Introduction

Gess is a game that was invented by the Puzzles and Games Ring of the Archimedeans Mathematics Society, the Mathematical Society of Cambridge University. The rules were first published in Volume 53 of Eureka, the journal of the Archimedeans, in an article written by Paul Bolchover. It is an excellent board game, entertaining, challenging, and fun.

The name 'gess' comes from two existing games - Go and chess. It is played on a Go board with Go stones, but plays like chess. It is pronounced as "guess".

Yes, this is a long writeup. But once you understand it, it's not difficult! Please read and be patient! It's worth it!

Starting the game

The stones are placed inside the squares of the Go board, instead of on the corners like for the game of Go. The game always starts with the stones in a particular pattern shown below.

`X`
represents a black stone,
`O`
represents a white stone,
`.`
represents an empty square.

```   ABCDEFGHIJKLMNOPQRST
20                      20
19  .X.X.XXXXXXXX.X.X.  19
18  XXX.X.XXXX.X.X.XXX  18
17  .X.X.XXXXXXXX.X.X.  17
16  ..................  16
15  ..................  15
14  .X..X..X..X..X..X.  14
13  ..................  13
12  ..................  12
11  ..................  11
10  ..................  10
9  ..................   9
8  ..................   8
7  .O..O..O..O..O..O.   7
6  ..................   6
5  ..................   5
4  .O.O.OOOOOOOO.O.O.   4
3  OOO.O.OOOO.O.O.OOO   3
2  .O.O.OOOOOOOO.O.O.   2
1                       1
ABCDEFGHIJKLMNOPQRST
```

Note that the coordinates extend beyond the grid marked, that will be explained later.

Pieces

The most confusing part of gess is identifying the pieces of the game. First, you need to understand a footprint - a footprint is any 3 by 3 block of squares. For example, the footprint centred at F4 in the starting position has 3 white stones in it. A footprint may be partially off the board - for example, the footprint centred at B18 has 4 black stones and 3 'imaginary' squares. It may even be mostly off the board - the footprint centred at T2 has only 1 white stone and only 2 squares actually on the board. The reason the coordinates extend beyond the grid is so footprints like these can be specified. "The footprint at F4" is shorthand for "the footprint centred at F4".

A piece, then, is a footprint that has at least one stone in it, but if there's more than one stone then they must all be of the same colour.

```6  .....
5  .....
4  ..X..
3  ..O..
2  .....
1
ABCDEF
```

In the part of the board shown above, there is a piece (centred) at C2, one at D2, one at E2, and one at C5, D5, and E5. There is no piece at B2 because there are no stones at that footprint, and there is no piece at C3 because the footprint has stones of both colours. The challenging thing to recognise is that one stone can potentially belong to up to nine pieces - but only one of those pieces can be moved, and once a piece is moved, the remaining stones in the neighbourhood arrange themselves into different types of pieces.

The next thing to know is how a piece moves. Each square of the footprint defines a part of how the piece moves. If there is a stone at the front centre square of the footprint, it can move forwards. If there is a stone at the front right corner square of the piece, then it can go diagonally in that direction. Each of the eight periphery squares determines if the piece can move in the corresponding direction - if there is a stone in the square, then the piece can move in that direction. The centre square also has a role in determining how the piece moves - if the centre square is empty, then the piece can move a maximum of 3 squares, if it is full, the piece can move as far as it likes (until a stone must be removed from play - more on that later).

Just as chess has its kings, gess has rings. Look at the starting position, and you will notice that the piece at L3 is a white piece, with all 8 periphery squares full and the centre square empty. This is called a white ring. There's a black ring at L18. The ring in gess is like the king in chess - the object of the game is to destroy all your opponent's rings. Note that there is nothing special about the particular stones that make the rings in the starting position. Any group of stones, moved in any way, anywhere on the board that makes the shape of a ring is considered to be a ring piece. A player can have as many rings as he or she can make, even pairs of adjacent rings sharing stones on the periphery. A player can even destroy one of his or her rings, by moving a piece which shares a partial footprint with the ring, provided that the player has another ring elsewhere. This is very different from chess, where a player is given only one king and cannot make another king.

Have another look at the start position of the board. Look at the white side of the board, see if you can see any patterns. There is a piece at C3 which can move as far as it likes up, down, or sideways. It behaves very much like a rook. There's another one at R3. The pieces at F3 and O3 can move any amount in diagonal directions - these are like bishops. The piece at I3 behaves very much like a queen. And the piece at L3 is a ring, like a king. The pieces at C6, F6, I6, L6, O6, and R6 are very much like pawns, except they can only move up to 3 squares even on their first move, and there is no en passant rule. (There are no pieces in gess equivalent to the knights in chess.) The black stones make a mirror image of the white stones. The similarities between these pieces and the pieces of chess are intentional, it makes it easy to remember the starting positions of the stones.

Playing

One player is called White, the other player is called Black. Play consists of the players alternating turns (Black goes first). A turn consists of a player choosing a piece of his or her own colour and moving it at least one square. A piece can move as far as it is allowed by the presence or absence of a stone at its centre until a stone is removed from play. If any stones from the piece being moved end up off the marked grid, they are removed from play. If any stones that are not part of the piece being moved, end up under the footprint of the destination of the piece, they are removed from play. (Examples of stones being removed from play are in the next paragraph - it's difficult to make the rule clear, but it's easy to understand the examples.) All stones in the piece are moved from the starting footprint to the destination footprint, keeping their relative positions within the footprints. The game continues until one player has no rings, and this player is the loser. If one player moves so the opponent's last ring is threatened unless it is moved, that player must say 'gess' or 'check' (or is not allowed destroy the ring on the next move). If one player moves so the opponent's last ring is threatened and cannot be saved, that player may say 'mate' or 'checkmate' to save time. (However, it is the opponent's privilege to challenge the mate and continue to play. With the many possible combinations of pieces and moves in gess, it can be easy to overlook a potential defense and prematurely call 'mate'.)

A few examples of valid moves and invalid moves will help. Consider the piece at C3, the 'rook'-like piece. It can move forward, backward, left, or right as far as it likes - until it ends up in a position where one or more stones would be removed from play. If it chose to go forward one square, no stones are removed - the + shape of the stones would just be moved up one square. If the piece goes two squares, no stones are removed. If it goes three squares, then a white stone which is not part of the piece being moved is under the destination footprint. That white stone would be removed, the 5 stones of the 'rook' piece would be moved forward 3 squares. It cannot go more than 3 squares forward. The 'rook' piece cannot go more than 1 square to the right (and if it did go to the right, the white player would lose 2 stones). The 'rook' cannot go more than one square to the left, either, because once it goes one square to the left a stone is lost. Sometimes strategy demands the sacrifice of a stone in this way, but it'd be an idiotic first move.

Another move might be moving the piece at L4 diagonally down and right one square. Not only would this remove 3 white stones, it would destroy the only white ring, so this would be suicide. It is, however, a valid move - just as knocking the king over in a game of chess to resign is a valid move.

Now for some actual advice, to give you a feel for playing the game. Two potential openings for White are:

```H6 - J8 (the third 'pawn' diagonally up and right 2 squares)
M6 - L7 (the fourth 'pawn' diagonally up and left 1 square)
```
This forms a piece at K8 looking like
```.O.
.O.
...
```
This piece can move forward any number of squares. It is a 'lance', pointed at the opponent's ring. It can be moved forward fast, to take at least one opposing stone (and possibly as many as 3). Normally the retaliation only takes the front stone, leaving the other stone free to act as a pawn and take even more opposing stones.

Another strategy is to make a second ring.

```F6 - F7 (move the second pawn out of the way)
E3 - E6 (move the 'diamond' opposite the ring out of the way)
B3 - E3 (form a second ring)
```
Be sure to move the 'diamond' shape on the opposite side of the board from the ring. Otherwise, you'll make two rings but they'll be sharing 3 stones on the right of the old one and the left of the new one. This is a lot less useful.

Enjoy!

If anyone would like to play a game, /msg me. It'll have to be like 'chess by mail', /msgs back and forth like "G10 - K14"… but I think it'd be fun!

References:
Scientific American, November 1994
http://www.cam.ac.uk/societies/archim/eureka/gess/

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