Edward Jackman ((email removed contact us for address) menet.com) posted this on April 19, 1995 on red.games.abstract, and send me a copy of it. He obtained permission of the Archemedean Mathematics Society for the reproduction of the article from Eureka. I added html commands to Edwards text, and changed part of the introduction reflecting the origins of the game. Peter Benie informed me about the Archemedians and their publication of Gess.
In his Mathematical Recreations column in Scientific American, November 1994, Ian Stewart wrote about the game.
Here is the starting setup:
- W - W - W W W W W W W W - W - W - 19
W W W - W - W W W W - W - W - W W W 18
- W - W - W W W W W W W W - W - W - 17
- - - - - - - - - - - - - - - - - - 16
- - - - - - - - - - - - - - - - - - 15
- W - - W - - W - - W - - W - - W - 14
- - - - - - - - - - - - - - - - - - 13
- - - - - - - - - - - - - - - - - - 12
- - - - - - - - - - - - - - - - - - 11
- - - - - - - - - - - - - - - - - - 10
- - - - - - - - - - - - - - - - - - 9
- - - - - - - - - - - - - - - - - - 8
- B - - B - - B - - B - - B - - B - 7
- - - - - - - - - - - - - - - - - - 6
- - - - - - - - - - - - - - - - - - 5
- B - B - B B B B B B B B - B - B - 4
B B B - B - B B B B - B - B - B B B 3
- B - B - B B B B B B B B - B - B - 2
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a b c d e f g h i j k l m n o p q r s t
(Note that the grid is labelled on square beyond the
edge of the board in all directions. Since, as
described below, a piece is named by its center,
you need this labelling to refer to the pieces that
extend beyond the edge of the board.)
There are two players, black and white, each having 43 stones of his or her own color. They take turns to move, with black starting.
Each turn a player moves a 'piece' -- but a piece is defined as all the stones of that player's color contained with ANY 3x3 area that has NO stones belonging to the opposing player. For example, in the starting setup, black could move the 'piece' at qrs567 which contains a single stone at r7. Instead of that, black could move the piece at pqr678 -- and although this piece contains the exact same stone as qrs567 it is a different piece and moves differently. The center of the piece can be anywhere on the 18x18 grid of squares on the board -- this means that if the center of a piece is on the edge or corner of the board, part of the piece extends virtually beyond the boundaries of the go board.
The way a piece moves is elegantly simple.
The 3x3 group of stones moves as a unit. How it moves is defined by the stones themselves. If there is a stone in the center, the piece can move any unobstructed distance. If the center is empty, the piece can move up to three squares. Each stone on the perimeter of a piece allows the piece to move in that direction.
Here's a diagram of a piece:
NW N NE
W C E
SW S SE
If there is a stone at 'C', the piece can move any
distance -- if not, it may move up to 3 squares
only. If there is a stone at 'NW' the piece may
move northwest. If there is a stone at 'N' the
piece may move north, etc. The piece is a little
map that tells you exactly how far and what
direction it can move.
Examples:
B - B This 'piece' can move - B B <-- any unobstructed distance B - B diagonally or east. W - W This is not a piece W - - <-- because there are stones - - B of both colors in it. - - W This 'piece' can move - - W <-- east, south or northeast - W - 1, 2 or 3 squares. - B - This 'piece' may move - - - <-- forward (north) only and - - - may only move 1-3 squaresThe footprint of a piece is the entire 3x3 region that it occupies. When you move the piece, as soon as the footprint overlaps any other stones of either color, the movement stops and all the stones that were overlapped are removed permanently from the game. It is perfectly legal to capture some of your own stones this way. Capturing is alway optional -- a move can always stop short of capturing. A piece may move partially beyond the edge of the board -- if so, all stones that are beyond the physical board are eliminated.
The squares on the grid are numbered from 2 to 19 vertically and lettered from b to s horizontally. Remember, pieces can go off the board, so there are 'invisible' rows 1 and 20 and columns a and t as well. A piece is referred to by the coordinates of its central square. The piece g5 covers the squares f4, f5, f6, g4, g5, g6, h4, h5, h6.
The object is to capture your opponent's last 'ring'. A ring is exactly that -- a ring of eight stones around an empty center. Each player begins the game with one ring, (White at klm 17-19 and Black at klm 2-4) but may form more if possible.
Here are some example moves:
White to move. In this diagram, white would like to attack the black ring at the left.
- - - - - - - - W - - - - - - - - - 8
- - - - - - - - - W W W W W - - - - 7
- - - - - - - - W - W W - W - - - - 6
- B B B - - B - - - - W W W - - - - 5
- B - B - - - - - - - - W W - - - - 4
- B B B - - - - - - - - W W - - - - 3
- - - - - - - - - - - - - - - - - - 2
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If white moves 'k7' as far to the southwest as possible,
black stone at h5 stops its movement and this is the result:
- - - - - - - - - - - - - - - - - 8
- - - - - - - - - - - W W W - - - - 7
- - - - - - W - - - - W - W - - - - 6
- B B B - - - W W - - W W W - - - - 5
- B - B - - W - W - - - W W - - - - 4
- B B B - - - - - - - - W W - - - - 3
- - - - - - - - - - - - - - - - - - 2
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1.) k7-i5 (captures a black stone at h5)
But White instead can win with o3-f3:
- - - - - - - - W - - - - - - - - - 8
- - - - - - - - - W W W W W - - - - 7
- - - - - - - - W - W W - W - - - - 6
- B B B - - B - - - - W W W - - - - 5
- B - W W - - - - - - - - - - - - - 4
- B B W W - - - - - - - - - - - - - 3
- - - - - - - - - - - - - - - - - - 2
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1.) o3-f3 (captures black stones at f3 and f4,
destroying the black ring and winning
the game.
Edward Jackman