World
Game
Of
Sprouts
Association

Some Normal/Misere Dependencies

On the basis of my periodic pivot tables I want to present some dependencies between normal and misere games. I hope AB can check it. As well I hope AB can be stronger by means of it.

So

Gz- number Grundy (iPj)+ normal game iPj (iPj)- misere game iPj

1)i,j=6n,6m+3 (n,m>=0) Gz=(iPj)+=(iPj)- Exception: 0P0

2)i,j=6n+1,6m+4 (n,m>0) Gz=(iPj)+=(iPj)-

3)i=6n+1,6m+4 (n,m>0) j=6k,6l+3 (k,l>=0) Gz=(iPj)+=(iPj+1)-

4)i,j=6n+2,6m+5 (n,m>=0) Gz=(iPj)+=(iPj)- Exception: 2P2

5)i=6n+1,6m+4 (n,m>=0) j=6k+2,6l+5 (k,l>=0) Gz=(iPj)+=(iPj)-

I have not described the dependencies in i=6n,6m+3 j=6k+2,6l+5 because of many exceptions under small k,l.

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