. Change color of all opposite colored squared surrounded by moved piece and another piece of the same color. Must capture.
Reversi (Othello) D E Moriarty and R Miikkulainen, “Discovering Complex Othello Strategies Through Evolutionary Neural Networks” Created a strong player without any initial knowledge, by breeding a program! Evolutionary Start with a “population” of 100 “random” programs. Have a competition, and kill the 90 losers. Breed the 10 winners by “mixing” their “genes” with a bit of “mutation.” Do the same for many generations (1000’s).
Positional Strategy Programs quickly learned the basic positional strategy: Take corners. Avoid neighbors of corners Take neighbors of neighbors of corners. Mobility Strategy Keep low piece count Restrict opponents moves Discovered only once in Japan, and then everyone learnt it from them.
Mobility vs Positional The mobility strategy (learned by the ENN) looks like it is loosing, but converts it to a win in the last 3-4 moves!
But… Specially designed programs to play Othello still do even better eg. Bill or Logistello.