Hitting a Prime in 2.43 Dice Rolls (On Average)
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Citation of Original Publication
Alon, Noga, and Yaakov Malinovsky. “Hitting a Prime in 2.43 Dice Rolls (On Average).” The American Statistician 77, no. 3 (July 3, 2023): 301–3. https://doi.org/10.1080/00031305.2023.2179664.
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This is the submitted manuscript of an article published by Taylor & Francis in The American Statistician on 15 May 2023, available online: http://www.tandfonline.com/doi/10.1080/00031305.2023.2179664
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Abstract
What is the number of rolls of fair 6-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
, showing that the expectation is
2.4284.. and the variance is 6.2427... This is a solution of a puzzle suggested a few
years ago by DasGupta in the Bulletin of the IMS, 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.