mastering chess
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Mastering Chess. An overview of common chess AI. Adam Veres. Everybody knows chess, right?. ELO Rating System. Important context on how players are rated Arpad Elo Hungarian-born, American physics professor – creator. ELO Rating System, cont. - PowerPoint PPT PresentationTRANSCRIPT
Mastering ChessAn overview of common chess AI
Adam Veres
Everybody knows chess, right?
Important context on how players are rated
• Arpad Elo• Hungarian-born, American physics
professor – creator.
ELO Rating System
• Numerical system for calculating relative skill level of players
• Higher number = better player• Players avoid situations that damage
their ELO.• Picking events
• Not just chess
ELO Rating System, cont.
Senior Master 2400+Master 2200+ (This encompasses the 93-98th percentile of all rated players in America)Expert 2000+‘A’ Player 1800+‘B’ Player 1600+‘C’ Player 1400+‘D’ Player 1200+‘E’ Player 1000+‘F’ Player 800+‘G’ Player 600+‘H’ Player 400+‘I’ Player -400
USCF Rating Tiers
Some history on computers playing chess• ~1770• The Turk• Fake automaton• Wolfgang von Kempelen
Hungarian inventor
Computer chess!
• 1951 developed, on paper, a program capable of playing a full game of chess
• Work backwards from ‘win’ conditions and accept moves that work towards that goal
• Turing assumed infinite processing power and storage space
• Ratio W/B
Alan Turing
• 1986 - The Chessmaster 2000• The manufacturer rated the game at 2000 Elo
USCF, in reality it plays at approximately 1750-1800 USCF.
• This is “B” rated in 1986!• Best selling
Chess seriesof all time.
Chessmaster
1997 IBM’s Deep Blue defeats Gary Kasparov after a six game match.Deep Blue relied on hardware for to evaluate over 200 million moves per second
Deep Blue
• Deep Fritz version 10 ran on a machine running two Intel Core 2 Duo processors.
• 8 million moves per second• Average depth search of 17-18 using heuristics
to evaluate choices• About 6 billion possible positions observed
before actually making a move• Vladimir Krammik loses 2-4 to Deep Fritz• 5 piece tablebase allowed for end-game, 6
piece widely available
Beyond Deep Blue
• SSDF – Swedish Chess Computer Association
• Tests computer chess programs and produces a rating
• 2012 “Deep Rybka 4 x64” 3221 rating
• Tested on x64 2GB Q6600 2,4 GHz
Computer chess ratings
Board Representation• List of all pieces• 8x8 2D array• 0x88
2 boards next to each other. Makes move-legality checks a simple AND with the hex number 0x88
• Bitboard 64 bit sequence of bits. Series of bitboards.
• Stream based• Huffman Encoding
More common chess positions (pawns/empties) stored with less bits
Algorithmic Considerations
• Type A Brute Force. Checks bad and trivial
moves unnecessarily.• Type B
Quiescent Search – evaluate minimax game trees
Only a few moves are evaluated
Main Search Types
• Alpha-beta pruning widely used to reduce search space
• Negascout – directional search algorithm to find minimax value of a node in a tree
Type B
• Nalimov endgame tablebase. 5 or fewer pieces is solved. USSR born programmer
• 6 pieces is solved except some trivial cases such as 5 pieces versus 1 king
• 7 pieces have been somewhat analyzed• All of these make certain assumptions to prune
the branching possibilities. Eg: Castling is no longer possible
“Tablebases”
One last interesting note:It is estimated that doubling the computer’s speed adds only 50-70 ELO to a given chess algorithm
Heuristics are much better than brute force!
Last Thoughts
• Digital computers applied to games'. n.d. AMT's contribution to 'Faster than thought', ed. B.V. Bowden, London 1953. Published by Pitman Publishing. TS with MS corrections. R.S. 1953b
• “Deep Blue”. IBM.http://www-03.ibm.com/ibm/history/ibm100/us/en/icons/deepblue/
• “The Last Man vs Machine?”. Chess News.http://en.chessbase.com/home/TabId/211/PostId/4003504
• “Important Official Rules of the Kramnik versus Fritz match”. Chess Daily News and Information. http://susanpolgar.blogspot.com/2006/11/important-official-rules-of-kramnik.html
• Levy, David; Newborn, Monty (1991), How Computers Play Chess, Computer Science Press, ISBN 0-7167-8121-2
References
• Searching for Solutions in Games and Artificial Intelligence (1994) by Victor L. Allis
• SSDF. Swedish Chess Computer Association. http://ssdf.bosjo.net/
• Some images from Wikimedia Foundation• “Did a Computer Bug Help Deep Blue beat Kasparov”.
Wired.com. http://www.wired.com/playbook/2012/09/deep-blue-computer-bug/
References