Openings and Endgames

PSU CS410/510GAMES Lecture 10
July 25, 2000

• Probability
  • Review: probability [esai]. For logical statements A and B
    • definitions
      • P(A) is the probability that A holds: 0 <= P(A) <= 1 where P(A) = 1 is certainty that A holds.
      • P(A|B) is the probability that A holds in those worlds where B holds
    • axioms
      • P(not A) = 1 - P(A)
      • P(A and B) = P(A) P(B|A)
      • If A and B are equivalent, then P(A) = P(B)
    • corollaries
      • P(A or B) = P(A) + P(B) - P(A and B)
      • Bayes' Rule: P(A|B) = P(A) P(B|A) / P(B)
    • Cox's Theorem: good representation (c.f. Arrow's Theorem)
  • Probability and conventional games
    • Exhaustive approach
    • Monte Carlo approach
    • Bayes Nets and influence diagrams
    • Markov Decision Processes
  • Example: Yacht
    • Basics: the game of Yacht
    • Local optimality and greedy moves
    • Global optimality via state transitions
    • From one-player to two-player
• Hidden Information
  • Review: hidden information
  • Normal Form games
  • Extensive Form games
  • Properties of a normal form game
    • Dominance
    • Saddle point
    • Constant-sum and scaling
    • Calculating mixed strategies: 2x2
      • guessing
      • exploration
      • algebra
    • Calculating mixed strategies: mxn via linear programming
    • Non-constant-sum normal form games
  • Hidden strategy, probability, and expectimax
    • Rock-Scissors-Paper again
    • GIBson
  • Example: DungeonQuest combat
  • Beyond normal form: Poker, Stratego