Amazons

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Amazons, (Game of the Amazons, El Juego de las Amazonas) a two-player abstract strategy game invented in 1988 by Walter Zamkauskas of Argentina. El Juego de las Amazonas is a trademark of Ediciones de Mente. In 1998 and 1999, Hiroyuki Iida organized the first two computer Amazons championships, which were held at the Computer Games Research Institute of Shizuoka University. Computer Amazons is played at the Computer Olympiad since London 2000. Amazons is usually played on a 10 x 10 board, but can be played on boards of arbitrary size.

The two players, White and Black are each given four amazons in predefined locations. A supply of markers (checkers, poker chips, etc.) is also required. White makes the first move with one of his amazons, which move like a queen in chess, except captures. Each move contains two mandatory parts, moving the amazon and throwing an arrow from its target square to one of its attacked empty squares, which is marked and permanently blocked. Amazon and the arrow can't land on or cross over any own or opponent amazon or arrow. The last player to be able to make a move, which includes throwing an arrow, wins.

=Computer Olympiads=
 * 5th Computer Olympiad, London 2000
 * 6th Computer Olympiad, Maastricht 2001
 * 7th Computer Olympiad, Maastricht 2002
 * 8th Computer Olympiad, Graz 2003
 * 9th Computer Olympiad, Ramat Gan 2004
 * 10th Computer Olympiad, Taipei 2005
 * 12th Computer Olympiad, Amsterdam 2007
 * 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
 * 19th Computer Olympiad, Leiden 2016
 * 20th Computer Olympiad, Leiden 2017

=Selected Programs= Gold medalists from the Computer Olympiad
 * 8 Queens Problem by Johan de Koning
 * Amazong by Jens Lieberum
 * Invader by Richard J. Lorentz, et al.

=Photos=

Maastricht 2002
Maastricht 2002 winners, Richard J. Lorentz, Jens Lieberum, Johan de Koning

Yokohama 2013
Yokohama 2013 award ceremony, Richard J. Lorentz, Johan de Koning, Jaap van den Herik

=Branching Factor= excerpt of Patrick Hensgens' 2001 master's thesis : In the initial position the first player has 2176 possible moves. This is a huge number, especially when compared to other AI games, where most games have a branching factor below 50 in the initial position (e.g., Chess 20, Lines of Action 36, Checkers 7, Draughts 9). Fortunately the branching factor in the game of Amazons decreases rapidly as the game progresses. In the endgame the branching factor is usually below 50.

Investigating the average branching factor of Amazons, we encounter a strange phenomenon. From the experiments we performed for finding the average branching factor we observed that this number is quite different for both players. The first player has an average branching factor of 374 while the second player has an average branching factor of 299. This means that to compute the game-tree complexity we need a formula that takes into account that both players have a different branching factor.

Furthermore, we observed that the average branching factor for both players increases with decreasing playing strength of both players.

=Selected Publications=

1999

 * Nobusuke Sasaki, Hiroyuki Iida (1999). Report on the First Open Computer-Amazons Championship. ICCA Journal, Vol. 22, No. 1

2000 ...
2001 2002 2003 2004
 * Patrick Hensgens, Jos Uiterwijk (2000). A Knowledge-Based Approach of Amazons. 5th Computer Olympiad Workshop
 * Michael Buro (2000). Simple Amazons Endgames and Their Connection to Hamilton Circuits in Cubic Subgrid Graphs. CG 2000, pdf
 * Hiroyuki Iida, Martin Müller (2000). Report on the Second Open Computer-Amazons Championship. ICGA Journal, Vol. 23, No. 1
 * Elwyn Berlekamp (2000). Sums of 2 X N Amazons. in F. Thomas Bruss and Lucien le Cam, eds. GameTheory, Optimal Stopping, Probability and Statistics: Papers in honor of Thomas S. Ferguson. Institute of Mathematical Statistics Lecture Notes - Monograph Series, Vol. 35
 * Tsuyoshi Hashimoto, Yoichiro Kajihara, Nobusuke Sasaki, Hiroyuki Iida, Jin Yoshimura (2001). An Evaluation Function for Amazons. Advances in Computer Games 9
 * Martin Müller (2001). Solving 5x5 Amazons. 6th Game Programming Workshop
 * Hiroyuki Iida (2001). 8QP wins Amazons tournament. ICGA Journal, Vol. 24, No. 3 » 6th Computer Olympiad
 * Patrick Hensgens (2001). A Knowledge-based Approach of the Game of Amazons. Master's thesis, Maastricht University, pdf
 * Richard J. Lorentz (2002). First-time entry Amazong wins Amazons tournament. ICGA Journal, Vol. 25, No. 3 » 7th Computer Olympiad
 * Richard J. Lorentz (2002). Finding Territory in Amazons. 7th Computer Olympiad Workshop
 * Raymond Georg Snatzke (2002). Exhaustive search in the game amazons. in Richard J. Nowakowski (ed) (2002). More Games of No Chance. Cambridge University Press, pdf
 * Martin Müller, Theodore Tegos (2002). Experiments in Computer Amazons. in Richard J. Nowakowski (ed) (2002). More Games of No Chance. Cambridge University Press
 * Henry Avetisyan, Richard J. Lorentz (2002). Selective Search in an Amazons Program. CG 2002
 * Theodore Tegos (2002). Shooting the last arrow. Master's thesis, University of Alberta, pdf
 * Jens Lieberum (2003). Amazong wins Amazons tournament. ICGA Journal, Vol. 26, No. 4 » 8th Computer Olympiad
 * Jens Lieberum (2003). An Evaluation Function for the Game of Amazons. Advances in Computer Games 10
 * Akop Karapetyan, Richard J. Lorentz (2004). Generating an Opening Book for Amazons. CG 2004
 * Johan de Koning (2004). 8QP regains Amazons title. ICGA Journal, Vol. 27, No. 3 » 9th Computer Olympiad
 * Raymond Georg Snatzke (2004). New results of exhaustive search in the game Amazons. Theoretical Computer Science, Vol. 303, No. 3

2005 ...

 * Richard J. Lorentz (2005). 8QP wins Amazons tournament. ICGA Journal, Vol. 28, No. 3 » 10th Computer Olympiad
 * Yoshinori Higashiuchi, Reijer Grimbergen (2005). Enhancing Search Efficiency by Using Move Categorization Based on Game Progress in Amazons. Advances in Computer Games 11
 * Jens Lieberum (2005). An evaluation function for the game of Amazons. Theoretical Computer Science, Vol. 349, No. 2
 * Julien Kloetzer, Hiroyuki Iida, Bruno Bouzy (2007). The Monte-Carlo approach in Amazons. CGW 2007, pdf
 * Mark Winands (2007). 8QP wins Amazons tournament. ICGA Journal, Vol. 30, No. 3 » 12th Computer Olympiad
 * Julien Kloetzer, Hiroyuki Iida, Bruno Bouzy (2008). A Comparative Study of Solvers for Amazons Endgames. CIG'08, pdf
 * Richard J. Lorentz (2008). Amazons Discover Monte-Carlo. CG 2008
 * Richard J. Lorentz (2009). Invader wins Amazons Tournament. ICGA Journal, Vol. 32, No. 1 » 13th Computer Olympiad
 * Julien Kloetzer (2009). Invader wins Amazons Tournament. ICGA Journal, Vol. 32, No. 2 » 14th Computer Olympiad
 * Julien Kloetzer, Hiroyuki Iida, Bruno Bouzy (2009). Playing Amazons Endgames. ICGA Journal, Vol. 32, No. 3, pdf

2010 ...

 * Julien Kloetzer (2010). Monte-Carlo Opening Books for Amazons. CG 2010
 * Julien Kloetzer (2010). Monte-Carlo Techniques: Applications to the Game of the Amazons. Ph.D. thesis, JAIST
 * Johan de Koning (2011). Invader prolongs Amazons Title. ICGA Journal, Vol. 34, No. 2 » 15th Computer Olympiad
 * Johan de Koning (2012). Invader wins Amazons Tournament. ICGA Journal, Vol. 35, No. 4 » 16th Computer Olympiad
 * Jiaxing Song (2013). An enhanced solver for the game of Amazons. Master's thesis, University of Alberta, pdf
 * Richard J. Lorentz (2013). INVADER Wins Amazons Tournament. ICGA Journal, Vol. 36, No. 4 » 17th Computer Olympiad

2015 ...

 * Jiaxing Song, Martin Müller (2015). An Enhanced Solver for the Game of Amazons. IEEE Transactions on Computational Intelligence and AI in Games, Vol. 7, No. 1, pdf preprint
 * Richard J. Lorentz (2017). Invader wins eighth Amazons gold medal. ICGA Journal, Vol. 39, Nos. 3-4 » 20th Computer Olympiad 2017

=External Links=

Game

 * ICGA: Amazons by Richard J. Lorentz
 * Amazons (ICGA Tournaments)
 * Game of the Amazons from Wikipedia
 * Amazons from The Chess Variant Pages
 * Tabletop: Amazons
 * Research Related to the Game of Amazons by Martin Müller, University of Alberta
 * Invader - A Program that Plays the Game of Amazons by Richard J. Lorentz

Misc

 * Amazon (Fairy chess piece) from Wikipedia
 * Amazons (female warriors) from Wikipedia

=References=

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