World
Game
Of
Sprouts
Association

Symbology Explained

Last week Roman Khorkov proposed two principles of misere play using symbology that might be obscure to some:

Gz= (x^y + (6n+2)spots)+ = (x^y + (6n+2)spots)-
Gz= (x^y + (6n+5)spots)+ = (x^y + (6n+5)spots)-

We will denote the normal-play Grundy number of position r by G₊(r), and the misere-play Grundy number of position r by G_-(r). A biosphere consisting of k initial spots will be written as (k spots).

Now let q be any sprouts position (including the empty game) and let n >= 0. Then

G₊(q + (6n+2 spots))=G_-(q + (6n+2 spots))

and

G₊(q + (6n+5 spots))=G_-(q + (6n+5 spots))

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