Adversarial Search
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Adversarial Search Board games
description
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. - PowerPoint PPT Presentation
Transcript of 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
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
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
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
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
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
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
More efficiency
Take care of repeated states, resulting from different permutations
Use Transposition table Read 6.6 for state of art news
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
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.
Chess on PCs
2002 FRITZ program on a PC against Vladimir Karamnik. The 8 game match ended in a draw
