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Created page with "'''Home * Games * Backgammon''' FILE:Backgammon lg.png|border|right|thumb| A Backgammon Set <ref>A backgammon set, consisting of a board, two sets of 15 c..."
'''[[Main Page|Home]] * [[Games]] * Backgammon'''
[[FILE:Backgammon lg.png|border|right|thumb| A Backgammon Set <ref>A backgammon set, consisting of a board, two sets of 15 checkers, two pairs of dice, a [https://en.wikipedia.org/wiki/Backgammon#Doubling_cube doubling cube], and dice cups, Image by [https://commons.wikimedia.org/wiki/User:Ptkfgs Ptkfgs], March 6, 2013, [https://en.wikipedia.org/wiki/Backgammon Backgammon from Wikipedia], [https://en.wikipedia.org/wiki/Wikimedia_Commons Wikimedia Commons]</ref> ]]
'''Backgammon''',<br/>
a turn-based two-player [https://en.wikipedia.org/wiki/Tables_%28board_game%29 tables] board game of [https://en.wikipedia.org/wiki/Game_of_chance chance] and strategy with 15 checkers each on a board of 24 spaces or points. One moves according to rolls of a pair of dice, trying to bring own checkers home and bear them off before the opponent does <ref>[http://www.bkgm.com/ Backgammon Galore]</ref>. Opponent checkers can be "hit" and returned to the start.
=Computer Backgammon=
Backgammon programs were pioneered in the late 70s by [[Hans Berliner]] with focus on [[Tapered Eval|smooth evaluation]], and by [[Gerald Tesauro]] from the late 80s, who successfully applied [[Neural Networks]] and [[Temporal Difference Learning]] to his Backgammon playing programs. Computer backgammon is regularly played at [[Computer Olympiad|Computer Olympiads]], organized by the [[ICGA]] <ref>[https://www.game-ai-forum.org/icga-tournaments/game.php?id=11 Backgammon (ICGA Tournaments)]</ref>.
=[[Computer Olympiad|Computer Olympiads]]<span id="Olympiad"></span>=
* [[1st Computer Olympiad#Backgammon|1st Computer Olympiad, London 1989]]
* [[2nd Computer Olympiad#Backgammon|2nd Computer Olympiad, London 1990]]
* [[4th Computer Olympiad#Backgammon|4th Computer Olympiad, London 1992]]
* [[7th Computer Olympiad#Backgammon|7th Computer Olympiad, Maastricht 2002]]
* [[8th Computer Olympiad#Backgammon|8th Computer Olympiad, Graz 2003]]
* [[11th Computer Olympiad#Backgammon|11th Computer Olympiad, Turin 2006]]
* [[12th Computer Olympiad#Backgammon|12th Computer Olympiad, Amsterdam 2007]]
* [[16th Computer Olympiad#Backgammon|16th Computer Olympiad, Tilburg 2011]]
* [[18th Computer Olympiad#Backgammon|18th Computer Olympiad, Leiden 2015]]
* [[19th Computer Olympiad#Backgammon|19th Computer Olympiad, Leiden 2016]]
=Photos=
[[FILE:Backgammon2015.jpg|none|border|text-bottom|640px|link=https://icga.leidenuniv.nl/?page_id=1467]]
[[18th Computer Olympiad#Backgammon|18th Computer Olympiad 2015]], Backgammon medalists: [[Frank Berger]] (Bronze for [https://www.game-ai-forum.org/icga-tournaments/program.php?id=63 BGBlitz]), <br/>[[Nikolaos Papahristou]] (Gold for [https://www.game-ai-forum.org/icga-tournaments/program.php?id=712 Palamedes]), and [[Nardy Pillards]] (Silver for [https://www.game-ai-forum.org/icga-tournaments/program.php?id=62 GNU Backgammon]) <ref>[https://icga.leidenuniv.nl/?page_id=1467 18th Computer Olympiad - Day 6 Photos] by [[Jan Krabbenbos]]</ref>
=Evaluation=
In the late 70s at [[Carnegie-Mellon University]], [[Hans Berliner]] developed the [[Backgammon]] playing program '''BKG 9.8''' for the [[PDP-10]] to research the principles of [[Evaluation|evaluation]] for another game than chess with a much higher [[Branching Factor|branching factor]] of more than 800 at every node <ref>[[Hans Berliner]] ('''1977'''). ''[http://www.bkgm.com/articles/Berliner/ExperiencesInEvaluationWithBKG/index.html Experiences in Evaluation with BKG, a Program That Plays Backgammon]''. [[Conferences#IJCAI1977|IJCAI, 1977]], hosted by [http://www.bkgm.com/ Backgammon Galore]</ref>. Early versions of BKG played badly even against weak players, but Berliner noticed that its critical mistakes were always at transitions apparently due to [[Evaluation Discontinuity|evaluation discontinuity]]. He applied principles of [https://en.wikipedia.org/wiki/Fuzzy_logic fuzzy logic] to [[Tapered Eval|smooth out]] the transition between phases, and by July 1979, BKG 9.8 was strong enough to play against the ruling world champion [https://en.wikipedia.org/wiki/Luigi_Villa Luigi Villa]. It won the match 7–1, becoming the first computer program to defeat a world champion in any game. Berliner states that the victory was largely a matter of luck, as the computer received more favorable dice rolls <ref>[https://en.wikipedia.org/wiki/Hans_Berliner Hans Berliner from Wikipedia]</ref> <ref>[[Hans Berliner]] ('''1980'''). ''[http://www.bkgm.com/articles/Berliner/BackgammonProgramBeatsWorldChamp/ Backgammon Computer Program Beats World Champion]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 14</ref>.
=Learning=
In the late 80s, [[IBM]] researcher [[Gerald Tesauro]] pioneered in applying [[Neural Networks]] to Backgammon - first within his program [https://en.wikipedia.org/wiki/Neurogammon Neurogammon], which won the Gold medal at the [[1st Computer Olympiad#Backgammon|1st Computer Olympiad]] 1989 - and further improved by ''TD-Lambda'' based [[Temporal Difference Learning]] within [https://en.wikipedia.org/wiki/TD-Gammon TD-Gammon] <ref>[[Richard Sutton]], [[Andrew Barto]] ('''1998'''). ''[http://www.incompleteideas.net/sutton/book/the-book.html Reinforcement Learning: An Introduction]''. [https://en.wikipedia.org/wiki/MIT_Press MIT Press], [http://www.incompleteideas.net/sutton/book/ebook/node108.html 11.1 TD-Gammon]</ref>.
=Publications=
==1977 ...==
* [[Hans Berliner]] ('''1977'''). ''BKG - A Program that Plays Backgammon''. Technical Report, [[Carnegie Mellon University]]
* [[Hans Berliner]] ('''1977'''). ''[http://www.bkgm.com/articles/Berliner/ExperiencesInEvaluationWithBKG/index.html Experiences in Evaluation with BKG, a Program That Plays Backgammon]''. [[Conferences#IJCAI1977|IJCAI, 1977]], hosted by [http://www.bkgm.com/ Backgammon Galore]
* [[Hans Berliner]] ('''1979'''). ''[http://www.bkgm.com/articles/Berliner/EvaluationFunctionsLargeDomains/ On the Construction of Evaluation Functions for Large Domains]''. [[Conferences#IJCAI1979|IJCAI 1979]], Vol. 1, hosted by [http://www.bkgm.com/ Backgammon Galore]
* Editor ('''1979'''). ''Computer Backgammon''. [[Personal Computing#3_8|Personal Computing, Vol. 3, No. 8]], pp. 81
==1980 ...==
* [[Hans Berliner]] ('''1980'''). ''[http://www.bkgm.com/articles/Berliner/BackgammonProgramBeatsWorldChamp/ Backgammon Computer Program Beats World Champion]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 14, hosted by [http://www.bkgm.com/ Backgammon Galore]
* [[Hans Berliner]] ('''1980'''). ''[http://www.bkgm.com/articles/Berliner/ComputerBackgammon/index.html Computer Backgammon]''. [[Scientific American]], Vol. 242, No. 6, hosted by [http://www.bkgm.com/ Backgammon Galore]
==1985 ...==
* [[Gerald Tesauro]], [[Terrence J. Sejnowski]] ('''1987'''). ''A 'Neural' Network that Learns to Play Backgammon''. [http://www.informatik.uni-trier.de/~ley/db/conf/nips/nips1987.html#TesauroS87 NIPS 1987]
* [[Gerald Tesauro]] ('''1988'''). ''Connectionist Learning of Expert Backgammon Evaluations''. [http://www.informatik.uni-trier.de/~ley/db/conf/icml/ml1988.html#Tesauro88 ML, 1988]
* [[Gerald Tesauro]] ('''1988'''). ''Neural network defeats creator in backgammon match''. Technical report no. CCSR-88-6, Center for Complex Systems Research, [[University of Illinois at Urbana-Champaign]]
* [[Gerald Tesauro]] ('''1989'''). ''NEUROGAMMON: A Neural-Network Backgammon Learning Program''. [[1st Computer Olympiad#Workshop|Heuristic Programming in Artificial Intelligence 1]]
* [[Gerald Tesauro]] ('''1989'''). ''[http://www.mitpressjournals.org/doi/abs/10.1162/neco.1989.1.3.321?journalCode=neco Neurogammon Wins Computer Olympiad]''. Neural Computation Vol. 1, No. 3
* [[Gerald Tesauro]], [[Terrence J. Sejnowski]] ('''1989'''). ''A Parallel Network that Learns to Play Backgammon''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 39, No. 3
==1990 ...==
* [[Gerald Tesauro]] ('''1992'''). ''Temporal Difference Learning of Backgammon Strategy''. [http://www.informatik.uni-trier.de/~ley/db/conf/icml/ml1992.html#Tesauro92 ML 1992]
* [[Justin A. Boyan]] ('''1992'''). ''Modular Neural Networks for Learning Context-Dependent Game Strategies''. Master's thesis, [https://en.wikipedia.org/wiki/University_of_Cambridge University of Cambridge], [http://www.cs.cmu.edu/~jab/cv/pubs/boyan.backgammon-thesis.pdf pdf]
* [[Gerald Tesauro]] ('''1994'''). ''TD-Gammon, a Self-Teaching Backgammon Program, Achieves Master-Level Play''. [http://www.informatik.uni-trier.de/~ley/db/journals/neco/neco6.html#Tesauro94 Neural Computation Vol. 6, No. 2]
==1995 ...==
* [[Gerald Tesauro]] ('''1995'''). ''Temporal Difference Learning and TD-Gammon''. [[ACM#Communications|Communications of the ACM]], Vol. 38, No. 3
* [[Michael Buro]] ('''1999'''). ''Efficient Approximation of Backgammon Race Equities.'' [[ICGA Journal#22_3|ICCA Journal, Vol 22, No. 3]],[http://www.cs.ualberta.ca/~mburo/ps/book.pdf pdf]
==2000 ...==
* [[Michael Buro]] ('''2001'''). ''Efficient Approximation of Backgammon Race Equities.'' [[Advances in Computer Games 9]], [http://www.cs.ualberta.ca/~mburo/ps/bgequ.pdf pdf]
* [[Gerald Tesauro]] ('''2002'''). ''Programming backgammon using self-teaching neural nets''. [http://www.informatik.uni-trier.de/~ley/db/journals/ai/ai134.html#Tesauro02 Artificial Intelligence Vol. 134 No. 1-2]
* [[Frank Berger]] ('''2002'''). ''BGBlitz wins Backgammon tournament''. [[ICGA Journal#25_3|ICGA Journal, Vol. 25, No. 3]] » [[7th Computer Olympiad#Backgammon|7th Computer Olympiad]]
* [[Frank Berger]] ('''2002'''). ''Backgammon at the 7th Computer Olympiad''. [[ICGA Journal#25_4|ICGA Journal, Vol. 25, No. 4]] » [[7th Computer Olympiad#Backgammon|7th Computer Olympiad]]
* [[Frank Berger]] ('''2003'''). ''BGBlitz wins Backgammon tournament''. [[ICGA Journal#26_4|ICGA Journal, Vol. 26, No. 4]] » [[8th Computer Olympiad#Backgammon|8th Computer Olympiad]]
* [[Thomas Hauk]], [[Michael Buro]], [[Jonathan Schaeffer]] ('''2004'''). ''[http://link.springer.com/chapter/10.1007/11674399_4 *-Minimax Performance in Backgammon]''. [[CG 2004]]
==2005 ...==
* [[Frank Berger]] ('''2006'''). ''GnuBG wins Backgammon tournament''. [[ICGA Journal#29_3|ICGA Journal, Vol. 29, No. 3]] » [[11th Computer Olympiad#Backgammon|11th Computer Olympiad]]
* [[François van Lishout]], [[Guillaume Chaslot]], [[Jos Uiterwijk]] ('''2007'''). ''[https://www.researchgate.net/publication/228378473_Monte-Carlo_tree_search_in_backgammon Monte-Carlo Tree Search in Backgammon]''. [[CGW 2007]]
* [[Frank Berger]] ('''2007'''). ''BGBlitz wins Backgammon tournament''. [[ICGA Journal#30_2|ICGA Journal, Vol. 30, No. 2]] » [[12th Computer Olympiad#Backgammon|12th Computer Olympiad]]
* [[Wee Chong Oon]], [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/h/Henz:Martin.html Martin Henz] ('''2007'''). ''[http://www.aaai.org/Library/AAAI/2007/aaai07-098.php M2ICAL Analyses HC-Gammon]''. [http://www.informatik.uni-trier.de/~ley/db/conf/aaai/aaai2007.html#OonH07 AAAI 2007] <ref>[http://satirist.org/learn-game/systems/gammon/hc-gammon.html The hillclimbing HC-Gammon] from [http://satirist.org/learn-game/ Machine Learning in Games] by [[Jay Scott]]</ref>
==2010 ...==
* [[Marco Wiering]] ('''2010'''). ''[https://scholar.google.com/citations?view_op=view_citation&hl=en&user=xVas0I8AAAAJ&cstart=20&citation_for_view=xVas0I8AAAAJ:_kc_bZDykSQC Self-play and using an expert to learn to play backgammon with temporal difference learning]''. [http://www.scirp.org/journal/jilsa/ Journal of Intelligent Learning Systems and Applications], Vol. 2, No. 2
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2011'''). ''Training Neural Networks to Play Backgammon Variants Using Reinforcement Learning''. Proceedings of [http://conference.researchbib.com/?eventid=6400 Evogames 2011], Part I, LNCS 6624, [http://ai.uom.gr/nikpapa/publications/Training%20NN%20to%20Play%20Backgammon%20Variants%20Using%20RL.pdf pdf]
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2011'''). ''[https://www.conftool.net/acg13/index.php?page=browseSessions&form_session=5 Improving Temporal Difference Performance in Backgammon Variants]''. [[Advances in Computer Games 13]], [http://ai.uom.gr/nikpapa/publications/Improving%20Temporal%20Difference%20Learning%20in%20Backgammon%20Variants_ACG13.pdf pdf]
* [[Frank Berger]] ('''2012'''). ''Palamedes wins Backgammon Tournament''. [[ICGA Journal#35_1|ICGA Journal, Vol. 35, No. 1]] » [[16th Computer Olympiad#Backgammon|16th Computer Olympiad]]
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2013'''). ''AnyGammon: Playing backgammon variants using any board size''. [http://dblp.uni-trier.de/db/conf/fdg/fdg2013.html FDG-2013], [http://www.fdg2013.org/program/festival/anygammon.pdf pdf]
==2015 ...==
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2015'''). ''Constructing Pin Endgame Databases for the Backgammon Variant Plakoto''. [[Advances in Computer Games 14]] <ref>[https://en.wikipedia.org/wiki/Plakoto Plakoto from Wikipedia]</ref>
=Forum Posts=
* [https://www.stmintz.com/ccc/index.php?id=25139 Chess, Backgammon and Neural Nets (NN)] by [[Torsten Schoop]], [[CCC]], August 20, 1998
* [https://www.stmintz.com/ccc/index.php?id=359097 Neural nets in backgammon] by [[Albert Silver]], [[CCC]], April 07, 2004
* [http://www.talkchess.com/forum/viewtopic.php?t=15442 A SNAC, anyone?] by [[Jan Brouwer]], [[CCC]], July 30, 2007
* [http://www.talkchess.com/forum/viewtopic.php?t=24403 What is the best backgammon software?] by M. Ansari, [[CCC]], October 15, 2008
* [http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=138559 Backgammon is not chess!] by Joe Russell, [http://www.bgonline.org/forums/ BGonline.org Forums], March 08, 2013
=External Links=
* [https://en.wikipedia.org/wiki/Backgammon Backgammon from Wikipedia]
* [http://www.bkgm.com/ Backgammon Galore]
: [http://www.bkgm.com/rules.html Rules of Backgammon]
==Computer Backgammon==
* [https://www.game-ai-forum.org/icga-tournaments/game.php?id=11 Backgammon (ICGA Tournaments)]
* [http://www.bkgm.com/articles/page07.html#programming Backgammon Articles: Using Computers to Improve Your Game] hosted by the [http://www.bkgm.com/ Backgammon Galore]
* [http://satirist.org/learn-game/systems/gammon/ the neural net backgammon programs] from [http://satirist.org/learn-game/ Machine Learning in Games] by [[Jay Scott]]
* [http://www.cs.cornell.edu/boom/2001sp/Tsinteris/gammon.htm Neural Network learns Backgammon] by [http://kimtsi.com/ Kimon Tsinteris] and David Wilson
* [http://www.fibs.com/ FIBS, the First Internet Backgammon Server]
==Backgammon Programs==
* [http://www.bkgm.com/software.html Backgammon Software] from [http://www.bkgm.com/ Backgammon Galore]
* [https://www.bgblitz.com/index.html BGBlitz]
* [http://www.gnubg.org/ GNU Backgammon]
* [http://www.backgammoned.net/all-about-backgammon/jellyfish.html Jellyfish]
* [http://ai.uom.gr/nikpapa/Palamedes/ Palamedes]
* [https://www.bgsnowie.com/ Snowie]
=References=
<references />
'''[[Games|Up one Level]]'''
[[FILE:Backgammon lg.png|border|right|thumb| A Backgammon Set <ref>A backgammon set, consisting of a board, two sets of 15 checkers, two pairs of dice, a [https://en.wikipedia.org/wiki/Backgammon#Doubling_cube doubling cube], and dice cups, Image by [https://commons.wikimedia.org/wiki/User:Ptkfgs Ptkfgs], March 6, 2013, [https://en.wikipedia.org/wiki/Backgammon Backgammon from Wikipedia], [https://en.wikipedia.org/wiki/Wikimedia_Commons Wikimedia Commons]</ref> ]]
'''Backgammon''',<br/>
a turn-based two-player [https://en.wikipedia.org/wiki/Tables_%28board_game%29 tables] board game of [https://en.wikipedia.org/wiki/Game_of_chance chance] and strategy with 15 checkers each on a board of 24 spaces or points. One moves according to rolls of a pair of dice, trying to bring own checkers home and bear them off before the opponent does <ref>[http://www.bkgm.com/ Backgammon Galore]</ref>. Opponent checkers can be "hit" and returned to the start.
=Computer Backgammon=
Backgammon programs were pioneered in the late 70s by [[Hans Berliner]] with focus on [[Tapered Eval|smooth evaluation]], and by [[Gerald Tesauro]] from the late 80s, who successfully applied [[Neural Networks]] and [[Temporal Difference Learning]] to his Backgammon playing programs. Computer backgammon is regularly played at [[Computer Olympiad|Computer Olympiads]], organized by the [[ICGA]] <ref>[https://www.game-ai-forum.org/icga-tournaments/game.php?id=11 Backgammon (ICGA Tournaments)]</ref>.
=[[Computer Olympiad|Computer Olympiads]]<span id="Olympiad"></span>=
* [[1st Computer Olympiad#Backgammon|1st Computer Olympiad, London 1989]]
* [[2nd Computer Olympiad#Backgammon|2nd Computer Olympiad, London 1990]]
* [[4th Computer Olympiad#Backgammon|4th Computer Olympiad, London 1992]]
* [[7th Computer Olympiad#Backgammon|7th Computer Olympiad, Maastricht 2002]]
* [[8th Computer Olympiad#Backgammon|8th Computer Olympiad, Graz 2003]]
* [[11th Computer Olympiad#Backgammon|11th Computer Olympiad, Turin 2006]]
* [[12th Computer Olympiad#Backgammon|12th Computer Olympiad, Amsterdam 2007]]
* [[16th Computer Olympiad#Backgammon|16th Computer Olympiad, Tilburg 2011]]
* [[18th Computer Olympiad#Backgammon|18th Computer Olympiad, Leiden 2015]]
* [[19th Computer Olympiad#Backgammon|19th Computer Olympiad, Leiden 2016]]
=Photos=
[[FILE:Backgammon2015.jpg|none|border|text-bottom|640px|link=https://icga.leidenuniv.nl/?page_id=1467]]
[[18th Computer Olympiad#Backgammon|18th Computer Olympiad 2015]], Backgammon medalists: [[Frank Berger]] (Bronze for [https://www.game-ai-forum.org/icga-tournaments/program.php?id=63 BGBlitz]), <br/>[[Nikolaos Papahristou]] (Gold for [https://www.game-ai-forum.org/icga-tournaments/program.php?id=712 Palamedes]), and [[Nardy Pillards]] (Silver for [https://www.game-ai-forum.org/icga-tournaments/program.php?id=62 GNU Backgammon]) <ref>[https://icga.leidenuniv.nl/?page_id=1467 18th Computer Olympiad - Day 6 Photos] by [[Jan Krabbenbos]]</ref>
=Evaluation=
In the late 70s at [[Carnegie-Mellon University]], [[Hans Berliner]] developed the [[Backgammon]] playing program '''BKG 9.8''' for the [[PDP-10]] to research the principles of [[Evaluation|evaluation]] for another game than chess with a much higher [[Branching Factor|branching factor]] of more than 800 at every node <ref>[[Hans Berliner]] ('''1977'''). ''[http://www.bkgm.com/articles/Berliner/ExperiencesInEvaluationWithBKG/index.html Experiences in Evaluation with BKG, a Program That Plays Backgammon]''. [[Conferences#IJCAI1977|IJCAI, 1977]], hosted by [http://www.bkgm.com/ Backgammon Galore]</ref>. Early versions of BKG played badly even against weak players, but Berliner noticed that its critical mistakes were always at transitions apparently due to [[Evaluation Discontinuity|evaluation discontinuity]]. He applied principles of [https://en.wikipedia.org/wiki/Fuzzy_logic fuzzy logic] to [[Tapered Eval|smooth out]] the transition between phases, and by July 1979, BKG 9.8 was strong enough to play against the ruling world champion [https://en.wikipedia.org/wiki/Luigi_Villa Luigi Villa]. It won the match 7–1, becoming the first computer program to defeat a world champion in any game. Berliner states that the victory was largely a matter of luck, as the computer received more favorable dice rolls <ref>[https://en.wikipedia.org/wiki/Hans_Berliner Hans Berliner from Wikipedia]</ref> <ref>[[Hans Berliner]] ('''1980'''). ''[http://www.bkgm.com/articles/Berliner/BackgammonProgramBeatsWorldChamp/ Backgammon Computer Program Beats World Champion]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 14</ref>.
=Learning=
In the late 80s, [[IBM]] researcher [[Gerald Tesauro]] pioneered in applying [[Neural Networks]] to Backgammon - first within his program [https://en.wikipedia.org/wiki/Neurogammon Neurogammon], which won the Gold medal at the [[1st Computer Olympiad#Backgammon|1st Computer Olympiad]] 1989 - and further improved by ''TD-Lambda'' based [[Temporal Difference Learning]] within [https://en.wikipedia.org/wiki/TD-Gammon TD-Gammon] <ref>[[Richard Sutton]], [[Andrew Barto]] ('''1998'''). ''[http://www.incompleteideas.net/sutton/book/the-book.html Reinforcement Learning: An Introduction]''. [https://en.wikipedia.org/wiki/MIT_Press MIT Press], [http://www.incompleteideas.net/sutton/book/ebook/node108.html 11.1 TD-Gammon]</ref>.
=Publications=
==1977 ...==
* [[Hans Berliner]] ('''1977'''). ''BKG - A Program that Plays Backgammon''. Technical Report, [[Carnegie Mellon University]]
* [[Hans Berliner]] ('''1977'''). ''[http://www.bkgm.com/articles/Berliner/ExperiencesInEvaluationWithBKG/index.html Experiences in Evaluation with BKG, a Program That Plays Backgammon]''. [[Conferences#IJCAI1977|IJCAI, 1977]], hosted by [http://www.bkgm.com/ Backgammon Galore]
* [[Hans Berliner]] ('''1979'''). ''[http://www.bkgm.com/articles/Berliner/EvaluationFunctionsLargeDomains/ On the Construction of Evaluation Functions for Large Domains]''. [[Conferences#IJCAI1979|IJCAI 1979]], Vol. 1, hosted by [http://www.bkgm.com/ Backgammon Galore]
* Editor ('''1979'''). ''Computer Backgammon''. [[Personal Computing#3_8|Personal Computing, Vol. 3, No. 8]], pp. 81
==1980 ...==
* [[Hans Berliner]] ('''1980'''). ''[http://www.bkgm.com/articles/Berliner/BackgammonProgramBeatsWorldChamp/ Backgammon Computer Program Beats World Champion]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 14, hosted by [http://www.bkgm.com/ Backgammon Galore]
* [[Hans Berliner]] ('''1980'''). ''[http://www.bkgm.com/articles/Berliner/ComputerBackgammon/index.html Computer Backgammon]''. [[Scientific American]], Vol. 242, No. 6, hosted by [http://www.bkgm.com/ Backgammon Galore]
==1985 ...==
* [[Gerald Tesauro]], [[Terrence J. Sejnowski]] ('''1987'''). ''A 'Neural' Network that Learns to Play Backgammon''. [http://www.informatik.uni-trier.de/~ley/db/conf/nips/nips1987.html#TesauroS87 NIPS 1987]
* [[Gerald Tesauro]] ('''1988'''). ''Connectionist Learning of Expert Backgammon Evaluations''. [http://www.informatik.uni-trier.de/~ley/db/conf/icml/ml1988.html#Tesauro88 ML, 1988]
* [[Gerald Tesauro]] ('''1988'''). ''Neural network defeats creator in backgammon match''. Technical report no. CCSR-88-6, Center for Complex Systems Research, [[University of Illinois at Urbana-Champaign]]
* [[Gerald Tesauro]] ('''1989'''). ''NEUROGAMMON: A Neural-Network Backgammon Learning Program''. [[1st Computer Olympiad#Workshop|Heuristic Programming in Artificial Intelligence 1]]
* [[Gerald Tesauro]] ('''1989'''). ''[http://www.mitpressjournals.org/doi/abs/10.1162/neco.1989.1.3.321?journalCode=neco Neurogammon Wins Computer Olympiad]''. Neural Computation Vol. 1, No. 3
* [[Gerald Tesauro]], [[Terrence J. Sejnowski]] ('''1989'''). ''A Parallel Network that Learns to Play Backgammon''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 39, No. 3
==1990 ...==
* [[Gerald Tesauro]] ('''1992'''). ''Temporal Difference Learning of Backgammon Strategy''. [http://www.informatik.uni-trier.de/~ley/db/conf/icml/ml1992.html#Tesauro92 ML 1992]
* [[Justin A. Boyan]] ('''1992'''). ''Modular Neural Networks for Learning Context-Dependent Game Strategies''. Master's thesis, [https://en.wikipedia.org/wiki/University_of_Cambridge University of Cambridge], [http://www.cs.cmu.edu/~jab/cv/pubs/boyan.backgammon-thesis.pdf pdf]
* [[Gerald Tesauro]] ('''1994'''). ''TD-Gammon, a Self-Teaching Backgammon Program, Achieves Master-Level Play''. [http://www.informatik.uni-trier.de/~ley/db/journals/neco/neco6.html#Tesauro94 Neural Computation Vol. 6, No. 2]
==1995 ...==
* [[Gerald Tesauro]] ('''1995'''). ''Temporal Difference Learning and TD-Gammon''. [[ACM#Communications|Communications of the ACM]], Vol. 38, No. 3
* [[Michael Buro]] ('''1999'''). ''Efficient Approximation of Backgammon Race Equities.'' [[ICGA Journal#22_3|ICCA Journal, Vol 22, No. 3]],[http://www.cs.ualberta.ca/~mburo/ps/book.pdf pdf]
==2000 ...==
* [[Michael Buro]] ('''2001'''). ''Efficient Approximation of Backgammon Race Equities.'' [[Advances in Computer Games 9]], [http://www.cs.ualberta.ca/~mburo/ps/bgequ.pdf pdf]
* [[Gerald Tesauro]] ('''2002'''). ''Programming backgammon using self-teaching neural nets''. [http://www.informatik.uni-trier.de/~ley/db/journals/ai/ai134.html#Tesauro02 Artificial Intelligence Vol. 134 No. 1-2]
* [[Frank Berger]] ('''2002'''). ''BGBlitz wins Backgammon tournament''. [[ICGA Journal#25_3|ICGA Journal, Vol. 25, No. 3]] » [[7th Computer Olympiad#Backgammon|7th Computer Olympiad]]
* [[Frank Berger]] ('''2002'''). ''Backgammon at the 7th Computer Olympiad''. [[ICGA Journal#25_4|ICGA Journal, Vol. 25, No. 4]] » [[7th Computer Olympiad#Backgammon|7th Computer Olympiad]]
* [[Frank Berger]] ('''2003'''). ''BGBlitz wins Backgammon tournament''. [[ICGA Journal#26_4|ICGA Journal, Vol. 26, No. 4]] » [[8th Computer Olympiad#Backgammon|8th Computer Olympiad]]
* [[Thomas Hauk]], [[Michael Buro]], [[Jonathan Schaeffer]] ('''2004'''). ''[http://link.springer.com/chapter/10.1007/11674399_4 *-Minimax Performance in Backgammon]''. [[CG 2004]]
==2005 ...==
* [[Frank Berger]] ('''2006'''). ''GnuBG wins Backgammon tournament''. [[ICGA Journal#29_3|ICGA Journal, Vol. 29, No. 3]] » [[11th Computer Olympiad#Backgammon|11th Computer Olympiad]]
* [[François van Lishout]], [[Guillaume Chaslot]], [[Jos Uiterwijk]] ('''2007'''). ''[https://www.researchgate.net/publication/228378473_Monte-Carlo_tree_search_in_backgammon Monte-Carlo Tree Search in Backgammon]''. [[CGW 2007]]
* [[Frank Berger]] ('''2007'''). ''BGBlitz wins Backgammon tournament''. [[ICGA Journal#30_2|ICGA Journal, Vol. 30, No. 2]] » [[12th Computer Olympiad#Backgammon|12th Computer Olympiad]]
* [[Wee Chong Oon]], [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/h/Henz:Martin.html Martin Henz] ('''2007'''). ''[http://www.aaai.org/Library/AAAI/2007/aaai07-098.php M2ICAL Analyses HC-Gammon]''. [http://www.informatik.uni-trier.de/~ley/db/conf/aaai/aaai2007.html#OonH07 AAAI 2007] <ref>[http://satirist.org/learn-game/systems/gammon/hc-gammon.html The hillclimbing HC-Gammon] from [http://satirist.org/learn-game/ Machine Learning in Games] by [[Jay Scott]]</ref>
==2010 ...==
* [[Marco Wiering]] ('''2010'''). ''[https://scholar.google.com/citations?view_op=view_citation&hl=en&user=xVas0I8AAAAJ&cstart=20&citation_for_view=xVas0I8AAAAJ:_kc_bZDykSQC Self-play and using an expert to learn to play backgammon with temporal difference learning]''. [http://www.scirp.org/journal/jilsa/ Journal of Intelligent Learning Systems and Applications], Vol. 2, No. 2
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2011'''). ''Training Neural Networks to Play Backgammon Variants Using Reinforcement Learning''. Proceedings of [http://conference.researchbib.com/?eventid=6400 Evogames 2011], Part I, LNCS 6624, [http://ai.uom.gr/nikpapa/publications/Training%20NN%20to%20Play%20Backgammon%20Variants%20Using%20RL.pdf pdf]
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2011'''). ''[https://www.conftool.net/acg13/index.php?page=browseSessions&form_session=5 Improving Temporal Difference Performance in Backgammon Variants]''. [[Advances in Computer Games 13]], [http://ai.uom.gr/nikpapa/publications/Improving%20Temporal%20Difference%20Learning%20in%20Backgammon%20Variants_ACG13.pdf pdf]
* [[Frank Berger]] ('''2012'''). ''Palamedes wins Backgammon Tournament''. [[ICGA Journal#35_1|ICGA Journal, Vol. 35, No. 1]] » [[16th Computer Olympiad#Backgammon|16th Computer Olympiad]]
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2013'''). ''AnyGammon: Playing backgammon variants using any board size''. [http://dblp.uni-trier.de/db/conf/fdg/fdg2013.html FDG-2013], [http://www.fdg2013.org/program/festival/anygammon.pdf pdf]
==2015 ...==
* [[Nikolaos Papahristou]], [[Ioannis Refanidis]] ('''2015'''). ''Constructing Pin Endgame Databases for the Backgammon Variant Plakoto''. [[Advances in Computer Games 14]] <ref>[https://en.wikipedia.org/wiki/Plakoto Plakoto from Wikipedia]</ref>
=Forum Posts=
* [https://www.stmintz.com/ccc/index.php?id=25139 Chess, Backgammon and Neural Nets (NN)] by [[Torsten Schoop]], [[CCC]], August 20, 1998
* [https://www.stmintz.com/ccc/index.php?id=359097 Neural nets in backgammon] by [[Albert Silver]], [[CCC]], April 07, 2004
* [http://www.talkchess.com/forum/viewtopic.php?t=15442 A SNAC, anyone?] by [[Jan Brouwer]], [[CCC]], July 30, 2007
* [http://www.talkchess.com/forum/viewtopic.php?t=24403 What is the best backgammon software?] by M. Ansari, [[CCC]], October 15, 2008
* [http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=138559 Backgammon is not chess!] by Joe Russell, [http://www.bgonline.org/forums/ BGonline.org Forums], March 08, 2013
=External Links=
* [https://en.wikipedia.org/wiki/Backgammon Backgammon from Wikipedia]
* [http://www.bkgm.com/ Backgammon Galore]
: [http://www.bkgm.com/rules.html Rules of Backgammon]
==Computer Backgammon==
* [https://www.game-ai-forum.org/icga-tournaments/game.php?id=11 Backgammon (ICGA Tournaments)]
* [http://www.bkgm.com/articles/page07.html#programming Backgammon Articles: Using Computers to Improve Your Game] hosted by the [http://www.bkgm.com/ Backgammon Galore]
* [http://satirist.org/learn-game/systems/gammon/ the neural net backgammon programs] from [http://satirist.org/learn-game/ Machine Learning in Games] by [[Jay Scott]]
* [http://www.cs.cornell.edu/boom/2001sp/Tsinteris/gammon.htm Neural Network learns Backgammon] by [http://kimtsi.com/ Kimon Tsinteris] and David Wilson
* [http://www.fibs.com/ FIBS, the First Internet Backgammon Server]
==Backgammon Programs==
* [http://www.bkgm.com/software.html Backgammon Software] from [http://www.bkgm.com/ Backgammon Galore]
* [https://www.bgblitz.com/index.html BGBlitz]
* [http://www.gnubg.org/ GNU Backgammon]
* [http://www.backgammoned.net/all-about-backgammon/jellyfish.html Jellyfish]
* [http://ai.uom.gr/nikpapa/Palamedes/ Palamedes]
* [https://www.bgsnowie.com/ Snowie]
=References=
<references />
'''[[Games|Up one Level]]'''
