Hitting a Prime in 2.43 Dice Rolls (On Average)

Noga Alon and Yaakov Malinovsky

The American Statistician, 2023, vol. 77, issue 3, 301-303

Abstract: What is the number of rolls of fair six-sided dice until the first time the total sum of all rolls is a prime? We compute the expectation and the variance of this random variable up to an additive error of less than 10−4 . This is a solution to a puzzle suggested by DasGupta in the Bulletin of the Institute of Mathematical Statistics, where the published solution is incomplete. The proof is simple, combining a basic dynamic programming algorithm with a quick Matlab computation and basic facts about the distribution of primes.

Date: 2023
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DOI: 10.1080/00031305.2023.2179664

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