GESS -- a New chess/go variant

Gess was invented by the Puzzles and Games Ring of the Archimedeans Mathematics Society, which is the mathematical society of Cambridge University (UK). The rules were first published, together with a sample game, by Paul Bolchover in Eureka, Vol. 53, the periodical of the Archimedeans.

In his Mathematical Recreations column in Scientific American, November 1994, Ian Stewart wrote about the game.

See also:

• Peter Chatterton's Gess Applet. (Link.)

GESS

Played on a the squares of an 18x18 grid of a Go board using standard Go stones.

Here is the starting setup:

Note that the squares at the border of the board may not be occupied by stones: they can be omitted from the board, and only help to establish 3 by 3 areas (see below). Thus, effectively, the board is not 20 by 20, but 18 by 18 squares.

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:

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:

This 'piece' can move any unobstructed distance diagonally or east.

This is not a piece because there are stones of both colors in it.

This 'piece' can move east, south or northeast 1, 2 or 3 squares.

This 'piece' may move forward (north) only and may only move 1-3 squares

The 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.

If white moves 'k7' as far to the southwest as possible, black stone at h5 stops its movement and this is the result:

1. k7-i5 (captures a black stone at h5)

But White instead can win with o3-f3:

1. o3-f3 (captures black stones at f3 and f4, destroying the black ring and winning the game.)