Game of the Amazons

Game of the Amazons

a b c d e f g h i j 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h i j 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

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											10
9											9
8											8
7											7
6											6
5											5
4											4
3											3
2											2
1											1
	a	b	c	d	e	f	g	h	i	j

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

	a	b	c	d	e	f	g	h	i	j
10											10
9											9
8											8
7											7
6											6
5											5
4											4
3											3
2											2
1											1
	a	b	c	d	e	f	g	h	i	j

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

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

Generalized Amazons is PSPACE-complete.

References

• Müller, Martin and Tegos, Theodore (2002). "Experiments in computer Amazons". More Games of No Chance. MSRI Publications 42, Cambridge Univ. Press. pp. 243–257. http://www.msri.org/publications/books/Book42/files/muller.pdf. 
• Snatzke, Raymond George (2002). "Exhaustive search in Amazons". More Games of No Chance. MSRI Publications 42, Cambridge Univ. Press. pp. 261–278. http://www.msri.org/publications/books/Book42/files/snatzke.pdf. 
• Amazons on ChessVariants.org - history and a sample game of Amazons. Also you can download a program for Windows, which plays Amazons game.
• Gamazon - open source program, which plays Amazons (Linux only)
• The Game of the Amazons
• Transpose by Kadon Enterprises