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

How many Dice Rolls Would It Take to Reach Your Favorite Kind of Number?