In the game described here, also called Green Hackenbush, each player is allowed to delete any edge; in game terminology it's an impartial game.

In the more complicated partisan variants of Hackenbush each player has different moves available:

• In Blue-Red Hackenbush each edge is colored either blue or red. The first player is only allowed to delete blue edges, and the second player is only allowed to delete red edges.
• Blue-Red-Green Hackenbush is similar, except that green edges can be deleted by either player.