January 10, 2007
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 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.
G+(q + (6n+2 spots))=G-(q + (6n+2 spots))
G+(q + (6n+5 spots))=G-(q + (6n+5 spots))
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