Misere Hackenbush Flowers

Abstract

We show that any disjunctive sum of Hackenbush Flowers $G$ has as evil twin $G^* \in {G, G+*}$ such that the outcomes of $G$ under normal and mis\`ere play are the same as the outcomes of $G^*$ under mis\`ere and normal play respectively. We also show that, under mis\`ere play, any Green Hackenbush position that has a single edge incident with the ground is equivalent to a nim-heap.