Search In Games

PSU CS410/510GAMES Lecture 3
April 17, 2002

• Single Agent Search
  • Some solitaire games
    • n-puzzle
    • Sokoban
    • Rubik's Cube
  • Search and ``Branching Factor''
  • Heuristic Search
  • Pruning and guidance
    • Depth-First Branch and Bound
    • A*
    • LDS
  • Relation to two-player case
• Adversary Search
  • Reminder: conditions
    • two player
    • zero sum
    • perfect information
    • deterministic
    • alternating, terminating
  • Minimax Search
    • Terminology: first player is ``maximizer'', opponent is ``minimizer''.
    • Completed game has a definite score. (Intervals [-1.0 ... 1.0] or [-1000 ... 1000] are popular.)
    • Maximizer wants to make outcome of the game as positive as possible, minimizer as negative as possible.
    • Symmetry: can negate scores and switch minimizer w. maximizer. This leads to negamax search.
  • The "easy" minimax theorem
    • base case: choose the winning option
    • inductive case
      • choose the option damaging opponent since zero sum
      • know this option since perfect info deterministic
      • induction terminates since game terminates
      • induction step: compute opponent minimax value since alternating