  The Game of Cycles is a two-player impartial mathematical game, introduced by
Francis Su in his book Mathematics for Human Flourishing (2020). The game is
played on simple planar graphs in which players take turns marking edges using
a sink-source rule. In Alvarado et al., the authors determine who is able to
win on graphs with certain types of symmetry using a mirror-reverse strategy.
In this paper, we analyze the game for specific types of cactus graphs using a
modified version of the mirror-reverse strategy.
