Like many mathematics teachers, the authors often find that students who struggle with a difficult concept may be assisted by the use of a well-chosen graph or other visual representation. While one should not rely solely on such tools, they can suggest possible theorems which then might be proved with the proper rigor. Even when a picture suggests false leads, that situation may be equally interesting. In this article, the authors describe some expected values and variances for the game they have termed "Coin ToGa" (for "Coin" "To"ssing "Ga"me), and then extend earlier results by carefully examining suggestive pictorial and experimental evidence. Additionally, they include some useful exercises for calculus students with a background in basic probability. (Contains 3 tables and 3 figures.)