
TL;DR
This paper establishes a relationship between normal and misère play outcomes for disjunctive sums of Hackenbush Flowers, introducing the concept of an evil twin, and shows that certain Green Hackenbush positions are equivalent to nim-heaps under misère play.
Contribution
It introduces the concept of evil twins for Hackenbush Flowers and characterizes Green Hackenbush positions with a single incident edge as nim-heaps under misère play.
Findings
Existence of an evil twin G* for any disjunctive sum of Hackenbush Flowers
Equivalence of certain Green Hackenbush positions to nim-heaps under misère play
Outcome relationships between normal and misère play for these positions
Abstract
We show that any disjunctive sum of Hackenbush Flowers has as evil twin such that the outcomes of under normal and mis\`ere play are the same as the outcomes of 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.
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Taxonomy
TopicsArtificial Intelligence in Games · Digital Games and Media
