# Gess the Game

## Paul Bolchover

Gess (pronounced “guess”) is a game for two players that was originally conceived by the Puzzles and Games Ring of the Archimedeans as a generalised form of chess.

### The rules

Gess is played on a grid of 18 squares by 18 squares. Each player starts with 43 identical stones, one player being Black, and the other being White. (When playing gess, the most practical arrangement is to use the squares of a go board, each player using 43 go stones.) Play proceeds alternately, with Black starting.

Each 3 × 3 square which is entirely or partially on the board, and which contains at least one of a player’s stones and none of his opponent’s is known as a piece, and is referred to by the location of its central square. (If the centre is off the board, it is referred to in the obvious way, and this accounts for the slightly odd manner in which the board is labelled.) Assuming there are no obstructing stones (see below), pieces move as follows.

The non-central squares in the piece determine the directions in which the piece is able to move; for example, if a piece has a stone in its central forward square, then it is able to move straight forwards; if it has a stone in its rear left square, then it is able to move diagonally backwards and left.

If the piece has a stone in the central square, then it may move an unlimited number of squares in any of the permitted directions, otherwise it may only move up to 3 squares in the permitted directions.

For example, in Figure 1, the piece at d15 may move an unlimited number of squares diagonally forwards and left, forwards and right, or straight backwards. The piece at j15 may move up to 3 squares, either forwards or to the left. The piece at q16 may only move backwards, up to 3 squares, whereas the piece at q15 may not move at all, since it does not have a valid direction in which to move. (It can move an unlimited number of squares but in no direction. It should also be noted that a ‘move’ that does not change the appearance of the board is not allowed.)

Note that you can have pieces which are partly off the board (for example, if you have a single stone in a corner, you may move it diagonally inwards for up to 3 squares), and pieces may also be moved partially, but not entirely, off the board, and any stones in the piece which end up off the board are removed.

A piece may only continue moving in a given direction if at each stage its footprint (in other words the 3 × 3 square) doesn’t cover any other stones of either colour. If stones are covered, then they are taken (removed from the board) and the move ends. To give an example, the piece at e5 in Figure 2 may move to i9 and take the white stone at i10, but in the similar position to the right, the piece at m5 may only move as far as p8, and if it does it takes the black stone at p9.

The initial position is shown in Figure 3. You should recognise it as having pieces analogous to rook, bishop, queen, king, bishop, and rook in that order, with six pawns in front. (There is obviously no possibility of producing a knight.) Note however that there are distinct differences; for example, the ‘bishops’ cannot move out until a space on one side or the other is cleared. A piece that moves like a king—a 3 × 3 square with all of its outer squares containing stones, but with no central stone—is known as a ring. The object of the game is to capture (or disable) your opponent’s ring or rings; if at the end of a move either player has no ring then he loses: the player who has just moved being considered first, so you cannot use part of your ring to take your opponent’s ring or rings. It is possible to have more than one ring at a time—indeed this may be considered desirable—and you may destroy one or more of your own rings provided that you still have at least one at the end of your move.

## A sample game

 Black: P. Bolchover White: R. Michaels
 1 f6–f7 Preparing to form a powerful diagonal piece later after e3–e6. ... p15–m12 Controls the centre, and blocks a long-range attack upon White’s ring. It also builds up an attack on the central block. Both the last moves announce the players’ intention to form a second ring. 2 e3–e6 Forms a diagonal piece attacking White’s ring, and prepares to form a second ring. However, it doesn’t do much defensively. ... p18–p15 Defends the centre. 3 b3–e3 Forms a ring. Note the many strong attacks forwards, but each of these attacks will disable one of Black’s rings. ... e15–h12 Opens a line against Black’s second ring and reinforces the centre. b13–d15 might be a good move in the future. 4 m6–l7 Opens a line for the forwards piece centred on m3.

 ... m12–j9 White goes for the exchange but pins l14 to the White ring. It does, however, open a diagonal line for White, while blocking one for Black. 5 i6–i7 h6–i7 or j6–k7 might be better. ... h15–k12 Reinforces White’s ring and opens up his queen. 6 i7–i10 Opens up the centre for both players. It is unclear who has the advantage in this position. Overall, the move is probably bad, as it exposes Black’s second ring. ... m15–j12 The White pawns are starting to look slightly too far advanced. 7 o6–o7 Attacking the pinned White pawn. ... s18–p18 Forming a double ring. 8 p7–m10 Opening up an attack on the weak l11 square. ... k18–k12 Probably the best way of defending. 9 j3–j10 ... k13–j12 10 j9–j10 j9–k10 would leave the Black ring under attack. ... q15–r14 Initiating a diagonal attack on the Black ring. 11 e6–h6 Blocking the attack. ... j13–j12 12 j9–j10 ... c13–c15 Preparing for a flank attack and increasing the pressure on Black, who looks very weak defensively, but has a strong attack against White’s ring. 13 j10–k11 Removing the obstructing stone. ... c17–c7 Note that this move is illegal, since the piece can only move as far as c8, but as neither player noticed it at the time the move stands.

 14 g3–j3 Forming a double ring for extra protection. ... h18–k18 15 k11–i13 Note that White could kill Black’s rings, but in doing so would destroy his own ring, and hence would lose. ... k18–k15 16 m3–m13 Disabling the White piece centred on k15. ... b7–e4 Threatening moves such as e3–h3. 17 j3–m3 ... r14–o11 Disabling the Black piece centred on m13. 18 r8–r6 ... o11–j6 Mate.

Reproduced from Eureka 53 pages 24-27.