This paper uses variations in a popular parlor game to provide useful instructional benefits. The paper builds a classroom activity to nudge students towards thinking in a backward-inductive manner. The pedagogic innovation is in introducing the game repeatedly with progressively smaller action spaces in every repetition. As the numbers of available actions become smaller and smaller in the reduced games, students stumble on to the backwardly inductive winning strategy. The described procedures are also useful in laying down the intuitive foundations of the concepts of dominant strategies, and first- and second-mover advantages.