Artificial Intelligence Expert Systems Game Playing

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Artificial Intelligence / Expert SystemsGame
Playing

• Justin Gaudry
• May 25, 2007

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Game-Playing AI Features

• Simple Structures with Complex Strategies
• Well-Defined Rules and Performance Measurements
• Readily Automated Environments
• Impossibility of Complete Analysis
• Models

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Game-Playing AI Features

• Limited Playing Piece Types
• Limited Ways to Move
• Broad State Space
• Size of Board
• Piece Type
• Move Type

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Game Decision Methods

• State Space Search with Constraints and Pruning
• Heuristics
• Knowledge Database of Known Patterns and Move
  Sequences

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Determinism

• Deterministic
• No Random Feature Inherent in Game
• Still Cannot Predict Opponents Move
• Chess, Checkers
• Non-Deterministic
• Some Element of Chance
• Dice, Cards, Some Kind of Randomness
• Complicates Search Considerably
• Searches Distinct Areas of State Space
• Backgammon, Cards

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Types of Games

• Complete
• Entire Knowledge of Current State Available to
  Both Players
• Games where board and pieces are visible
• Chess, checkers, tic-tac-toe, backgammon
• Incomplete
• Some Element of Secrecy
• Cards, Scrabble

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Types of Games

• Zero-sum games
• Win, Lose, or Draw
• Rational
• Assume Opponent Always Chooses the Best Move
• Adversarial
• Each Player Trying to Win and Trying to Cause
  Other Player to Lose

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Evaluation Functions

• Measurements of Value of Next-Ply States
• Static
• Evaluate from One Static Position
• Weighted Linear Functions
• Better State Achieves Higher Weight According to
  Combination of Features

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Minimax

• Two-Player Game
• Rational
• Assume Opponent Will Choose Worst Move for Player
  and Best Move for Opponent
• Look at Possibilities for Player After Opponent
  Move

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Minimax

• Player Will Choose Maximum Value at 2-Ply Level
  (Static Evaluation Function)
• Opponent Will Choose Minimum of Players Maximum
  Values at 1-Ply Level
• Player Chooses Maximum of Opponents Values at
  Current Level
• Bounded Lookahead

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Minimax

• For All My Possible Moves
• For All Opponents Possible Moves
• The Value to the Opponent is Minimum Value for Me
  at My Next Turn
• Endfor
• The Value to Me is Maximum Value of Opponents
  Calculation
• Endfor

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Minimax Weaknesses

• Must Consider Strengths of Own Current Position
  As Well
• At Min Level, Opponent Must Consider Strengths of
  Its Own Current Position
• Incorporate Current Position Values with
  Calculated Minimax Value

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Other Weaknesses

• Sequence Problem
• A Particular Move May Be Good Overall But in a
  Bad Sequence
• Horizon Effect
• A Very Good String of Moves May Lead to an
  Eventual Overall Loss
• Limiting Depth of Ply Will Prevent the Discovery
  of the Weakness

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Alpha-Beta Pruning

• Minimax Prunes Only At Current Level
• Alpha-Beta Pruning Prunes at Each Min Level
  Examined in Minimax Calculation for Current
• Considerably Reduces the Amount of Nodes Examined
  in the Eventual Search Path

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Alpha-Beta Pruning

• Alpha is max for max nodes descendants
• Beta is min for min nodes descendants
• If current is max
• if alpha gt parents beta
• cut off
• endif
• Endif
• If current is min
• if beta lt parents alpha
• cut off
• endif
• Endif