mastering chess

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