Hex

a [|two-player] [|zero-sum] and [|perfect information] [|abstract strategy], [|connection] [|board game] played on a [|hexagonal grid] composed of [|hexagons] arranged in an n × n [|orthodiagonal] [|Quadrilateral], most common an 11x11, 13x13 or 19x19 [|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. toc =History= Hex was invented by the Danish mathematician [|Piet Hein] called Polygon, appeared in the Danish newspaper [|Politiken] on December 26, 1942, and independently by the American mathematician John Nash in 1947, who, according to the biography [|A Beautiful Mind], advocated 14x14 as the optimal size. In 1952 [|Parker Brothers] marketed a version called Hex and the name stuck.
 * Home * Games * Hex**
 * [[image:Hexposition02.jpg link="https://en.wikipedia.org/wiki/Hex_%28board_game%29"]] ||~  || **Hex**,
 * A rendering of a Hex game on a 19x19 board ||~  ||^   ||
 * A rendering of a Hex game on a 19x19 board ||~  ||^   ||

Since 2000, Computer Hex is regularly played at the Computer Olympiads. In 2003, 7x7 Hex was [|solved] by Ryan Hayward, Yngvi Björnsson, Michael Johanson, Morgan Kan, Nathan Po, Jack van Rijswijck.

=Computer Olympiads=
 * 5th Computer Olympiad, London 2000
 * 8th Computer Olympiad, Graz 2003
 * 9th Computer Olympiad, Ramat Gan 2004
 * 11th Computer Olympiad, Turin 2006
 * 13th Computer Olympiad, Beijing 2008
 * 14th Computer Olympiad, Pamplona 2009
 * 15th Computer Olympiad, Kanazawa 2010
 * 16th Computer Olympiad, Tilburg 2011
 * 17th Computer Olympiad, Yokohama 2013
 * 18th Computer Olympiad, Leiden 2015

=Photos= Ryan Hayward, Philip Henderson and Broderick Arneson (operating [|Hex Kriger]) ||
 * [[image:WolveTeam2.JPG]] ||
 * Members of the [|Wolve Team] at the Computer Olympiad, Turin 2006
 * [[image:HexKrigerWolve.JPG]] ||
 * [[image:HexKrigerWolve.JPG]] ||

=Hex Programs= Ross Hayward, Frédéric Maire || Alpha-Beta || Michael Johanson, Morgan Kan, Martin Müller, Geoff Ryan || Alpha-Beta, Solver ||
 * ~ Programs ||~ Authors ||~ Search Algorithm ||
 * [|Hex Kriger] || Rune Rasmussen, Cameron Browne, Auden Ellertsen,
 * [|Hex Nash] || Jeffrey Vanneste ||  ||
 * [|Hexy] || Vadim Anshelevich || Alpha-Beta ||
 * [|MIMHex] || Jakub Pawlewicz || MCTS, RAVE UCT ||
 * [|MoHex] || Philip Henderson, Broderick Arneson, Ryan Hayward || MCTS, UCT, Solver ||
 * [|Mongoose] || Ryan Hayward, Yngvi Björnsson, Michael Johanson || Alpha-Beta ||
 * [|Queenbee] || Jack van Rijswijck || Alpha-Beta ||
 * [|Six] || Gábor Melis || Alpha-Beta ||
 * [|Wolve] || Ryan Hayward, Broderick Arneson, Philip Henderson,
 * [|Yopt] || Abdallah Saffidine, Tristan Cazenave || MCTS, RAVE UCT ||

=Publications=

1953

 * Claude E. Shannon (**1953**). //[|Computers and Automata]//. Proceedings of the Institute of Radio Engineers Vol. 41, No. 10

1959

 * Martin Gardner (**1959**). //The Game of Hex//. in //[|The Scientific American Book of Mathematical Puzzles and Diversions]//. pp 73-83.[|Simon & Schuster]

1977

 * Claude Berge (**1977**). //L'Art Subtil du Hex//. (French) Supplied with a version of the game that was marketed in France in 1977

1980 ...

 * Claude Berge (**1981**). //Some remarks about the Hex problem//. in [|David A. Klarner] (ed): //The Mathematical Gardner//, pages 25-27. Wadsworth International, [|amazon.com]
 * Stefan Reisch (**1981**). //[|Hex ist PSPACE-vollständig]//. [|Acta Informatica Vol. 15, No. 2] (German)
 * Georgy Adelson-Velsky, Vladimir Arlazarov, Mikhail Donskoy (**1988**). //Algorithms for Games//. Springer-Verlag, New York, NY. ISBN 3-540-96629-3. [|amazon.com]

2000 ...

 * Vadim Anshelevich (**2000**). //[|The Game of Hex: The Hierarchical Approach]//. Combinatorial Game Theory Workshop, [|MSRI, Berkeley]
 * Cameron Browne (**2000**). //[|Hex Strategy: Making the Right Connections]//. [|A K Peters]
 * Jack van Rijswijck (**2000**). //Computer Hex: Are Bees better than Fruitflies?// M.Sc. Thesis, University of Alberta, [|pdf]
 * Vadim Anshelevich (**2000**). //[|The Game of Hex: An Automatic Theorem Proving Approach to Game Programming]//. Proceedings of the Seventeenth National Conference on Artificial Intelligence, [|pdf]
 * Jack van Rijswijck (**2000**). //Partition Search in Hex//. 5th Computer Olympiad Workshop
 * Vadim Anshelevich (**2000**). //The Game of Hex: The Hierarchical Approach and its Discovery//. 5th Computer Olympiad Workshop
 * Vadim Anshelevich (**2000**). //Hexy wins Hex Tournament//. ICGA Journal, Vol. 23, No. 3, [|pdf]
 * Ian Stewart (**2000**). //Hex Marks the Spot//. [|Scientific American], September 2000
 * 2001**
 * Jing Yang, Simon Liao, Mirek Pawlak (**2001**). //On a Decomposition Method for Finding Winning Strategy in Hex Game//. ADCOG21, [|pdf]
 * 2002**
 * Vadim Anshelevich (**2002**). //[|A hierarchical approach to computer Hex]//. Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence, [|pdf]
 * Jing Yang, Simon Liao, Mirek Pawlak (**2002**). //Another solution for Hex 7x7//. Technical report, [|University of Manitoba]. [|pdf]
 * Jing Yang, Simon Liao, Mirek Pawlak (**2002**). //A New Solution for 7x7 Hex Game//. [|pdf]
 * Jing Yang, Simon Liao, Mirek Pawlak (**2002**). //[|New Winning and Losing Positions for 7x7 Hex]//. CG 2002, [|pdf]
 * 2003**
 * Jack van Rijswijck (**2003**). //Search and evaluation in Hex//. Technical report, University of Alberta, [|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, [|pdf]
 * Gábor Melis, Ryan Hayward (**2003**). //Six wins Hex Tournament (8th Computer Olympiad 2003 Graz)//. ICGA Journal, Vol. 26, No. 4, [|pdf] » 8th Computer Olympiad
 * [|Stefan Kiefer] (**2003**). //Die Menge der Virtuellen Verbindungen im Spiel Hex ist PSPACE-vollständig//. Studienarbeit Nr. 1887, [|University of Stuttgart], [|pdf] (German)
 * 2004**
 * Rune Rasmussen, Frédéric Maire (**2004**). //An Extension of the H-Search Algorithm for Artificial Hex Players//. AI'2004, [|pdf]
 * Jan Willemson, Yngvi Björnsson (**2004**). //Six wins hex tournament//. ICGA Journal, Vol. 27, No. 3 » 9th Computer Olympiad

2005 ...

 * Kohei Noshita (**2005**). //Union-Connections and Straightforward Winning Strategies in Hex//. ICGA Journal, Vol. 28, No. 1, [|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. [|pdf]
 * [|Thomas Maarup] (**2005**) //Everything You Always Wanted to Know About Hex But Were Afraid to Ask//. Masters thesis, [|University of Southern Denmark], [|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 Claude Berge (CT'04 Paris), pp. 45–60, 2006. [|zipped ps]
 * Ryan Hayward, Jack van Rijswijck (**2006**). //Hex and Combinatorics//. Discrete Math 306, [|pdf]
 * Rune Rasmussen, Frédéric Maire, Ross Hayward (**2006**). //A Move Generating Algorithm for Hex Solvers//. [|pdf]
 * Jack van Rijswijck (**2006**). //Set Colouring Games//. Ph.D. thesis, University of Alberta, [|pdf]
 * Ryan Hayward (**2006**). //Six Wins Hex tournament//. ICGA Journal, Vol. 29, No 3, [|pdf] » 11th Computer Olympiad
 * Ryan Hayward, Broderick Arneson, Philip Henderson (**2006**). //[|Automatic Strategy Verification for Hex]//. CG 2006, [|pdf]
 * 2007**
 * Rune Rasmussen (**2007**). //Algorithmic Approaches for Playing and Solving Shannon Games//. Ph.D. thesis, [|University of Queensland], [|pdf]
 * Rune Rasmussen, Frédéric Maire, Ross Hayward (**2007**). //[|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**). //[|Apply Heuristic Search to Discover a New Winning Solution in Hex Game]//. Proceedings of the [|Fourth International Conference on Fuzzy Systems and Knowledge Discovery] - Volume 04
 * 2008**
 * Philip Henderson, Ryan Hayward (**2008**). //[|Probing the 4-3-2 Edge Template in Hex]//. CG 2008, [|pdf]
 * 2009**
 * Broderick Arneson, Ryan Hayward, Philip Henderson (**2009**). //Wolve 2008 wins Hex tournament//. ICGA Journal, Vol. 32, No. 1 » 13th Computer Olympiad
 * Philip Henderson, Broderick Arneson, Ryan Hayward (**2009**). //Solving 8×8 Hex//. [|IJCAI-09], [|pdf]
 * Broderick Arneson, Ryan Hayward, Philip Henderson (**2009**). //MoHex wins Hex tournament//. ICGA Journal, Vol. 32, No. 2, [|pdf] » 14th Computer Olympiad

2010 ...

 * Philip Henderson, Broderick Arneson, Ryan Hayward (**2010**). //[|Hex, Braids, the Crossing Rule, and XH-Search]//. Advances in Computer Games 12, [|pdf]
 * Tristan Cazenave, Abdallah Saffidine (**2010**). //Monte-Carlo Hex//. [|pdf]
 * Broderick Arneson, Ryan Hayward, Philip Henderson (**2010**). //MoHex wins Hex Tournament//. ICGA Journal, Vol. 33, No. 3, [|pdf] » 15th Computer Olympiad
 * Broderick Arneson, Ryan Hayward, Philip Henderson (**2010**). //Solving Hex: Beyond Humans//. CG 2010, [|pdf]
 * Broderick Arneson, Ryan Hayward, Philip Henderson (**2010**). //Monte Carlo Tree Search in Hex//. IEEE Transactions on Computational Intelligence and AI in Games, Vol. 2, No. 4, [|pdf]
 * Philip Henderson (**2010**). //Playing and Solving the Game of Hex//. (Ph.D. thesis under committee review ), [|pdf]
 * 2011**
 * Henry Brausen, Ryan Hayward, Martin Müller, Abdul Qadir, David Spies (**2011**). //[|Blunder Cost in Go and Hex]//. Advances in Computer Games 13
 * 2012**
 * Ryan Hayward (**2012**). //MoHex wins Hex Tournament//. ICGA Journal, Vol. 35, No. 2 » 16th Computer Olympiad
 * 2013**
 * Ryan Hayward, Broderick Arneson, Shih-Chieh Huang, Jakub Pawlewicz (**2013**). //MOHEX Wins Hex Tournament//. ICGA Journal, Vol. 36, No. 3, [|pdf] » 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, [|pdf]

2015 ...

 * Xi Liang (**2015**). //[|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//. [|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//. [|CoRR abs/1507.04383] » 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//. [|TrustCom/BigDataSE/|ISPA 2015], [|pdf]
 * Xi Liang, Ting-Han Wei, I-Chen Wu (**2015**). //Solving Hex Openings Using Job-Level UCT Search//. ICGA Journal, Vol. 38, No. 3
 * Jakub Pawlewicz, Ryan Hayward (**2015**). //[|Sibling Conspiracy Number 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, Vol. 39, No. 1 » 18th Computer Olympiad

=Forum Posts=
 * [|bitboard algorithm needed] by Daniel Shawul, CCC, July 08, 2011
 * [|Re: Possible Search Algorithms for GPUs?] by Daniel Shawul, CCC, January 07, 2012 » GPU, Flood Fill Algorithms

=External Links=
 * [|Hex (board game) from Wikipedia]
 * [|HexWiki]
 * [|Sensei's Library: Hex]
 * [|Hex (ICGA Tournaments)]
 * [|ICGA: Hex] by Vadim Anshelevich
 * [|University of Alberta Computer Hex Research Group]
 * [|hex - javhar1] by Jack van Rijswijck
 * [|Hex] by [|Thomas Maarup]
 * [|About Hex] from [|MazeWorks - Java Games and Puzzles]
 * [|The abstract board game Hex] by Tijs Krammer
 * [|HEX: Answers to common questions] by David Boll
 * [|Answers to infrequently asked questions about the game of Hex] by Bert Enderton
 * [|Kwaku Ananse: Hex] by [|Ralf Poschmann] (German)
 * [|Little Golem - online board games] by [|Richard Malaschitz]
 * [|Little Golem - FAQ] by [|Edward D. Collins]
 * [|Sechseckpflaster] (German) a little off topic, may be for outdoor Hex ...
 * [|Hexagonal chess from Wikipedia]
 * [|Sannin shogi from Wikipedia]

=References= =What links here?= include page="Hex" component="backlinks" limit="100"
 * Up one Level**