Here is an attempt to describe the rules of Go precisely. This is actually for a generalization of Go that I call MANGO, which stands for MAth Nerd Go

Equipment

To play Mango, you need the following:

• A countable set, I.
• A set, C, whose members are subsets of I, each of which contains exactly two members of I.
• Three subsets of I, called E, B, and W, such that their union is I, and the intersections of any pair of them is empty.
• A real-valued function F, whose domain is I.
• A function, T, whose range is {0,1}, that is defined on the real numbers.

Definitions

If P is a finite subset of C, and n is a member of I, then the INDEX of n in P is the number of elements of P that contain n.

A finite subset, P, of C is called a PATH if the following conditions are met:

• Each element of I has an index in P of 0, 1, or 2.
• There are exactly two elements of I whose index in P is 1.

An element of I whose index in a path is 1 is called an ENDPOINT of the path. An element of I whose index in a path is 2 is called an INTERIOR point of the path.

Let S be one of the sets B or W. Let s be a member of S. Let L be the set of all members, e, of E, such that there is a path whose endpoints are s and e, and whose interior points are all in S or E. Let z be the sum over L of F. Then s is ALIVE if T(z) = 1.

The ordered triple (E,B,W) is called the CONFIGURATION.

Playing

The players must first obtain a Mango set. This consists of agreeing to the sets I, C, E, B, and W, and the functions F and T.

The players must agree to an initial score for each player.

The players than decide who shall have the first turn. Players alternate turns.

On a players turn, that player may do one of two things:

• The player may PASS. It then becomes the other players turn.
• The player may make a LEGAL MOVE.

Note that a player *MUST* either pass or play a legal move. If there is no legal move, the player is forced to pass.

A MOVE consists of performing several actions. In the following, if it is Black's turn we will use the symbol M to refer to the set B and the symbol H to refer to the set set W. If it is White's turn, M will be W and H will be B. Here are the actions that are taken by a player on that players turn:

1. A member, n, of E is selected.
2. n is removed from E and added to M.
3. All members of H that are not alive at the end of the above step are removed from H and placed in E.
4. All members of M that are not alive at the end of the previous step are removed from M and placed in E.

A move is a LEGAL MOVE if the configuration, (E,B,W), produced by the move is new.

The game ends when two consecutive turns are passes.

Scoring

Each player uses the following procedure to compute his score. We will use the symbol M to refer to B if the player is Black, and to refer to W if the player is White.

We use the symbol H to refer I-(E union M).

The player starts with the initial score agreed upon at the start of the game.

For each m in M, the player receives F(m) points.

A player receives F(n) points for each member, n, of E for which the following conditions both hold:

1. There exists a path with n as one endpoint and the other endpoint in M, and which contains no members of H as interior points.
2. All paths that contain n as one endpoint and a member of H as the other endpoint contain a member of M as an interior point.

The player with the most points wins.

Example

To play ordinary 19x19 Go, with a 5.5 point Komi, the players might agree to the following:

• I = { (x,y) | x and y are integers in [1,19] }
• C = { {(x,y),(u,v)} | (x,y) and (u,v) are in I, (x-u)^2+(y-v)^2 = 1 }
• B = W = {}
• E = I
• The initial scores are 0 for Black, 5.5 for White.
• It is Blacks turn.
• F((x,y)) = 1
• T(z) = int((z+360)/361)

To play a Go-like game on an infinite board, the playersmight agree to this:

• I = { (x,y) | x and y are integers }
• C = { {(x,y),(u,v)} | (x,y) and (u,v) are in I, (x-u)^2+(y-v)^2 = 1 }
• B = W = {}
• E = I
• Initial scores are Black:0, White:0.
• It is Black to move.
• F((x,y)) = exp(-x^2-y^2)
• T(z) = 1 if z > 1/1000, otherwise T(z) = 0