World

Game

Of

Sprouts

Association

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)-Josh Purinton has now provided the following explication:

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

We will denote the normal-play Grundy number of positionrby G_{+}(r), and the misere-play Grundy number of position r by G_{-}(r). A biosphere consisting ofkinitial spots will be written as (kspots).Now let

qbe any sprouts position (including the empty game) and letn>= 0. ThenGand_{+}(q+ (6n+2 spots))=G_{-}(q+ (6n+2 spots))G_{+}(q+ (6n+5 spots))=G_{-}(q+ (6n+5 spots))

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