Computers Playing Games

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Computers Playing Games

• Arif Zaman
• CS 101

2
Acknowledgements

• Portions of this are taken from MITs
  open-courseware 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

3
Why Computers 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).

4
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 Enemy Strategy
A B
My Strategy X 10 -10
My Strategy Y -2 40
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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)

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History

• 1949 Claude Shannon paper on Chess
• 1951 Alan Turing simulation on Checkers
• 1955 Chess Program using a-ß.
• 1966 MacHack
• 1990 Belle (harware assist)
• 2000 Deep Blue (serious hardware)

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Top-down Program

• Repeat Until Done
• DrawBoard
• GetPlayerMove
• CheckLegalMove also check if game over
• MakePlayerMove
• DrawBoard
• FindLegalMoves also check if game over
• EvaluateLegalMoves
• MakeBestMove

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Static Position Evaluator

• Given a position, come up with a value.
• Values are 01 or 0infinity or
  infinityinfinity.
• 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.

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Game Tree Mini-Max
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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.

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Deep Blue

• 32 node supercomputer, each with eight special
  chess processors.
• 50 100 billion moves in 3 mins with a 13-30 ply
  search

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Other Tricksa-ß pruning

• a-ß pruning We do not need to look at every
  possible move, especially if we have a good
  candidate.
• Lookup Tables for opening moves.

• Example of 3-2-2- ply search

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Other TricksQuiessence Search

• Quiessence Static evaluate at peaceful
  situations. Go deeper into fights.
• Tree Folding Memo-ization
• Special program for endgames.

• Variable depth trees result from quiessence
  searches.

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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 mystery ?.
• Othello has a very interesting story.

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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.

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Reversi (Othello)

• D E Moriarty and R Miikkulainen, Discovering
  Complex Othello StrategiesThrough
  EvolutionaryNeural Networks
• Created a strong player without any initial
  knowledge, by breeding!

• Start with a population of 100 random
  programs.
• Kill the 90 losers in a competition. Breed the 10
  winners by re-combining their genes with a
  bit of mutation.
• Repeat for 1000s of generations.

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Positional Strategy

• 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.

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Mobility vs Positional

• The mobility strategy (learned by ENN
  Evolutionary Neural Network) looks like it is
  loosing, but converts it to a win in the last 3-4
  moves!

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But

• Specially designed programs to play Othello still
  do even better eg. Bill or Logistello.

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More Complexities

• Randomness
• Dice games
• Ludo
• Monopoly
• Learn Probability Theory, and maximize chance of
  winning, or expected points.

• Multi-player Games
• Collusion strategies
• Scrabble, Monopoly
• Card games
• Use AI to recognize typical player types and
  weaknesses. Try to predict human response.

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Write your own game!

• By the end of this course, you should have most
  of the tools to write your own game player.
• If you are interested, it will help to take Data
  Structures, so that you can represent trees on a
  computer.