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Presentation on theme: "Parallel Programming in Chess Simulations"— Presentation transcript:
Slide1
Parallel Programming in Chess Simulations
Tyler Patton
Slide2
Discussion:
Background
Sequential Optimizations
Parallelization of chess
Slide3
Background: What is Chess?
Strategic 2 player game64 tiles16 pieces per playerObjective to capture the opponents king
Slide4
Background: Chess ELO
Created by Arpad
Elo
to improve chess ratings
Players of equal ELO have an equal chance to win
A difference of 400 ELO gives a win 97% of the
time to the higher rated player
Basic formula:
Performance Rating =
Opponents’ Total Ratings + 400*(wins-losses)
Number of games
Average Player rating: 1200
Highest player rating: 2850 (Magnus Carlson)
Slide5
Background: Scope
First estimate of the number of positions:
64! / 32!*(8!)
2
*(2!)
6
=10
43
(Shannon)
Tight upper bound:
=10
50
(Dr. Allis)
Number of possible game variations:
10
120
(Shannon number)
Given ~10
3
starting moves and 40 move pair average
Slide6
Background: History of chess engines
1950: Alan Turing develops Turbochamp.1962: Adam Kotok of MIT develops first “credible” chess program.1997: Deep blue defeats Gary Kasparov in 6 gamesPresent: Stockfish 6 holds a rating of 3309
Minimax: Evaluate a given move, the opponents responses and your responses to your opponent’s moves… etc.Proceed to the next move and repeat.Choose the tree which yields the best ending evaluationAssume the opponent always chooses the best move
Slide10
Sequential Optimizations:Alpha-Beta Pruning
Alpha is the maximum score the player is guaranteed for a branchBeta is the minimum score the opponent is guaranteed for a branchAllows for eliminations of branches in the search treeEliminates branches if the opponent would never allow the positionOrdered node complexity: O(bd/2)Random order complexity: O(b3d/4)
Slide11
Sequential Optimizations:Alpha-Beta Pruning
Slide12
Sequential Optimizations: Transposition Table
Stores the history of search evaluations
Positions that been searched are likely to be reached again
Before a branch is searched the transpositions table is checked and gives the result if able
Implemented as a hash table
Slide13
Parallelization of Chess:Parallelizing Alpha-Beta pruning
Goal: Use multiple processors to simultaneously search different branches of the game tree
Drawback: Dependency on the alpha
value
Processors are dependent on each other for updated alpha values which cause communication
locks
Parallel algorithms tend to be less efficient since the alpha value is not as strong
Parallel implementation only has equivalent efficiency to the sequential algorithm if the first move if the best one examined
Slide14
Parallelization of Chess:Principal Variation Splitting
Early technique for parallelizing alpha-betaAssumptions: The game tree is well orderedThe leftmost path is the bestUpdates alpha after a branch is searched
Slide15
Parallelization of Chess:Typical Speedup
Principal Variation SplittingImplemented using 4 or fewer Processors with a speedup of ~3.5The Younger Brothers Wait Concept achieved a speedup of 140 on 256 nodesCilkChess parallel engine is shown to be scalable up to 1000 nodes with a similar speedup to The Younger Brothers Wait Concept
Slide16
Parallelization of Chess:Looking to the future
The best algorithm for large numbers of processors and indefinite tree size is
unknown
Explore new algorithms that don’t rely on communication
pitfalls
Optimizations to existing algorithms and techniques are still possible
i.e. making the new alpha available to each processor when its found as opposed to when a processor finishes a
