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Adversarial Search

Adversarial Search. Board games. Games. 2 player zero-sum games Utility values at end of game – equal and opposite Games that are easy to represent Chess – average branching factor 35 Games need to make decisions even when optimal decisions are infeasible in limited time.

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Adversarial Search

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  1. Adversarial Search Board games

  2. Games • 2 player zero-sum games • Utility values at end of game – equal and opposite • Games that are easy to represent • Chess – average branching factor 35 • Games need to make decisions even when optimal decisions are infeasible in limited time

  3. Evaluation fn for Tic-Tac-Toe • if position p is win for MAX • E(p) = 100 • If position p is win for MIN • E(p) = -100 • If not win position for either • E(p) = open lines for MAX – open lines for MIN

  4. Alpha - beta • Backed up Lower bound is alpha value • Backed up upper bound is beta value • Alpha at max can never decrease • Beta at MIN can never increase

  5. pruning • If beta at any MIN <= alpha of any of its MAX ancestors final backed up value = its beta value • If alpha at any MAX >= beta at any of its MIN ancestors final backed up value = its alpha value

  6. Updating alpha and beta • Alpha at MAX node = current largest final backed up value of its successors • Beta at MIN node = current smallest final backed up value of its successors

  7. Search efficiency • In time alpha-beta search proceeds to depth d, simple minimax just proceeds to depth d/2 • Search reduces effective branching factor from b to √b

  8. Good heuristics • Examine best moves first • Capture piece • take care of threats • Move forward • Move backward • Use Iterative deepening • Evaluate best moves for one ply • Evaluate best moves for 2 ply… • Abort search if time constraint enforced

  9. More efficiency • Take care of repeated states, resulting from different permutations • Use Transposition table • Read 6.6 for state of art news

  10. State of the art • IBM’s Deep Blue defeated grandmaster Gary Kasparov in 1997, in a 6 game match • 30 processors with 480 custom VLSI chess processors • Average search speed – 126 million nodes per second • Evaluation function had 8000 features • Database of 700,000 grandmaster games were used

  11. Power? • IBM contributed the success to hardware • Developers maintained that search extensions and evaluation functions more critical • Deep blue team declined a chance for a rematch with Kasparov.

  12. Chess on PCs • 2002 FRITZ program on a PC against Vladimir Karamnik. The 8 game match ended in a draw

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