A turn-based game on a directed graph in which a player tries to force a designated target set. Its winning region is a least fixed point: add that player's vertices with some winning successor and the opponent's vertices with all successors winning. The finite-graph version uses the same construction as a winning-position attractor in an infinite game.
With disjoint terminal wins for two players and infinite plays valued as draws, compute both reachability attractors while keeping terminals fixed. Entry ranks give terminating winning strategies; positions outside both regions admit defence avoiding a forced loss. A cycle alone is not a certificate of a draw if it also offers a forceable winning exit.
New to topics? Read the docs here!