Alpha-Beta And Other Pruning Techniques

PSU CS410/510GAMES Lecture 6
July 11, 2000

• Alpha-Beta (AB)
  • Depth-First Branch-and-Bound; trying best children first in single-agent search
  • Two-player search trees
  • Win pruning in perfect two-player search: ``alpha''
  • Draw pruning in perfect two-player search: ``beta''
  • Pruning with heuristic-valued leaves
  • The full AB pruning technique
    • The basic idea: the ``AB window''
    • Implementations
      • Mutual recursion (Korf)
      • Window flipping
    • Performance
      • Worst case: no improvement
      • Best case: 1/2 exponent
        • o(b^(d/2) + b^(d/2) - 1) (proof)
        • implications of performance: double depth search
      • ``Average case'': 3/4 exponent
        • 30% extra search depth
        • Proof (Pearl) hard: board-splitting
        • Assumptions iffy
  • Enhancements
    • Move ordering using heuristic function
    • Move ordering using saved values: iterative deepening
    • Narrowing the window
• Other Pruning Techniques
  • Quiescence search
  • ``Best-first minimax'' (Korf) = ``Principal Variation Search''