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Published byDiana York Modified about 1 year ago

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Adversarial Search Board games

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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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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

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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

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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

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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

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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

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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

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

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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

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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.

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

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