25,161
edits
Changes
Hex
,Created page with "'''Home * Games * Hex''' FILE:Hexposition02.jpg|border|right|thumb|A rendering of a Hex game on a 19x19 board <ref>[https://en.wikipedia.org/wiki/Hex_%28b..."
'''[[Main Page|Home]] * [[Games]] * Hex'''
[[FILE:Hexposition02.jpg|border|right|thumb|A rendering of a Hex game on a 19x19 board <ref>[https://en.wikipedia.org/wiki/Hex_%28board_game%29 Hex (board game) from Wikipedia]</ref> ]]
'''Hex''',<br/>
a [https://en.wikipedia.org/wiki/Two-player_game two-player] [https://en.wikipedia.org/wiki/Zero-sum_%28game_theory%29 zero-sum] and [https://en.wikipedia.org/wiki/Perfect_information perfect information] [https://en.wikipedia.org/wiki/Abstract_strategy abstract strategy], [https://en.wikipedia.org/wiki/Connection_game connection] [https://en.wikipedia.org/wiki/Board_game board game] played on a [https://en.wikipedia.org/wiki/Hex_map hexagonal grid] composed of [https://en.wikipedia.org/wiki/Hexagon hexagons] <ref>[https://en.wikipedia.org/wiki/Honeycomb Honeycomb from Wikipedia]</ref> arranged in an n × n [https://en.wikipedia.org/wiki/Orthodiagonal_quadrilateral orthodiagonal] [https://en.wikipedia.org/wiki/Quadrilateral Quadrilateral], most common an 11x11, 13x13 or 19x19 [https://en.wikipedia.org/wiki/Rhombus Rhombus]. The goal is to connect the opposing sides of own colors with own stones - or to prevent the opponent from doing so, by alternately placing stones on a single cell.
=History=
Hex was invented by the Danish mathematician [https://en.wikipedia.org/wiki/Piet_Hein_%28Denmark%29 Piet Hein] called Polygon, appeared in the Danish newspaper [https://en.wikipedia.org/wiki/Politiken Politiken] on December 26, 1942, and independently by the American mathematician [[Mathematician#JFNash|John Nash]] in 1947, who, according to the biography [https://en.wikipedia.org/wiki/A_Beautiful_Mind_%28book%29 A Beautiful Mind], advocated 14x14 as the optimal size. In 1952 [https://en.wikipedia.org/wiki/Parker_Brothers Parker Brothers] marketed a version called Hex and the name stuck <ref>[http://www.hexwiki.org/index.php?title=History_of_Hex History of Hex - HexWiki]</ref> .
Since [[5th Computer Olympiad#Hex|2000]], Computer Hex is regularly played at the [[Computer Olympiad|Computer Olympiads]]. In 2003, 7x7 Hex was [https://en.wikipedia.org/wiki/Solved_game solved] by [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] <ref>[[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] ('''2003'''). ''Solving 7x7 Hex: Virtual Connections and Game-state Reduction''. [[Advances in Computer Games 10]], [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR03.pdf pdf]</ref> .
=[[Computer Olympiad|Computer Olympiads]]=
* [[5th Computer Olympiad#Hex|5th Computer Olympiad, London 2000]]
* [[8th Computer Olympiad#Hex|8th Computer Olympiad, Graz 2003]]
* [[9th Computer Olympiad#Hex|9th Computer Olympiad, Ramat Gan 2004]]
* [[11th Computer Olympiad#Hex|11th Computer Olympiad, Turin 2006]]
* [[13th Computer Olympiad#Hex|13th Computer Olympiad, Beijing 2008]]
* [[14th Computer Olympiad#Hex|14th Computer Olympiad, Pamplona 2009]]
* [[15th Computer Olympiad#Hex|15th Computer Olympiad, Kanazawa 2010]]
* [[16th Computer Olympiad#Hex|16th Computer Olympiad, Tilburg 2011]]
* [[17th Computer Olympiad#Hex|17th Computer Olympiad, Yokohama 2013]]
* [[18th Computer Olympiad#Hex|18th Computer Olympiad, Leiden 2015]]
=Photos=
[[FILE:WolveTeam2.JPG|none|border|text-bottom|640px]]
Members of the [https://www.game-ai-forum.org/icga-tournaments/program.php?id=135 Wolve Team] at the [[11th Computer Olympiad#Hex|Computer Olympiad, Turin 2006]] <ref>[[Ryan Hayward]] ('''2006'''). ''Six Wins Hex Tournament''. [[ICGA Journal#29_3|ICGA Journal, Vol. 29, No 3]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptTorino.pdf pdf]</ref><br/>[[Ryan Hayward]], [[Philip Henderson]] and [[Broderick Arneson]] (operating [https://www.game-ai-forum.org/icga-tournaments/program.php?id=136 Hex Kriger])
[[FILE:HexKrigerWolve.JPG|none|border|text-bottom|640px]]
=Hex Programs=
<ref>[https://www.game-ai-forum.org/icga-tournaments/game.php?id=7 Hex (ICGA Tournaments)]</ref>
{| class="wikitable"
|-
! Programs
! Authors
! [[Search|Search Algorithm]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=136 Hex Kriger]
| [[Rune Rasmussen]], [[Cameron Browne]], [[Auden Ellertsen]],<br/>[[Ross Hayward]], [[Frédéric Maire]]
| [[Alpha-Beta]]
|-
| [http://itunes.apple.com/app/id397349481 Hex Nash]
| [[Jeffrey Vanneste]]
|
|-
| [http://home.earthlink.net/%7Evanshel/ Hexy]
| [[Vadim Anshelevich]]
| [[Alpha-Beta]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=649 MIMHex]
| [[Jakub Pawlewicz]]
| [[Monte-Carlo Tree Search|MCTS]], [[UCT|RAVE UCT]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=555 MoHex]
| [[Philip Henderson]], [[Broderick Arneson]], [[Ryan Hayward]]
| [[Monte-Carlo Tree Search|MCTS]], [[UCT]], Solver
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=276 Mongoose]
| [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]]
| [[Alpha-Beta]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=132 Queenbee]
| [[Jack van Rijswijck]]
| [[Alpha-Beta]]
|-
| [http://six.retes.hu/ Six]
| [[Gábor Melis]]
| [[Alpha-Beta]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=135 Wolve]
| [[Ryan Hayward]], [[Broderick Arneson]], [[Philip Henderson]],<br/>[[Michael Johanson]], [[Morgan Kan]], [[Martin Müller]], [[Geoff Ryan]]
| [[Alpha-Beta]], Solver
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=556 Yopt]
| [[Abdallah Saffidine]], [[Tristan Cazenave]]
| [[Monte-Carlo Tree Search|MCTS]], [[UCT|RAVE UCT]]
|}
=Publications=
<ref>[http://sites.google.com/site/javhar1/hexbibliography Hex bibliography] by [[Jack van Rijswijck]]</ref> <ref>[http://sites.google.com/site/javhar1/javharpublications Javhar publications] by [[Jack van Rijswijck]]</ref>
==1953==
* [[Claude Shannon|Claude E. Shannon]] ('''1953'''). ''[http://www.jnorman.com/cgi-bin/hss/38411 Computers and Automata]''. Proceedings of the Institute of Radio Engineers Vol. 41, No. 10 <ref>In [[Vadim Anshelevich]] ('''2002'''). ''[http://portal.acm.org/citation.cfm?id=512148.512154&coll=DL&dl=GUIDE&CFID=19278566&CFTOKEN=41682182 A hierarchical approach to computer Hex]''. Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence, [http://home.earthlink.net/~vanshel/VAnshelevich-ARTINT.pdf pdf], [[Vadim Anshelevich]] acknowledged [[Claude Shannon]], who build an analogue Hex-playing machine using electrical [https://en.wikipedia.org/wiki/Resistor resistor] circuits, which was model in Anshelevich's program [https://www.game-ai-forum.org/icga-tournaments/program.php?id=131 Hexy]</ref> <ref>[[Hex]] is a special case of the [https://en.wikipedia.org/wiki/Shannon_switching_game Shannon Switching Game], from [[Jack van Rijswijck]] ('''2003'''). ''Search and evaluation in Hex''. Technical report, [[University of Alberta]], [http://home.fuse.net/swmeyers/y-hex.pdf pdf]</ref> <ref>[http://www.althofer.de/3-hirn-grant--fischer.html Thomas Fischer] ('''2009'''). ''Bridg-It – Beating Shannon’s Analog Heuristic''. [http://www.minet.uni-jena.de/Math-Net/reports/sources/2009/09-07report.pdf pdf]</ref>
==1959==
* [[Martin Gardner]] ('''1959'''). ''The Game of Hex''. in ''[http://www.librarything.com/work/5317022 The Scientific American Book of Mathematical Puzzles and Diversions]''. pp 73-83.[https://en.wikipedia.org/wiki/Simon_%26_Schuster Simon & Schuster]
==1977==
* [[Mathematician#CBerge|Claude Berge]] ('''1977'''). ''L'Art Subtil du Hex''. (French) Supplied with a version of the game that was marketed in France in 1977
==1980 ...==
* [[Mathematician#CBerge|Claude Berge]] ('''1981'''). ''Some remarks about the Hex problem''. in [http://www.plambeck.org/oldhtml/mathematics/klarner/ David A. Klarner] (ed): ''The Mathematical Gardner'', pages 25-27. Wadsworth International, [http://www.amazon.com/Mathematical-Gardner-David-Klarner/dp/0534980155 amazon.com]
* [[Mathematician#SReisch|Stefan Reisch]] ('''1981'''). ''[http://www.springerlink.com/content/v6k3233j5725892p/ Hex ist PSPACE-vollständig]''. [http://ftp.math.utah.edu/pub//tex/bib/toc/actainfo.html#15%282%29:December:1981 Acta Informatica Vol. 15, No. 2] (German) <ref>[https://en.wikipedia.org/wiki/PSPACE PSPACE from Wikipedia]</ref> <ref>[https://en.wikipedia.org/wiki/PSPACE-complete PSPACE-complete from Wikipedia]</ref>
* [[Georgy Adelson-Velsky]], [[Vladimir Arlazarov]], [[Mikhail Donskoy]] ('''1988'''). ''Algorithms for Games''. Springer-Verlag, New York, NY. ISBN 3-540-96629-3. [http://www.amazon.com/Algorithms-Games-Georgy-M-Adelson-Velsky/dp/0387966293 amazon.com]
==2000 ...==
* [[Vadim Anshelevich]] ('''2000'''). ''[http://www.msri.org/realvideo/ln/msri/2000/gametheory/anshelevich/1/index.html The Game of Hex: The Hierarchical Approach]''. Combinatorial Game Theory Workshop, [https://en.wikipedia.org/wiki/Mathematical_Sciences_Research_Institute MSRI, Berkeley]
* [[Cameron Browne]] ('''2000'''). ''[http://www.crcpress.com/product/isbn/9781568811178 Hex Strategy: Making the Right Connections]''. [https://en.wikipedia.org/wiki/A_K_Peters,_Ltd. A K Peters]
* [[Jack van Rijswijck]] ('''2000'''). ''Computer Hex: Are Bees better than Fruitflies?'' M.Sc. Thesis, [[University of Alberta]], [http://sites.google.com/site/javhar1/AreBeesBetterThanFruitfliesThesis.pdf pdf]
* [[Vadim Anshelevich]] ('''2000'''). ''[http://portal.acm.org/citation.cfm?id=721449 The Game of Hex: An Automatic Theorem Proving Approach to Game Programming]''. Proceedings of the Seventeenth National Conference on Artificial Intelligence, [http://home.earthlink.net/%7Evanshel/VAnshelevich-01.pdf pdf] <ref>[http://www.aaai.org/Awards/paper.php AAAI-2000 Outstanding Paper Awards]</ref>
* [[Jack van Rijswijck]] ('''2000'''). ''Partition Search in Hex''. [[5th Computer Olympiad#Workshop|5th Computer Olympiad Workshop]]
* [[Vadim Anshelevich]] ('''2000'''). ''The Game of Hex: The Hierarchical Approach and its Discovery''. [[5th Computer Olympiad#Workshop|5th Computer Olympiad Workshop]]
* [[Vadim Anshelevich]] ('''2000'''). ''Hexy wins Hex Tournament''. [[ICGA Journal#23_3|ICGA Journal, Vol. 23, No. 3]], [http://home.earthlink.net/%7Evanshel/Ansh-MSO-Results.pdf pdf]
* [[Mathematician#IStewart|Ian Stewart]] ('''2000'''). ''Hex Marks the Spot''. [https://en.wikipedia.org/wiki/Scientific_American Scientific American], September 2000
'''2001'''
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2001'''). ''On a Decomposition Method for Finding Winning Strategy in Hex Game''. ADCOG21, [http://zernike.uwinnipeg.ca/~s_liao/pdf/adcog21.pdf pdf]
'''2002'''
* [[Vadim Anshelevich]] ('''2002'''). ''[http://portal.acm.org/citation.cfm?id=512148.512154&coll=DL&dl=GUIDE&CFID=19278566&CFTOKEN=41682182 A hierarchical approach to computer Hex]''. Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence, [http://home.earthlink.net/%7Evanshel/VAnshelevich-ARTINT.pdf pdf]
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2002'''). ''Another solution for Hex 7x7''. Technical report, [https://en.wikipedia.org/wiki/University_of_Manitoba University of Manitoba]. [http://hex.kosmanor.com/hex/Papers/ylp-TR.pdf pdf]
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2002'''). ''A New Solution for 7x7 Hex Game''. [http://hex.kosmanor.com/hex/Papers/cg02-ylp02.pdf pdf]
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2002'''). ''[http://www.springerlink.com/content/j0116ufv4utg21ly/ New Winning and Losing Positions for 7x7 Hex]''. [[CG 2002]], [http://zernike.uwinnipeg.ca/~s_liao/pdf/cg02.pdf pdf]
'''2003'''
* [[Jack van Rijswijck]] ('''2003'''). ''Search and evaluation in Hex''. Technical report, [[University of Alberta]], [http://home.fuse.net/swmeyers/y-hex.pdf pdf]
* [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] ('''2003'''). ''Solving 7x7 Hex: Virtual Connections and Game-state Reduction''. [[Advances in Computer Games 10]], [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR03.pdf pdf]
* [[Gábor Melis]], [[Ryan Hayward]] ('''2003'''). ''Six wins Hex Tournament (8th Computer Olympiad 2003 Graz)''. [[ICGA Journal#26_4|ICGA Journal, Vol. 26, No. 4]], [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/grazRpt.pdf pdf] » [[8th Computer Olympiad#Hex|8th Computer Olympiad]]
* [http://www.comlab.ox.ac.uk/people/stefan.kiefer/ Stefan Kiefer] ('''2003'''). ''Die Menge der Virtuellen Verbindungen im Spiel Hex ist PSPACE-vollständig''. Studienarbeit Nr. 1887, [https://en.wikipedia.org/wiki/University_of_Stuttgart University of Stuttgart], [http://www7.in.tum.de/um/bibdb/kiefer/STUD-1887.pdf pdf] (German)
'''2004'''
* [[Rune Rasmussen]], [[Frédéric Maire]] ('''2004'''). ''An Extension of the H-Search Algorithm for Artificial Hex Players''. AI'2004, [http://eprints.qut.edu.au/489/1/2004_AI04_RasmussenMaire.pdf pdf]
* [[Jan Willemson]], [[Yngvi Björnsson]] ('''2004'''). ''Six wins hex tournament''. [[ICGA Journal#27_3|ICGA Journal, Vol. 27, No. 3]] » [[9th Computer Olympiad#Hex|9th Computer Olympiad]]
==2005 ...==
* [[Kohei Noshita]] ('''2005'''). ''Union-Connections and Straightforward Winning Strategies in Hex''. [[ICGA Journal#28_1|ICGA Journal, Vol. 28, No. 1]], [http://chess.cs.uec.ac.jp/~noshita/hex88proof.pdf companion document 2006 as pdf]
* [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] ('''2005'''). ''Solving 7x7 Hex with domination, fill-in, and virtual connections''. Theoretical Computer Science, 349(2):123–139, 2005. [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR05.pdf pdf]
* [http://maarup.net/thomas/ Thomas Maarup] ('''2005''') ''Everything You Always Wanted to Know About Hex But Were Afraid to Ask''. Masters thesis, [https://en.wikipedia.org/wiki/University_of_Southern_Denmark University of Southern Denmark], [http://maarup.net/thomas/hex/hex3.pdf pdf]
'''2006'''
* [[Yngvi Björnsson]], [[Ryan Hayward]], [[Michael Johanson]], [[Jack van Rijswijck]] ('''2006'''). ''Dead Cell Analysis in Hex and the Shannon Game.'' In Graph Theory in Paris: Proceedings of a Conference in Memory of [[Mathematician#CBerge|Claude Berge]] (CT'04 Paris), pp. 45–60, 2006. [http://sites.google.com/site/javhar1/DeadCellAnalysis.zip zipped ps]
* [[Ryan Hayward]], [[Jack van Rijswijck]] ('''2006'''). ''Hex and Combinatorics''. Discrete Math 306, [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/Elsevier.pdf pdf]
* [[Rune Rasmussen]], [[Frédéric Maire]], [[Ross Hayward]] ('''2006'''). ''A Move Generating Algorithm for Hex Solvers''. [http://eprints.qut.edu.au/5121/1/5121_1.pdf pdf]
* [[Jack van Rijswijck]] ('''2006'''). ''Set Colouring Games''. Ph.D. thesis, [[University of Alberta]], [http://sites.google.com/site/javhar1/Set_Colouring_Games.pdf pdf]
* [[Ryan Hayward]] ('''2006'''). ''Six Wins Hex tournament''. [[ICGA Journal#29_3|ICGA Journal, Vol. 29, No 3]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptTorino.pdf pdf] » [[11th Computer Olympiad#Hex|11th Computer Olympiad]]
* [[Ryan Hayward]], [[Broderick Arneson]], [[Philip Henderson]] ('''2006'''). ''[http://link.springer.com/chapter/10.1007/978-3-540-75538-8_10 Automatic Strategy Verification for Hex]''. [[CG 2006]], [http://webdocs.cs.ualberta.ca/~hayward/papers/verify.pdf pdf]
'''2007'''
* [[Rune Rasmussen]] ('''2007'''). ''Algorithmic Approaches for Playing and Solving Shannon Games''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Queensland University of Queensland], [http://eprints.qut.edu.au/18616/1/01Thesis.pdf pdf]
* [[Rune Rasmussen]], [[Frédéric Maire]], [[Ross Hayward]] ('''2007'''). ''[http://eprints.qut.edu.au/12527/ A Template Matching Table for Speeding-Up Game-Tree Searches for Hex]''. 20th Australian Joint Conference on Artificial Intelligence
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2007'''). ''[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4406406 Apply Heuristic Search to Discover a New Winning Solution in Hex Game]''. Proceedings of the [http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4405868 Fourth International Conference on Fuzzy Systems and Knowledge Discovery] - Volume 04
'''2008'''
* [[Philip Henderson]], [[Ryan Hayward]] ('''2008'''). ''[http://link.springer.com/chapter/10.1007/978-3-540-87608-3_21 Probing the 4-3-2 Edge Template in Hex]''. [[CG 2008]], [http://webdocs.cs.ualberta.ca/~hayward/papers/probe432.pdf pdf]
'''2009'''
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2009'''). ''Wolve 2008 wins Hex tournament''. [[ICGA Journal#32_1|ICGA Journal, Vol. 32, No. 1]] » [[13th Computer Olympiad#Hex|13th Computer Olympiad]]
* [[Philip Henderson]], [[Broderick Arneson]], [[Ryan Hayward]] ('''2009'''). ''Solving 8×8 Hex''. [http://ijcai.org/papers09/contents.php IJCAI-09], [http://ijcai.org/papers09/Papers/IJCAI09-091.pdf pdf]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2009'''). ''MoHex wins Hex tournament''. [[ICGA Journal#32_2|ICGA Journal, Vol. 32, No. 2]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptPamplona.pdf pdf] » [[14th Computer Olympiad#Hex|14th Computer Olympiad]]
==2010 ...==
* [[Philip Henderson]], [[Broderick Arneson]], [[Ryan Hayward]] ('''2010'''). ''[http://www.springerlink.com/content/y8298h5713143289/ Hex, Braids, the Crossing Rule, and XH-Search]''. [[Advances in Computer Games 12]], [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/xhsearch.pdf pdf]
* [[Tristan Cazenave]], [[Abdallah Saffidine]] ('''2010'''). ''Monte-Carlo Hex''. [http://www.lamsade.dauphine.fr/%7Ecazenave/papers/hex.pdf pdf]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2010'''). ''MoHex wins Hex Tournament''. [[ICGA Journal#33_3|ICGA Journal, Vol. 33, No. 3]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptKanazawa.pdf pdf] » [[15th Computer Olympiad#Hex|15th Computer Olympiad]]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2010'''). ''Solving Hex: Beyond Humans''. [[CG 2010]], [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/beyond.pdf pdf]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2010'''). ''Monte Carlo Tree Search in Hex''. [[IEEE#TOCIAIGAMES|IEEE Transactions on Computational Intelligence and AI in Games]], Vol. 2, No. 4, [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/mcts-hex.pdf pdf]
* [[Philip Henderson]] ('''2010'''). ''Playing and Solving the Game of Hex''. (Ph.D. thesis under committee review <ref>[http://webdocs.cs.ualberta.ca/~ph/research.html Philip Henderson's Research Page]</ref> ), [http://webdocs.cs.ualberta.ca/%7Eph/Henderson-Philip-Fall2010.pdf pdf]
'''2011'''
* [[Henry Brausen]], [[Ryan Hayward]], [[Martin Müller]], [[Abdul Qadir]], [[David Spies]] ('''2011'''). ''[http://link.springer.com/chapter/10.1007/978-3-642-31866-5_19 Blunder Cost in Go and Hex]''. [[Advances in Computer Games 13]]
'''2012'''
* [[Ryan Hayward]] ('''2012'''). ''MoHex wins Hex Tournament''. [[ICGA Journal#35_2|ICGA Journal, Vol. 35, No. 2]] » [[16th Computer Olympiad#Hex|16th Computer Olympiad]]
'''2013'''
* [[Ryan Hayward]], [[Broderick Arneson]], [[Shih-Chieh Huang]], [[Jakub Pawlewicz]] ('''2013'''). ''MOHEX Wins Hex Tournament''. [[ICGA Journal#36_3|ICGA Journal, Vol. 36, No. 3]], [https://webdocs.cs.ualberta.ca/~hayward/papers/rptYokohama.pdf pdf] » [[17th Computer Olympiad#Hex|17th Computer Olympiad]]
* [[Shih-Chieh Huang]], [[Broderick Arneson]], [[Ryan Hayward]], [[Martin Müller]], [[Jakub Pawlewicz]] ('''2013'''). ''MoHex 2.0: a pattern-based MCTS Hex player''. [[CG 2013]], [https://webdocs.cs.ualberta.ca/~hayward/papers/m2.pdf pdf]
==2015 ...==
* [[Xi Liang]] ('''2015'''). ''[https://ir.nctu.edu.tw/handle/11536/127155?locale=en Job-Level Search for Solving Hex]''. Master's thesis, [[National Chiao Tung University]], advisor [[I-Chen Wu]]
* [[Xi Liang]], [[Ting-Han Wei]], [[I-Chen Wu]] ('''2015'''). ''Job-level UCT search for solving Hex''. [http://dblp.uni-trier.de/db/conf/cig/cig2015.html#LiangWW15 CIG 2015]
* [[Kei Takada]], [[Masaya Honjo]], [[Hiroyuki Iizuka]], [[Masahito Yamamoto]] ('''2015'''). ''Developing Computer Hex using Global and Local Evaluation based on Board Network Characteristics''. [[Advances in Computer Games 14]]
* [[S. Ali Mirsoleimani]], [[Aske Plaat]], [[Jaap van den Herik]], [[Jos Vermaseren]] ('''2015'''). ''Scaling Monte Carlo Tree Search on Intel Xeon Phi''. [http://arxiv.org/abs/1507.04383 CoRR abs/1507.04383] » [[Monte-Carlo Tree Search|MCTS]], [[Parallel Search]], [[x86-64]]
* [[S. Ali Mirsoleimani]], [[Aske Plaat]], [[Jaap van den Herik]], [[Jos Vermaseren]] ('''2015'''). ''Parallel Monte Carlo Tree Search from Multi-core to Many-core Processors''. [https://whova.com/portal/ieeet_201508/ TrustCom/BigDataSE/|ISPA 2015], [https://askeplaat.files.wordpress.com/2013/01/ispa2015.pdf pdf]
* [[Xi Liang]], [[Ting-Han Wei]], [[I-Chen Wu]] ('''2015'''). ''Solving Hex Openings Using Job-Level UCT Search''. [[ICGA Journal#38_3|ICGA Journal, Vol. 38, No. 3]]
* [[Jakub Pawlewicz]], [[Ryan Hayward]] ('''2015'''). ''[https://www.aaai.org/ocs/index.php/SOCS/SOCS15/paper/view/11040 Sibling Conspiracy Number Search]''. [https://en.wikipedia.org/wiki/Symposium_on_Combinatorial_Search SoCS 2015]
'''2016'''
* [[Kenny Young]], [[Ryan Hayward]] ('''2016'''). ''A Reverse Hex Solver''. [[CG 2016]]
'''2017'''
* [[Ryan Hayward]], [[Jakub Pawlewicz]], [[Kei Takada]], [[Tony van der Valk]] ('''2017'''). ''MOHEX Wins 2015 Hex 11x11 and Hex 13x13 Tournaments''. [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]] » [[18th Computer Olympiad#Hex|18th Computer Olympiad]]
=Forum Posts=
* [http://www.talkchess.com/forum/viewtopic.php?t=39659 bitboard algorithm needed] by [[Daniel Shawul]], [[CCC]], July 08, 2011
* [http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=442069&t=41853 Re: Possible Search Algorithms for GPUs?] by [[Daniel Shawul]], [[CCC]], January 07, 2012 » [[GPU]], [[King Pattern#FloodFillAlgorithms|Flood Fill Algorithms]]
=External Links=
* [https://en.wikipedia.org/wiki/Hex_%28board_game%29 Hex (board game) from Wikipedia]
* [http://www.hexwiki.org/index.php?title=Main_Page HexWiki]
* [http://senseis.xmp.net/?Hex Sensei's Library: Hex]
* [https://www.game-ai-forum.org/icga-tournaments/game.php?id=7 Hex (ICGA Tournaments)]
* [http://ilk.uvt.nl/icga/games/hex/ ICGA: Hex] by [[Vadim Anshelevich]]
* [http://webdocs.cs.ualberta.ca/%7Ehayward/hex/ University of Alberta Computer Hex Research Group]
* [http://sites.google.com/site/javhar1/hex hex - javhar1] by [[Jack van Rijswijck]]
* [http://maarup.net/thomas/hex/ Hex] by [http://maarup.net/thomas/ Thomas Maarup]
* [http://www.mazeworks.com/hex7/about/index.htm About Hex] from [http://www.mazeworks.com/home.htm MazeWorks - Java Games and Puzzles]
* [http://www.krammer.nl/hex/ The abstract board game Hex] by Tijs Krammer
* [http://www.mazeworks.com/hex7/hex_faq.html HEX: Answers to common questions] by David Boll
* [http://www.cs.cmu.edu/%7Ehde/hex/hexfaq/ Answers to infrequently asked questions about the game of Hex] by [[Bert Enderton]]
* [http://kwakuananse.twoday.net/stories/4906416/ Kwaku Ananse: Hex] by [http://kwakuananse.twoday.net/topics/Wer+ist+K%26ouml%3Bppnick/ Ralf Poschmann] (German)
* [http://www.littlegolem.net/jsp/ Little Golem - online board games] by [http://sk.linkedin.com/in/malaschitz Richard Malaschitz]
* [http://www.edcollins.com/golem/ Little Golem - FAQ] by [http://www.edcollins.com/index.html Edward D. Collins]
* [http://www.angermueller.de/pflaster_gartenplatten/sechseck/produktdaten2.htm Sechseckpflaster] (German) a little off topic, may be for outdoor Hex ...
* [https://en.wikipedia.org/wiki/Hexagonal_chess Hexagonal chess from Wikipedia]
* [https://en.wikipedia.org/wiki/Sannin_shogi Sannin shogi from Wikipedia]
=References=
<references />
'''[[Games|Up one Level]]'''
[[FILE:Hexposition02.jpg|border|right|thumb|A rendering of a Hex game on a 19x19 board <ref>[https://en.wikipedia.org/wiki/Hex_%28board_game%29 Hex (board game) from Wikipedia]</ref> ]]
'''Hex''',<br/>
a [https://en.wikipedia.org/wiki/Two-player_game two-player] [https://en.wikipedia.org/wiki/Zero-sum_%28game_theory%29 zero-sum] and [https://en.wikipedia.org/wiki/Perfect_information perfect information] [https://en.wikipedia.org/wiki/Abstract_strategy abstract strategy], [https://en.wikipedia.org/wiki/Connection_game connection] [https://en.wikipedia.org/wiki/Board_game board game] played on a [https://en.wikipedia.org/wiki/Hex_map hexagonal grid] composed of [https://en.wikipedia.org/wiki/Hexagon hexagons] <ref>[https://en.wikipedia.org/wiki/Honeycomb Honeycomb from Wikipedia]</ref> arranged in an n × n [https://en.wikipedia.org/wiki/Orthodiagonal_quadrilateral orthodiagonal] [https://en.wikipedia.org/wiki/Quadrilateral Quadrilateral], most common an 11x11, 13x13 or 19x19 [https://en.wikipedia.org/wiki/Rhombus Rhombus]. The goal is to connect the opposing sides of own colors with own stones - or to prevent the opponent from doing so, by alternately placing stones on a single cell.
=History=
Hex was invented by the Danish mathematician [https://en.wikipedia.org/wiki/Piet_Hein_%28Denmark%29 Piet Hein] called Polygon, appeared in the Danish newspaper [https://en.wikipedia.org/wiki/Politiken Politiken] on December 26, 1942, and independently by the American mathematician [[Mathematician#JFNash|John Nash]] in 1947, who, according to the biography [https://en.wikipedia.org/wiki/A_Beautiful_Mind_%28book%29 A Beautiful Mind], advocated 14x14 as the optimal size. In 1952 [https://en.wikipedia.org/wiki/Parker_Brothers Parker Brothers] marketed a version called Hex and the name stuck <ref>[http://www.hexwiki.org/index.php?title=History_of_Hex History of Hex - HexWiki]</ref> .
Since [[5th Computer Olympiad#Hex|2000]], Computer Hex is regularly played at the [[Computer Olympiad|Computer Olympiads]]. In 2003, 7x7 Hex was [https://en.wikipedia.org/wiki/Solved_game solved] by [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] <ref>[[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] ('''2003'''). ''Solving 7x7 Hex: Virtual Connections and Game-state Reduction''. [[Advances in Computer Games 10]], [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR03.pdf pdf]</ref> .
=[[Computer Olympiad|Computer Olympiads]]=
* [[5th Computer Olympiad#Hex|5th Computer Olympiad, London 2000]]
* [[8th Computer Olympiad#Hex|8th Computer Olympiad, Graz 2003]]
* [[9th Computer Olympiad#Hex|9th Computer Olympiad, Ramat Gan 2004]]
* [[11th Computer Olympiad#Hex|11th Computer Olympiad, Turin 2006]]
* [[13th Computer Olympiad#Hex|13th Computer Olympiad, Beijing 2008]]
* [[14th Computer Olympiad#Hex|14th Computer Olympiad, Pamplona 2009]]
* [[15th Computer Olympiad#Hex|15th Computer Olympiad, Kanazawa 2010]]
* [[16th Computer Olympiad#Hex|16th Computer Olympiad, Tilburg 2011]]
* [[17th Computer Olympiad#Hex|17th Computer Olympiad, Yokohama 2013]]
* [[18th Computer Olympiad#Hex|18th Computer Olympiad, Leiden 2015]]
=Photos=
[[FILE:WolveTeam2.JPG|none|border|text-bottom|640px]]
Members of the [https://www.game-ai-forum.org/icga-tournaments/program.php?id=135 Wolve Team] at the [[11th Computer Olympiad#Hex|Computer Olympiad, Turin 2006]] <ref>[[Ryan Hayward]] ('''2006'''). ''Six Wins Hex Tournament''. [[ICGA Journal#29_3|ICGA Journal, Vol. 29, No 3]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptTorino.pdf pdf]</ref><br/>[[Ryan Hayward]], [[Philip Henderson]] and [[Broderick Arneson]] (operating [https://www.game-ai-forum.org/icga-tournaments/program.php?id=136 Hex Kriger])
[[FILE:HexKrigerWolve.JPG|none|border|text-bottom|640px]]
=Hex Programs=
<ref>[https://www.game-ai-forum.org/icga-tournaments/game.php?id=7 Hex (ICGA Tournaments)]</ref>
{| class="wikitable"
|-
! Programs
! Authors
! [[Search|Search Algorithm]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=136 Hex Kriger]
| [[Rune Rasmussen]], [[Cameron Browne]], [[Auden Ellertsen]],<br/>[[Ross Hayward]], [[Frédéric Maire]]
| [[Alpha-Beta]]
|-
| [http://itunes.apple.com/app/id397349481 Hex Nash]
| [[Jeffrey Vanneste]]
|
|-
| [http://home.earthlink.net/%7Evanshel/ Hexy]
| [[Vadim Anshelevich]]
| [[Alpha-Beta]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=649 MIMHex]
| [[Jakub Pawlewicz]]
| [[Monte-Carlo Tree Search|MCTS]], [[UCT|RAVE UCT]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=555 MoHex]
| [[Philip Henderson]], [[Broderick Arneson]], [[Ryan Hayward]]
| [[Monte-Carlo Tree Search|MCTS]], [[UCT]], Solver
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=276 Mongoose]
| [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]]
| [[Alpha-Beta]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=132 Queenbee]
| [[Jack van Rijswijck]]
| [[Alpha-Beta]]
|-
| [http://six.retes.hu/ Six]
| [[Gábor Melis]]
| [[Alpha-Beta]]
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=135 Wolve]
| [[Ryan Hayward]], [[Broderick Arneson]], [[Philip Henderson]],<br/>[[Michael Johanson]], [[Morgan Kan]], [[Martin Müller]], [[Geoff Ryan]]
| [[Alpha-Beta]], Solver
|-
| [https://www.game-ai-forum.org/icga-tournaments/program.php?id=556 Yopt]
| [[Abdallah Saffidine]], [[Tristan Cazenave]]
| [[Monte-Carlo Tree Search|MCTS]], [[UCT|RAVE UCT]]
|}
=Publications=
<ref>[http://sites.google.com/site/javhar1/hexbibliography Hex bibliography] by [[Jack van Rijswijck]]</ref> <ref>[http://sites.google.com/site/javhar1/javharpublications Javhar publications] by [[Jack van Rijswijck]]</ref>
==1953==
* [[Claude Shannon|Claude E. Shannon]] ('''1953'''). ''[http://www.jnorman.com/cgi-bin/hss/38411 Computers and Automata]''. Proceedings of the Institute of Radio Engineers Vol. 41, No. 10 <ref>In [[Vadim Anshelevich]] ('''2002'''). ''[http://portal.acm.org/citation.cfm?id=512148.512154&coll=DL&dl=GUIDE&CFID=19278566&CFTOKEN=41682182 A hierarchical approach to computer Hex]''. Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence, [http://home.earthlink.net/~vanshel/VAnshelevich-ARTINT.pdf pdf], [[Vadim Anshelevich]] acknowledged [[Claude Shannon]], who build an analogue Hex-playing machine using electrical [https://en.wikipedia.org/wiki/Resistor resistor] circuits, which was model in Anshelevich's program [https://www.game-ai-forum.org/icga-tournaments/program.php?id=131 Hexy]</ref> <ref>[[Hex]] is a special case of the [https://en.wikipedia.org/wiki/Shannon_switching_game Shannon Switching Game], from [[Jack van Rijswijck]] ('''2003'''). ''Search and evaluation in Hex''. Technical report, [[University of Alberta]], [http://home.fuse.net/swmeyers/y-hex.pdf pdf]</ref> <ref>[http://www.althofer.de/3-hirn-grant--fischer.html Thomas Fischer] ('''2009'''). ''Bridg-It – Beating Shannon’s Analog Heuristic''. [http://www.minet.uni-jena.de/Math-Net/reports/sources/2009/09-07report.pdf pdf]</ref>
==1959==
* [[Martin Gardner]] ('''1959'''). ''The Game of Hex''. in ''[http://www.librarything.com/work/5317022 The Scientific American Book of Mathematical Puzzles and Diversions]''. pp 73-83.[https://en.wikipedia.org/wiki/Simon_%26_Schuster Simon & Schuster]
==1977==
* [[Mathematician#CBerge|Claude Berge]] ('''1977'''). ''L'Art Subtil du Hex''. (French) Supplied with a version of the game that was marketed in France in 1977
==1980 ...==
* [[Mathematician#CBerge|Claude Berge]] ('''1981'''). ''Some remarks about the Hex problem''. in [http://www.plambeck.org/oldhtml/mathematics/klarner/ David A. Klarner] (ed): ''The Mathematical Gardner'', pages 25-27. Wadsworth International, [http://www.amazon.com/Mathematical-Gardner-David-Klarner/dp/0534980155 amazon.com]
* [[Mathematician#SReisch|Stefan Reisch]] ('''1981'''). ''[http://www.springerlink.com/content/v6k3233j5725892p/ Hex ist PSPACE-vollständig]''. [http://ftp.math.utah.edu/pub//tex/bib/toc/actainfo.html#15%282%29:December:1981 Acta Informatica Vol. 15, No. 2] (German) <ref>[https://en.wikipedia.org/wiki/PSPACE PSPACE from Wikipedia]</ref> <ref>[https://en.wikipedia.org/wiki/PSPACE-complete PSPACE-complete from Wikipedia]</ref>
* [[Georgy Adelson-Velsky]], [[Vladimir Arlazarov]], [[Mikhail Donskoy]] ('''1988'''). ''Algorithms for Games''. Springer-Verlag, New York, NY. ISBN 3-540-96629-3. [http://www.amazon.com/Algorithms-Games-Georgy-M-Adelson-Velsky/dp/0387966293 amazon.com]
==2000 ...==
* [[Vadim Anshelevich]] ('''2000'''). ''[http://www.msri.org/realvideo/ln/msri/2000/gametheory/anshelevich/1/index.html The Game of Hex: The Hierarchical Approach]''. Combinatorial Game Theory Workshop, [https://en.wikipedia.org/wiki/Mathematical_Sciences_Research_Institute MSRI, Berkeley]
* [[Cameron Browne]] ('''2000'''). ''[http://www.crcpress.com/product/isbn/9781568811178 Hex Strategy: Making the Right Connections]''. [https://en.wikipedia.org/wiki/A_K_Peters,_Ltd. A K Peters]
* [[Jack van Rijswijck]] ('''2000'''). ''Computer Hex: Are Bees better than Fruitflies?'' M.Sc. Thesis, [[University of Alberta]], [http://sites.google.com/site/javhar1/AreBeesBetterThanFruitfliesThesis.pdf pdf]
* [[Vadim Anshelevich]] ('''2000'''). ''[http://portal.acm.org/citation.cfm?id=721449 The Game of Hex: An Automatic Theorem Proving Approach to Game Programming]''. Proceedings of the Seventeenth National Conference on Artificial Intelligence, [http://home.earthlink.net/%7Evanshel/VAnshelevich-01.pdf pdf] <ref>[http://www.aaai.org/Awards/paper.php AAAI-2000 Outstanding Paper Awards]</ref>
* [[Jack van Rijswijck]] ('''2000'''). ''Partition Search in Hex''. [[5th Computer Olympiad#Workshop|5th Computer Olympiad Workshop]]
* [[Vadim Anshelevich]] ('''2000'''). ''The Game of Hex: The Hierarchical Approach and its Discovery''. [[5th Computer Olympiad#Workshop|5th Computer Olympiad Workshop]]
* [[Vadim Anshelevich]] ('''2000'''). ''Hexy wins Hex Tournament''. [[ICGA Journal#23_3|ICGA Journal, Vol. 23, No. 3]], [http://home.earthlink.net/%7Evanshel/Ansh-MSO-Results.pdf pdf]
* [[Mathematician#IStewart|Ian Stewart]] ('''2000'''). ''Hex Marks the Spot''. [https://en.wikipedia.org/wiki/Scientific_American Scientific American], September 2000
'''2001'''
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2001'''). ''On a Decomposition Method for Finding Winning Strategy in Hex Game''. ADCOG21, [http://zernike.uwinnipeg.ca/~s_liao/pdf/adcog21.pdf pdf]
'''2002'''
* [[Vadim Anshelevich]] ('''2002'''). ''[http://portal.acm.org/citation.cfm?id=512148.512154&coll=DL&dl=GUIDE&CFID=19278566&CFTOKEN=41682182 A hierarchical approach to computer Hex]''. Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence, [http://home.earthlink.net/%7Evanshel/VAnshelevich-ARTINT.pdf pdf]
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2002'''). ''Another solution for Hex 7x7''. Technical report, [https://en.wikipedia.org/wiki/University_of_Manitoba University of Manitoba]. [http://hex.kosmanor.com/hex/Papers/ylp-TR.pdf pdf]
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2002'''). ''A New Solution for 7x7 Hex Game''. [http://hex.kosmanor.com/hex/Papers/cg02-ylp02.pdf pdf]
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2002'''). ''[http://www.springerlink.com/content/j0116ufv4utg21ly/ New Winning and Losing Positions for 7x7 Hex]''. [[CG 2002]], [http://zernike.uwinnipeg.ca/~s_liao/pdf/cg02.pdf pdf]
'''2003'''
* [[Jack van Rijswijck]] ('''2003'''). ''Search and evaluation in Hex''. Technical report, [[University of Alberta]], [http://home.fuse.net/swmeyers/y-hex.pdf pdf]
* [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] ('''2003'''). ''Solving 7x7 Hex: Virtual Connections and Game-state Reduction''. [[Advances in Computer Games 10]], [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR03.pdf pdf]
* [[Gábor Melis]], [[Ryan Hayward]] ('''2003'''). ''Six wins Hex Tournament (8th Computer Olympiad 2003 Graz)''. [[ICGA Journal#26_4|ICGA Journal, Vol. 26, No. 4]], [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/grazRpt.pdf pdf] » [[8th Computer Olympiad#Hex|8th Computer Olympiad]]
* [http://www.comlab.ox.ac.uk/people/stefan.kiefer/ Stefan Kiefer] ('''2003'''). ''Die Menge der Virtuellen Verbindungen im Spiel Hex ist PSPACE-vollständig''. Studienarbeit Nr. 1887, [https://en.wikipedia.org/wiki/University_of_Stuttgart University of Stuttgart], [http://www7.in.tum.de/um/bibdb/kiefer/STUD-1887.pdf pdf] (German)
'''2004'''
* [[Rune Rasmussen]], [[Frédéric Maire]] ('''2004'''). ''An Extension of the H-Search Algorithm for Artificial Hex Players''. AI'2004, [http://eprints.qut.edu.au/489/1/2004_AI04_RasmussenMaire.pdf pdf]
* [[Jan Willemson]], [[Yngvi Björnsson]] ('''2004'''). ''Six wins hex tournament''. [[ICGA Journal#27_3|ICGA Journal, Vol. 27, No. 3]] » [[9th Computer Olympiad#Hex|9th Computer Olympiad]]
==2005 ...==
* [[Kohei Noshita]] ('''2005'''). ''Union-Connections and Straightforward Winning Strategies in Hex''. [[ICGA Journal#28_1|ICGA Journal, Vol. 28, No. 1]], [http://chess.cs.uec.ac.jp/~noshita/hex88proof.pdf companion document 2006 as pdf]
* [[Ryan Hayward]], [[Yngvi Björnsson]], [[Michael Johanson]], [[Morgan Kan]], [[Nathan Po]], [[Jack van Rijswijck]] ('''2005'''). ''Solving 7x7 Hex with domination, fill-in, and virtual connections''. Theoretical Computer Science, 349(2):123–139, 2005. [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR05.pdf pdf]
* [http://maarup.net/thomas/ Thomas Maarup] ('''2005''') ''Everything You Always Wanted to Know About Hex But Were Afraid to Ask''. Masters thesis, [https://en.wikipedia.org/wiki/University_of_Southern_Denmark University of Southern Denmark], [http://maarup.net/thomas/hex/hex3.pdf pdf]
'''2006'''
* [[Yngvi Björnsson]], [[Ryan Hayward]], [[Michael Johanson]], [[Jack van Rijswijck]] ('''2006'''). ''Dead Cell Analysis in Hex and the Shannon Game.'' In Graph Theory in Paris: Proceedings of a Conference in Memory of [[Mathematician#CBerge|Claude Berge]] (CT'04 Paris), pp. 45–60, 2006. [http://sites.google.com/site/javhar1/DeadCellAnalysis.zip zipped ps]
* [[Ryan Hayward]], [[Jack van Rijswijck]] ('''2006'''). ''Hex and Combinatorics''. Discrete Math 306, [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/Elsevier.pdf pdf]
* [[Rune Rasmussen]], [[Frédéric Maire]], [[Ross Hayward]] ('''2006'''). ''A Move Generating Algorithm for Hex Solvers''. [http://eprints.qut.edu.au/5121/1/5121_1.pdf pdf]
* [[Jack van Rijswijck]] ('''2006'''). ''Set Colouring Games''. Ph.D. thesis, [[University of Alberta]], [http://sites.google.com/site/javhar1/Set_Colouring_Games.pdf pdf]
* [[Ryan Hayward]] ('''2006'''). ''Six Wins Hex tournament''. [[ICGA Journal#29_3|ICGA Journal, Vol. 29, No 3]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptTorino.pdf pdf] » [[11th Computer Olympiad#Hex|11th Computer Olympiad]]
* [[Ryan Hayward]], [[Broderick Arneson]], [[Philip Henderson]] ('''2006'''). ''[http://link.springer.com/chapter/10.1007/978-3-540-75538-8_10 Automatic Strategy Verification for Hex]''. [[CG 2006]], [http://webdocs.cs.ualberta.ca/~hayward/papers/verify.pdf pdf]
'''2007'''
* [[Rune Rasmussen]] ('''2007'''). ''Algorithmic Approaches for Playing and Solving Shannon Games''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Queensland University of Queensland], [http://eprints.qut.edu.au/18616/1/01Thesis.pdf pdf]
* [[Rune Rasmussen]], [[Frédéric Maire]], [[Ross Hayward]] ('''2007'''). ''[http://eprints.qut.edu.au/12527/ A Template Matching Table for Speeding-Up Game-Tree Searches for Hex]''. 20th Australian Joint Conference on Artificial Intelligence
* [[Jing Yang]], [[Simon Liao]], [[Mirek Pawlak]] ('''2007'''). ''[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4406406 Apply Heuristic Search to Discover a New Winning Solution in Hex Game]''. Proceedings of the [http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4405868 Fourth International Conference on Fuzzy Systems and Knowledge Discovery] - Volume 04
'''2008'''
* [[Philip Henderson]], [[Ryan Hayward]] ('''2008'''). ''[http://link.springer.com/chapter/10.1007/978-3-540-87608-3_21 Probing the 4-3-2 Edge Template in Hex]''. [[CG 2008]], [http://webdocs.cs.ualberta.ca/~hayward/papers/probe432.pdf pdf]
'''2009'''
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2009'''). ''Wolve 2008 wins Hex tournament''. [[ICGA Journal#32_1|ICGA Journal, Vol. 32, No. 1]] » [[13th Computer Olympiad#Hex|13th Computer Olympiad]]
* [[Philip Henderson]], [[Broderick Arneson]], [[Ryan Hayward]] ('''2009'''). ''Solving 8×8 Hex''. [http://ijcai.org/papers09/contents.php IJCAI-09], [http://ijcai.org/papers09/Papers/IJCAI09-091.pdf pdf]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2009'''). ''MoHex wins Hex tournament''. [[ICGA Journal#32_2|ICGA Journal, Vol. 32, No. 2]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptPamplona.pdf pdf] » [[14th Computer Olympiad#Hex|14th Computer Olympiad]]
==2010 ...==
* [[Philip Henderson]], [[Broderick Arneson]], [[Ryan Hayward]] ('''2010'''). ''[http://www.springerlink.com/content/y8298h5713143289/ Hex, Braids, the Crossing Rule, and XH-Search]''. [[Advances in Computer Games 12]], [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/xhsearch.pdf pdf]
* [[Tristan Cazenave]], [[Abdallah Saffidine]] ('''2010'''). ''Monte-Carlo Hex''. [http://www.lamsade.dauphine.fr/%7Ecazenave/papers/hex.pdf pdf]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2010'''). ''MoHex wins Hex Tournament''. [[ICGA Journal#33_3|ICGA Journal, Vol. 33, No. 3]], [http://webdocs.cs.ualberta.ca/~hayward/papers/rptKanazawa.pdf pdf] » [[15th Computer Olympiad#Hex|15th Computer Olympiad]]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2010'''). ''Solving Hex: Beyond Humans''. [[CG 2010]], [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/beyond.pdf pdf]
* [[Broderick Arneson]], [[Ryan Hayward]], [[Philip Henderson]] ('''2010'''). ''Monte Carlo Tree Search in Hex''. [[IEEE#TOCIAIGAMES|IEEE Transactions on Computational Intelligence and AI in Games]], Vol. 2, No. 4, [http://webdocs.cs.ualberta.ca/%7Ehayward/papers/mcts-hex.pdf pdf]
* [[Philip Henderson]] ('''2010'''). ''Playing and Solving the Game of Hex''. (Ph.D. thesis under committee review <ref>[http://webdocs.cs.ualberta.ca/~ph/research.html Philip Henderson's Research Page]</ref> ), [http://webdocs.cs.ualberta.ca/%7Eph/Henderson-Philip-Fall2010.pdf pdf]
'''2011'''
* [[Henry Brausen]], [[Ryan Hayward]], [[Martin Müller]], [[Abdul Qadir]], [[David Spies]] ('''2011'''). ''[http://link.springer.com/chapter/10.1007/978-3-642-31866-5_19 Blunder Cost in Go and Hex]''. [[Advances in Computer Games 13]]
'''2012'''
* [[Ryan Hayward]] ('''2012'''). ''MoHex wins Hex Tournament''. [[ICGA Journal#35_2|ICGA Journal, Vol. 35, No. 2]] » [[16th Computer Olympiad#Hex|16th Computer Olympiad]]
'''2013'''
* [[Ryan Hayward]], [[Broderick Arneson]], [[Shih-Chieh Huang]], [[Jakub Pawlewicz]] ('''2013'''). ''MOHEX Wins Hex Tournament''. [[ICGA Journal#36_3|ICGA Journal, Vol. 36, No. 3]], [https://webdocs.cs.ualberta.ca/~hayward/papers/rptYokohama.pdf pdf] » [[17th Computer Olympiad#Hex|17th Computer Olympiad]]
* [[Shih-Chieh Huang]], [[Broderick Arneson]], [[Ryan Hayward]], [[Martin Müller]], [[Jakub Pawlewicz]] ('''2013'''). ''MoHex 2.0: a pattern-based MCTS Hex player''. [[CG 2013]], [https://webdocs.cs.ualberta.ca/~hayward/papers/m2.pdf pdf]
==2015 ...==
* [[Xi Liang]] ('''2015'''). ''[https://ir.nctu.edu.tw/handle/11536/127155?locale=en Job-Level Search for Solving Hex]''. Master's thesis, [[National Chiao Tung University]], advisor [[I-Chen Wu]]
* [[Xi Liang]], [[Ting-Han Wei]], [[I-Chen Wu]] ('''2015'''). ''Job-level UCT search for solving Hex''. [http://dblp.uni-trier.de/db/conf/cig/cig2015.html#LiangWW15 CIG 2015]
* [[Kei Takada]], [[Masaya Honjo]], [[Hiroyuki Iizuka]], [[Masahito Yamamoto]] ('''2015'''). ''Developing Computer Hex using Global and Local Evaluation based on Board Network Characteristics''. [[Advances in Computer Games 14]]
* [[S. Ali Mirsoleimani]], [[Aske Plaat]], [[Jaap van den Herik]], [[Jos Vermaseren]] ('''2015'''). ''Scaling Monte Carlo Tree Search on Intel Xeon Phi''. [http://arxiv.org/abs/1507.04383 CoRR abs/1507.04383] » [[Monte-Carlo Tree Search|MCTS]], [[Parallel Search]], [[x86-64]]
* [[S. Ali Mirsoleimani]], [[Aske Plaat]], [[Jaap van den Herik]], [[Jos Vermaseren]] ('''2015'''). ''Parallel Monte Carlo Tree Search from Multi-core to Many-core Processors''. [https://whova.com/portal/ieeet_201508/ TrustCom/BigDataSE/|ISPA 2015], [https://askeplaat.files.wordpress.com/2013/01/ispa2015.pdf pdf]
* [[Xi Liang]], [[Ting-Han Wei]], [[I-Chen Wu]] ('''2015'''). ''Solving Hex Openings Using Job-Level UCT Search''. [[ICGA Journal#38_3|ICGA Journal, Vol. 38, No. 3]]
* [[Jakub Pawlewicz]], [[Ryan Hayward]] ('''2015'''). ''[https://www.aaai.org/ocs/index.php/SOCS/SOCS15/paper/view/11040 Sibling Conspiracy Number Search]''. [https://en.wikipedia.org/wiki/Symposium_on_Combinatorial_Search SoCS 2015]
'''2016'''
* [[Kenny Young]], [[Ryan Hayward]] ('''2016'''). ''A Reverse Hex Solver''. [[CG 2016]]
'''2017'''
* [[Ryan Hayward]], [[Jakub Pawlewicz]], [[Kei Takada]], [[Tony van der Valk]] ('''2017'''). ''MOHEX Wins 2015 Hex 11x11 and Hex 13x13 Tournaments''. [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]] » [[18th Computer Olympiad#Hex|18th Computer Olympiad]]
=Forum Posts=
* [http://www.talkchess.com/forum/viewtopic.php?t=39659 bitboard algorithm needed] by [[Daniel Shawul]], [[CCC]], July 08, 2011
* [http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=442069&t=41853 Re: Possible Search Algorithms for GPUs?] by [[Daniel Shawul]], [[CCC]], January 07, 2012 » [[GPU]], [[King Pattern#FloodFillAlgorithms|Flood Fill Algorithms]]
=External Links=
* [https://en.wikipedia.org/wiki/Hex_%28board_game%29 Hex (board game) from Wikipedia]
* [http://www.hexwiki.org/index.php?title=Main_Page HexWiki]
* [http://senseis.xmp.net/?Hex Sensei's Library: Hex]
* [https://www.game-ai-forum.org/icga-tournaments/game.php?id=7 Hex (ICGA Tournaments)]
* [http://ilk.uvt.nl/icga/games/hex/ ICGA: Hex] by [[Vadim Anshelevich]]
* [http://webdocs.cs.ualberta.ca/%7Ehayward/hex/ University of Alberta Computer Hex Research Group]
* [http://sites.google.com/site/javhar1/hex hex - javhar1] by [[Jack van Rijswijck]]
* [http://maarup.net/thomas/hex/ Hex] by [http://maarup.net/thomas/ Thomas Maarup]
* [http://www.mazeworks.com/hex7/about/index.htm About Hex] from [http://www.mazeworks.com/home.htm MazeWorks - Java Games and Puzzles]
* [http://www.krammer.nl/hex/ The abstract board game Hex] by Tijs Krammer
* [http://www.mazeworks.com/hex7/hex_faq.html HEX: Answers to common questions] by David Boll
* [http://www.cs.cmu.edu/%7Ehde/hex/hexfaq/ Answers to infrequently asked questions about the game of Hex] by [[Bert Enderton]]
* [http://kwakuananse.twoday.net/stories/4906416/ Kwaku Ananse: Hex] by [http://kwakuananse.twoday.net/topics/Wer+ist+K%26ouml%3Bppnick/ Ralf Poschmann] (German)
* [http://www.littlegolem.net/jsp/ Little Golem - online board games] by [http://sk.linkedin.com/in/malaschitz Richard Malaschitz]
* [http://www.edcollins.com/golem/ Little Golem - FAQ] by [http://www.edcollins.com/index.html Edward D. Collins]
* [http://www.angermueller.de/pflaster_gartenplatten/sechseck/produktdaten2.htm Sechseckpflaster] (German) a little off topic, may be for outdoor Hex ...
* [https://en.wikipedia.org/wiki/Hexagonal_chess Hexagonal chess from Wikipedia]
* [https://en.wikipedia.org/wiki/Sannin_shogi Sannin shogi from Wikipedia]
=References=
<references />
'''[[Games|Up one Level]]'''
