Two-Player Games And Minimax Search

PSU CS410/510GAMES Lecture 4
June 29, 2000

• Note: Search and ``Branching Factor''
• Deferred Topic: The Perfect Shuffle
  • Naive algorithms
    • swap every slot once: not even
    • riffle: min 14 riffles for randomness
    • attach random numbers and sort: clumsy
  • Doing it right in 3 easy steps
    • Requirements: defn ``random shuffle''?
      • uniform prob. of each card at each spot
      • implies inductive defn: first card random followed by random shuffle of remainder
    • 1: ``selection shuffle''
    • 2: avoiding the array slide
    • 3: avoiding the extra array
    • Shuffle implements definition
    • Up or down?
  • PRNGs and the limits of shuffling
    • LC and LFSR generators
    • Using enough bits
    • End effects
    • 2-player games and ``crypto shuffles''
    • ``Mental poker'' (Goldwasser & Micali)
• Deferred Topic: Special Considerations In Game SE
  • Bottlenecking: CPU vs. cache vs. RAM?
  • Correctness, completeness, V&V, and search
  • Asymptotic complexity matters!
  • Clarity
• Zero-Sum Iterated Games
  • zero-sum games
  • iterated games
  • The value of a game: well-defined games
  • Payoff matrices
  • Two player games and the minimax theorem
  • Probability and the expected value of a game
  • Hidden information and mixed strategies
• Minimax Search
  • Concept: minimize opponent's maximum (expected) available outcome
  • Zero-sum means maximize own minimum outcome
  • Perfect opponents only!