New Developments in Computer Chess

1
New Developments in Computer Chess

• Jaap van den Herik
• Tilburg centre for Creative Computing (TiCC)
• Faculty of Humanities
• Tilburg University
• Tilburg / The Netherlands
• SIKS-TiCC colloquium Tilburg University, 28
  January 2009
• room Tz7, 15.30 17.00 hours

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Contents

• Chess-Checkers-Go
• Technological Development
• Five Challenging Questions
• Principles and Possibilities
• Conditions (1st set)
• Opponent Model Search
• MCTS and UCT
• The 9-stone handicap match
• Conditions (2nd set)
• The idea of solving Chess
• Predictions

3

• Games, such as Chess, Checkers, and Go
• are an attractive pastime and
• scientifically interesting

4
Chess

• Much research has been performed in computer
  chess
• DEEP BLUE (IBM) defeated the world champion
  Kasparov in 1997
• FRITZ defeated Kramnik (December 2006)

5

• World Champion Programs
• KAISSA 1974 Stockholm
• CHESS 1977 Toronto
• BELLE 1980 Linz
• CRAY BLITZ 1983 New York
• CRAY BLITZ 1986 Keulen
• DEEP THOUGHT 1989 Edmonton
• REBEL 1992 Madrid
• FRITZ 1995 Hong Kong
• SHREDDER 1999 Paderborn
• JUNIOR 2002 Maastricht
• SHREDDER 2003 Graz
• JUNIOR 2004 Ramat-Gan
• ZAPPA 2005 Reykjavik
• JUNIOR 2006 Turin
• RYBKA 2007 Amsterdam
• RYBKA 2008 Beijing

6
Solving Checkers

• Schaeffer, Björnsson, Burch, Kishimoto, Müller,
  Lake, Lu, and Sutphen
• Spring 2007
• Checkers is Solved
• Science, Vol. 317, No. 5844, pp. 1518-1522

7
International Draughts

• Buggy best draughts program
• Human better than computer, but the margin is
  small
• Challenge More knowledge in program

8
Go

• Computer Go programs are weak
• Problem recognition of patterns
• Top Go programs Many Faces of Go and MoGoTitan

9

Technology and Future
Mechanization
1950
Computerization
1970
Information handling
1990
Intelligent Programs
Communication (ICT)
2000
Intelligent E-commerce
E-commerce
2005
Agent Technology
Ant Technology (Grid)
2010
2030
Singularity Point
10
Moores law

• The computer capacity is doubled every 18 months

11
Gliders law

• The bandwidth is doubled every 12 months

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Go for IT
Data Handling
Information Technology
Knowledge Engineering
Agent Technology
Grid Technology / Supercomputing
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Go for Intelligence
Games
Gaming
Serious Gaming
14
Go for Power
IBM 360 / 65 370 / 158 370 / 168
Supercomputers
PCs
1997 RS 6000 defeats Kasparov on Chess
TERAS
HUYGENS defeats Kim Myungwan on Go (9-stone
handicap)
15
Ray Kurzweil

• The Law of Accelerating Returns
• The Singularity Point
• The Singularity is Near

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A Singularity Point

• In 1997 DEEP BLUE defeated
• the human Chess World Champion
• Gary Kasparov
• ? Machine Intelligence outperformed
• Human Intelligence on chess

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Question

• When will Machine Intelligence outperform Human
  Intelligence on all areas of intelligence?
• Kurzweil The Singularity is Near
• 2045

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• The Singularity is a technological change so
  rapid and so profound that it represents a
  rupture in the fabric of human history.
• Some would say that we cannot comprehend the
  Singularity, at least with our current level of
  understanding, and that it is impossible
  therefore, to look past its event horizon and
  make sense of what lies beyond.

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Five Challenging Questions

• Can a computer play Chess and Go?
• Can a computer play at grandmaster level?
• Can a computer defeat the human world champion?
• Can a computer solve the game?
• Are some generic ideas applicable elsewhere?

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• Computer Olympiad
• Initiative of David Levy (1989)
• Since 1989 there have been 13 olympiads 4x
  Londen, 3x Maastricht, 1x Graz, 1x Ramat-Gan, 1x
  Taipei, 1x Turin, 1x Amsterdam, 1x Beijing
• Goal
• Finding the best computer program for each game
• Connecting programmers / researchers of different
  games
• Computers play each other in competition
• Demonstrations
• Man versus Machine
• Man Machine versus Man Machine
• The 14th Olympiad is in Pamplona, Spain, May
  11-18, 2009

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Overview
22
Minimax
3
2
3
7
2
4
3
23
a-ß Algorithm
3
3
ß-pruning
2
7
2
4
3
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The Strength of a-ß
More than thousand prunings
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The Importance of a-ß Algorithm
3
3
ß-pruning
2
4
3
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The Possibilities of Chess

• THE NUMBER OF DIFFERENT, REACHABLE
• POSITIONS IN CHESS IS
• (CHINCHALKAR) 1046

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A Clever Algorithm (a-ß)

• Saves the square root of the number of
  possibilities, ?n, this is more than
• 99.999999999999999999999
• 1 of 1046 1044
• ?1046 1023
• 44 23 21 (9s behind the decimal point)

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A Calculation (1st set)

• NUMBER OF POSSIBILITIES 1046
• SAVINGS BY a-? ALGORITHM 1023
• 1000 PARALLEL PROCESSORS 103
• POSITIONS PER SECOND 109
• LEADS TO 1023-12 1011 SECONDS
• A CENTURY IS 109 SECONDS
• SOLVING CHESS 102 CENTURIES
• SO 100 CENTURIES OR 10,000 YEAR
• WE RETURN TO THIS NUMBER.

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Using Opponents Strategy

• Well known Tic-Tac-Toe strategy
• R1 make 3-in-a-row if possible
• R2 prevent opponents 3-in-a-row
• if possible
• H1 occupy central square if possible
• H2 occupy corner square if possible

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Opponent-Model Search

• Iida, vd Herik, Uiterwijk, Herschberg (1993)
• Carmel and Markovitch (1993)
• Opponents evaluation function is known
  (unilateral the opponent uses minimax)
• This is the opponent model
• It is used to predict opponents moves
• Best response is determined, using the own
  evaluation function

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How did chess players envision the future of
non-human chess players?

• Euwe
• Timman
• Sosonko
• Donner
• De Groot
• Question Do you think that a computer will be
  able to play at grandmaster level?

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Euwe (June 10, 1980)

• I dont believe so.
• I am almost convinced of that, too

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Timman (June 22, 1980)

• If you would express it in ELO-points, than I
  believe that a computer will not be able to
  obtain more than ...... lets say
  ......2500 ELO-points.

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Sosonko (August 26, 1980)

• I havent thought about that so much, but I
  believe that it will certainly not be harmful for
  the human chess community. It will become more
  interesting. I am convinced that computer chess
  will play a increasingly important role. It will
  be very interesting, I think

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Donner (April 13, 1981)

• But the computer cannot play chess at all and
  will never be able to play the game, at least not
  the first two thousand years, (...)
• What it does now has nothing to do with chess.

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De Groot (June 19, 1981)

• No, certainly not. As a matter of fact, I
  believe it will not even possible that it can
  reach a stable master level.
• I believe it is possible that the computer can
  reach a master level, but not that it is a stable
  master.

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Contributions from Science

• Computers play stronger than humans.
• Computers can solve chess.
• Computers enable an alternative form of game
  experience.

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Provisional Conclusions on Chess

• Checkers is a frontrunner among the games
• Chess is a direct follower
• Kasparovs defeat has become a victory for brute
  force in combination with knowledge and opponent
  modelling

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Development of MoGo and MoGo Titan

• Started in 2006 by Sylvain Gelly and Yizao Wang
  at University of Paris-Sud
• August 2006 Takes the highest rank program on
  the 9x9 Computer Go Server. It still holds this
  rank for 2 years long.
• June 2007 wins the 12th Computer Olympiads in
  Amsterdam, and first program ever to defeat a
  professional on 9x9 in a blitz game.
• April 2008 wins the first non-blitz game against
  a professional.
• May 2008 involvement of the project GoForGo
  leading to MoGo-Titan.
• August 2008 wins the first match ever against a
  professional on 19x19 with 9 stones handicap
  (running on Huygens). This result is acknowledged
  as a milestone for AI.

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MOGO TITANIS THE NEW NAME

• MOGO is the French part
• and
• TITAN is the finding by Christian Huygens
• (a satellite moon around Saturnus)
• The name is taken as a tribute to Supercomputing
  in the Netherlands

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The 9 stone Match

• The professional commented
• I think theres no chance on nine stones, it
  would even be difficult with eight stones. MoGo
  played really well after getting a lead, every
  time I played aggressively, it just played
  safely, even when it meant sacrificing some
  stones. It didnt try to maximize the win and
  just played the most sure way to win. Its like a
  machine.

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• National Supercomputer in NL
• What When Flop/s Processors
• CDC Cyber205 1983 100 M100 1
• CDC Cyber205 1987 200 M 200 M 2
• Cray YMP 1990 1.3 G 1.3 G 4
• Cray C90 1994 4 G 4 G 4
• Cray C90 1997 12 G 12 G 12
• SGI Origin 2000 1 T 1 T 1024
• SGI Altix 2003 3.2 T 3.2 T 1440
• IBM p5 2007 15 T 15 T 1920
• IBM p6 2008 gt60 T gt60 T gt3000
• So the gain will be almost 1 M in 25 years

Software effort
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Huygens at SARA

• P6- architecture
• of processors 3328
• Water cooled
• MoGo had 800 processors at its disposal
• This was over 1000 times as powerful as the
• RS 6000 (1997) defeating Kasparov.

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Portland - Oregon

• August 8, 2008
• MoGo Titan plays Kom Myungwan
• A 9-stones handicap match
• The machine wins

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IBM Supercomputer Huygens Used

• MoGo using Huygens (provided by SARA) is called
  MoGo-Titan
• The processors are IBM Power6 at 4.7Ghz.
• Each node has 32 cores, and 256 GB of RAM.
• It uses generally 10 to 25 nodes, out of 104
  nodes.
• Parallelization is using OpenMPI.

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Human-Computer Matchesin Go

• For a long time, a prize of 40,000,000 NTD
  (1,400,000 ) for the first computer Go-playing
  program that would succeed in beating a Taipei Go
  Professional without handicap. The prize was
  donated by Ing Chang-Ki and was valid until 2000,
  due to the death of Ing Chang-Ki.
• 400,000 NTD (14,000 ) were offered to a program
  that would beat a professional at 9 stones.
  Numerous attempts were made but no program ever
  won.
• More information on the numerous attemps are
  listed here http//senseis.xmp.net/?IngPrize

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Evolution of the level of programs
Rank of the best programs9 dan 1 dan

9x9
19x19
20 kuy
1968 1978 1988
1998 2007 2008 (Albert
Zobrist)
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The Difference between Chess and Go

• Chess Search
• Tactics play an important role
• Go Pattern Recognition
• Strategy is much more important

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Two breakthroughs that enabled Go to play at
acceptable level

• 1. Monte Carlo Search
• (Brügmann and Bouzy)
• 2. UCT algorithm
• (Chaslot, Coulom, Kocsis)
• UCT stands for
• Upper Confidence bounds applied to Trees

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• Monte-Carlo Tree Search underlying idea

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• Exploration-exploitation dilemma If only the
  best moves are explored (too few explorations),
  the algorithm is focusing on a few moves, and
  moves that did not seem promising are
  forgotten. If too many moves are explored, the
  branching factor is too high and the search is
  not deep enoughAlternative solutions have to
  be found (Progressive strategies, RAVE, etc)

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• The Real Challenge is
• Can we solve chess?
• Answer is yes
• Next question is when?

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My First Educated Guess

• 10,000 years will be reduced
• to 1500 years
• and then it will take some years.

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• A First Conservative Estimate
• Chess will be solved
• in 3500 A.D.
• The result will be draw.

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Improvements on the Estimate

• MATJA GAMS (30 August 2005)
• In 2035 a machine takes 4 months to solve chess.
• VINCENT DIEPEVEEN (27 October 2005)
• In 2066 the game of chess is solved.

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• GAMS AND DIEPEVEEN RELY ON MOORES LAW
• Every 18 months the computer capacity is doubled.
• Therefore in 30 years (30 20 x 1.5)
• the law gives a speed up of 220 106

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A New Calculation (2nd set)

• NUMBER OF POSSIBILITIES 1046
• SAVINGS BY a-? ALGORITHM 1023
• 1000 PARALLEL PROCESSORS 103
• POSITIONS PER SECOND 1014 (9615 15-114)
• LEADS TO 1023-17 106 SECONDS
• A CENTURY IS 109 SECONDS
• SOLVING CHESS 10-3 CENTURIES
• So roughly 37 days in 2035.
• This is for Chess.

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When will Shogi be solved?

• In 2012 a Shogi program will defeat the World
  Champion (Iida, Sakuta, and Rollason, 2002)
• The difference with chess is then 15 years.
• (2012-1997)
• Tentative Conclusion
• Shogi will be solved before 2050.
• At this moment, it looks like a bold statement.

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CONCLUSIONS ON GAMES

• Computers will solve a range of games.
• New games will emerge.
• Humans will continuously learn from computers.
• The Games Research will envisage new games and
  even more new computer techniques.

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FUTURE EXPECTATIONS

• MoGo-Titan defeats a top Go player in
• 2008 - 9 stones handicap
• 2009 - 8 stones handicap
• 2010 - 7 stones handicap
• 2011 - 6 stones handicap
• 2012 - 5 stones handicap
• 2014 - 4 stones handicap
• 2016 - 3 stones handicap
• 2018 - 2 stones handicap
• 2019 - 1 stones handicap
• 2020 - MOGO-TITAN defeats the human Go World
  Champion
• The singularity point in Go is reached

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MESSAGE

• Ray Kurzweil (2007)
• The singularity point is near
• The general point is due
• 2030 (Kurzweil)
• 2048 (others)
• 2400 (disbelievers)
• Nobody will deny the development.
• Everybody will think about the future.