World
Game
Of
Sprouts
Association

### Sprouts Notation

Spots are numbered consecutively as they come into existence. Every move contains, at least, a string of the form f(g)h, where f and h are an existing spot or spots and g is a new spot. A move is from spot f to spot h with spot g being generated. The notation 4(17)6 is a move from spot 4 to spot 6 with the new spot, spot 17, being created.

An "enclosing" move is a move that creates a new region. To the basic f(g)h notation, a string of the form [L] is appended. L is a list of spots that the move separates from all other spots from which they can be separated. This list uses commas and dashes as needed, the dashes to indicate consecutively numbered spots. Thus [5,7,10-12] represents spots 5, 7, 10, 11, and 12. If L is empty, the [L] is omitted.

If a new spot g can be placed in either of two distinct regions, then the string f(g@i)h is used to specify the move in which spot g is accessible to live spot i. For a move for which there is no such spot i, the string f(g)h is used.

A final element of sprouts notation is the exclamation point. The exclamation point has two uses, specified in the following two paragraphs. The purpose of the exclamation point is to avoid subtle ambiguities that could prevent or hinder the reconstruction of a game. A general interpretation of the exclamation point is that it is an indicator of a violation of "clockwise expectations".

Suppose we are going to move f(g)h and that before we play this move spot f is already attached to two other spots ("neighbors"), one on each side. (A "neighbor" is a connected spot, alive or dead, with no intervening spots.) Suppose further that the position is such that we face a subtle choice in how we can draw the move. Suppose (first case) that we can draw the move so that an ant walking from spot g to spot f will notice that the left neighbor of spot f has a lower number than the right neighbor of spot f. And suppose (second case) that we can also draw the move so that such an ant would find the left neigbor of f to have a higher number than the right neighbor. Well, f(g)h would specify the first case, and f!(g)h the second. Similarly, if spot h has two preexisting neighbors such that an ant moving from spot g to spot h could find the left neighbor of h with a lower or higher number than the right neighbor, we would write f(g)h or f(g)!h, respectively.

For an enclosing move in which spot f is different from spot h, we might have the choice - even after all of the previous paragraphs have been applied - of drawing our move such that an ant walking from spot f through spot g and then to spot h and then on around the perimeter will be circling L in either a clockwise or counterclockwise direction. Given that choice, we write f(g)h[L] if the direction is clockwise and f(g)h![L] if the direction is counterclockwise.

(The previous paragraphs should be applied in top down order in working out the correct notation for a given move. Conflicts are always resolved in favor of the earlier paragraph.)

The notation prefers concision, then low numbers, and then commas. When these preferences have been respected perfectly, the game has been recorded in "canonical form".

A game transcription for a normal game of n spots is prefixed by "n+", and a game transcription for a misere game of n spots is prefixed by "n-". This prefix is followed by the names of the participants in parentheses, with the player moving first named first, and with an asterisk indicating the server. Other provenance information optionally can be placed in the parentheses. The postscript "I" indicates a win by Left, while "II" indicates a win by Right. Thus "3+ (Steinitz - Morphy *) 1(4)1[2] I" is the complete score of a normal game starting from three spots, proposed by Morphy, in which Steinitz chose to move first and which Morphy resigned after seeing Steinitz's first move.

(For additional Morphy/Steinitz games and for illustrated examples of sprouts notation, see Illustrative Games).