  Noga Alon and Yaakov Malinovsky recently studied the following game: you
start at 0, and keep rolling a fair standard die, and add the outcomes until
the sum happens to be prime. We generalize this in several ways, illustrating
the power of symbolic, rather than merely numeric, computation. We conclude
with polemics why the beautiful rigorous error estimate of Alon and Malinovsky
is only of theoretical interest, explaining why we were content, in our
numerous extensions, with non-rigorous, but practically-certain, estimates.
