Amazons, (Game of the Amazons, El Juego de las Amazonas)
a two-playerabstract strategy game invented in 1988 by Walter Zamkauskas of Argentina [1] . 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[2][3] . 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.
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.
a two-player abstract strategy game invented in 1988 by Walter Zamkauskas of Argentina [1] . 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 [2] [3] . 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.
Table of Contents
Computer Olympiads
Selected Programs
Gold medalists from the Computer OlympiadPhotos
Maastricht 2002
Yokohama 2013
Branching Factor
excerpt of Patrick Hensgens' 2001 master's thesis [8] :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
[9] [10]1999
2000 ...
- 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
2001- 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
2002- 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
2003- 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
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