Openings and Endgames

PSU CS410/510GAMES Lecture 9
July 20, 2000

• Shape of game space
• Openings
  • Sometimes a good-looking early move goes bad way later
  • In clocked games, want to not waste clock on known positions
  • Human players have (often vast) opening books
  • Computer opening book problems:
    • Human-generated books have bugs: opening traps or ``cooks'' [no learning = repeatable cooks]
    • Human-generated books have commentary and analysis: ``sympathy'' problem of dumping program into not-understood position
    • Strictly ``by the book'' deals poorly with transpositions, falling out of and back into book, irrelevant moves, etc.
      • Transposition table helps: implementation technique is to store book positions irremovably in t-table
        • Would prefer position classes, but...
        • Can explicitly indicate successor, or try to "rig" things by giving bonus in evaluation function for staying in book
    • Sympathy problem means transition to middle game not smooth (why am I here? What's in the t-table?)
  • When are we in middle game?
    • When out of book
    • When significant event happens (e.g. castling, material exchange)
    • When eff. branching factor goes up
• Endgames
  • When are we in the endgame?
    • When material is small
    • When branching factor becomes large
    • When terminal nodes are reached
  • Traditional endgame approach: programmed knowledge
    • Trades human work for generality
    • ``Theorem Proving'' approach
    • Problem: pattern matching
  • Which endgame positions are reachable? Who knows?
    • Idea: if game is monotonic in material, work backward = ``Retrograde analysis''
    • Dynamic programming technique: explore until conversion
    • Requires huge database (chess 5-piece = 150M positions)
    • Can profitably be calculated in parallel
  • Endgame oddities: chess
    • Discoveries: certain endgames are nonintuitive. Effective consequences?
    • Transition from middle game not always smooth: sacrifice to known (database or heuristic) win

Thanks to Dr. A.N. Walker of U. Nottingham for a web page with some ideas on this topic.