A partizan game played on a graph attached to the ground. Left removes blue edges and Right removes red edges; after a removal, all edges disconnected from the ground disappear. The player with no legal move loses under the normal-play convention.
A Hackenbush position whose graph is a single path attached to the ground at one endpoint. Finite red-blue stalks have dyadic rational game values; the initial monochromatic run determines the integer part and subsequent colors determine successive binary fractions.
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Hackenbush is a combinatorial game that involves two players who take turns removing edges from a graph. The game is typically played on a connected graph with vertices and edges, where edges are colored, often in two colors representing the two players, or one color for a player and another for the graph itself. Here’s how the game works: 1. **Initial Setup**: The game starts with a graph drawn on paper with vertices connected by edges.