Competing Agents and Adversary Search

PSU CS441/541 Lecture 5
October 25, 2001

• The Domain: Games
  • Zero Sum
  • Alternating
  • Terminating
  • Two Player
  • Deterministic
  • Perfect Information
  • ``Tractable to search''?
• Minimax
  • What is minimax?
  • Intractability of full minimax
    • trees, graphs, and search space sizes
  • Approximations for tractability
    • perfect opponent play
    • depth bounds and heuristic scoring
    • single score (emergent features)
• DFS In Minimax Game Trees
  • Why DFS?
  • Implementing minimax
    • mutual recursion
    • code sharing
    • negamax
  • Alpha-beta pruning
    • alpha-cutoffs
    • beta-cutoffs
    • importance of ordering
    • effectiveness of alpha-beta
      • (4/3)x depth in random case (Pearl)
      • 2x depth in best case
  • Transposition tables
    • combine transpositions
    • store previous search results
    • implemented as hash tables on game state
• Practical Considerations
  • Quiescence
    • for efficiency
    • for horizon effect
  • Iterative deepening
    • for time management
    • for pruning
    • with transposition tables
  • Opening book
  • Endgame
    • algorithmic
    • database
  • Expectimax
  • Better search algorithms
    • zero-window
    • partition search
    • MTD(f)