Game of the Amazons

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The Game of the Amazons
a b c d e f g h i j
10 a10 b10 c10 d10 black queen e10 f10 g10 black queen h10 i10 j10 10
9 a9 b9 c9 d9 e9 f9 g9 h9 i9 j9 9
8 a8 b8 c8 d8 e8 f8 g8 h8 i8 j8 8
7 a7 black queen b7 c7 d7 e7 f7 g7 h7 i7 j7 black queen 7
6 a6 b6 c6 d6 e6 f6 g6 h6 i6 j6 6
5 a5 b5 c5 d5 e5 f5 g5 h5 i5 j5 5
4 a4 white queen b4 c4 d4 e4 f4 g4 h4 i4 j4 white queen 4
3 a3 b3 c3 d3 e3 f3 g3 h3 i3 j3 3
2 a2 b2 c2 d2 e2 f2 g2 h2 i2 j2 2
1 a1 b1 c1 d1 white queen e1 f1 g1 white queen h1 i1 j1 1
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The starting position in The Game of the Amazons
Players 2
Age range 4+
Setup time 20 seconds
Playing time 30-60 minutes
Random chance None
Skill(s) required Tactics, strategy, position

The Game of the Amazons (in Spanish, El Juego de las Amazonas; often called Amazons for short) is a two-player abstract strategy game invented in 1988 by Walter Zamkauskas of Argentina. It is a member of the territorial game family, a distant relative of Go and chess. El Juego de las Amazonas (The Game of the Amazons) is a trademark of Ediciones de Mente.

The Game of the Amazons is played on a 10x10 chessboard (or an international checkerboard). Some players prefer to use a monochromatic board. The two players are White and Black; each player has four amazons (not to be confused with the amazon fairy chess piece), which start on the board in the configuration shown at right. A supply of markers (checkers, poker chips, etc.) is also required.

Rules[edit]

White moves first, and the players alternate moves thereafter. Each move consists of two parts: moving one of one's own amazons one or more empty squares in a straight line (orthogonally or diagonally), exactly as a queen moves in chess; it may not cross or enter a square occupied by an amazon of either color or an arrow. After moving, the amazon shoots an arrow from its landing square to another square, using another queenlike move. This arrow may travel in any orthogonal or diagonal direction (even backwards along the same path the amazon just traveled, into or across the starting square if desired). An arrow, like an amazon, cannot cross or enter a square where another arrow has landed or an amazon of either color stands. The square where the arrow lands is marked to show that it can no longer be used. The last player to be able to make a move wins. Draws are impossible.

a b c d e f g h i j
10 a10 b10 c10 d10 black queen e10 f10 g10 black queen h10 i10 j10 10
9 a9 b9 c9 d9 e9 f9 g9 black circle h9 i9 j9 9
8 a8 b8 c8 d8 e8 f8 g8 h8 i8 j8 8
7 a7 black queen b7 c7 d7 e7 f7 g7 h7 i7 j7 black queen 7
6 a6 b6 c6 d6 white queen e6 f6 g6 h6 i6 j6 6
5 a5 b5 c5 d5 e5 f5 g5 h5 i5 j5 5
4 a4 white queen b4 c4 d4 e4 f4 g4 h4 i4 j4 white queen 4
3 a3 b3 c3 d3 e3 f3 g3 h3 i3 j3 3
2 a2 b2 c2 d2 e2 f2 g2 h2 i2 j2 2
1 a1 b1 c1 d1 e1 f1 g1 white queen h1 i1 j1 1
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The diagram shows a possible first move by white: d1-d6/g9, i.e. amazon moved from d1 to d6 and fired arrow to g9.

Territory and Scoring[edit]

a b c d e f g h i j
10 a10 black circle b10 c10 d10 black queen e10 black circle f10 g10 h10 black circle i10 j10 10
9 a9 b9 black circle c9 black circle d9 black circle e9 f9 black circle g9 h9 i9 black circle j9 9
8 a8 black circle b8 black circle c8 white queen d8 black circle e8 black circle f8 black circle g8 black circle h8 black circle i8 black circle j8 black circle 8
7 a7 b7 c7 black circle d7 black circle e7 black circle f7 white queen g7 h7 i7 black circle j7 white queen 7
6 a6 b6 c6 black circle d6 e6 black circle f6 black circle g6 black circle h6 black circle i6 black circle j6 black circle 6
5 a5 b5 black circle c5 black circle d5 black circle e5 black queen f5 black circle g5 h5 black circle i5 j5 5
4 a4 b4 black circle c4 black circle d4 e4 f4 black circle g4 black circle h4 i4 j4 4
3 a3 black circle b3 black circle c3 d3 black circle e3 black circle f3 black circle g3 black circle h3 black circle i3 j3 3
2 a2 black circle b2 black circle c2 d2 black circle e2 white queen f2 black circle g2 black circle h2 i2 j2 2
1 a1 b1 c1 black circle d1 black queen e1 black circle f1 black circle g1 black queen h1 i1 j1 black circle 1
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A completed Amazons game. White has just moved f1-e2/f1. White now has 8 moves left, while Black has 31.

The strategy of the game is based on using arrows (as well as one's four amazons) to block the movement of the opponent's amazons and gradually wall off territory, trying to trap the opponents in smaller regions and gain larger areas for oneself. Each move reduces the available playing area, and eventually each amazon finds itself in a territory blocked off from all other amazons. The amazon can then move about its territory firing arrows until it no longer has any room to move. Since it would be tedious to actually play out all these moves, in practice the game usually ends when all of the amazons are in separate territories. The player with the largest amount of territory will be able to win, as the opponent will have to fill in her own territory more quickly.

Scores are sometimes used for tie-breaking purposes in Amazons tournaments. When scoring, it is important to note that although the number of moves remaining to a player is usually equal to the number of empty squares in the territories occupied by that player's amazons, it is nonetheless possible to have defective territories in which there are fewer moves left than there are empty squares. The simplest such territory is three squares of the same colour, not in a straight line, with the amazon in the middle (for example, a1+b2+c1 with the amazon at b2).

History[edit]

El Juego de las Amazonas was first published in Spanish in the Argentine puzzle magazine El Acertijo (number 4, December 1992). An approved English translation was written by Michael Keller and an article first appeared in the chess magazine NOST-Algia. Other game publications also published the rules, and the game gathered a small but devoted following. The Internet spread the game more widely, and it is considered by many aficionados to be one of the best and deepest abstract games.

Michael Keller wrote the first computer program to play the Game of the Amazons in 1994 (in Fortran with a text interface; a later version was written in Visual Basic; see References). Quite a few stronger programs have been written in recent years by various authors. There is usually an Amazons tournament at the annual Computer Olympiad.

An authorized version of the game appears in the Transpose collection by Kadon Enterprises.

Computational complexity[edit]

Generalized Amazons is PSPACE-complete.[1]

References[edit]

  1. ^ R. A. Hearn (2005-02-02). "Amazons is PSPACE-complete". arXiv:cs.CC/0502013.