Hitting a prime in 2.43 dice rolls (on average)
Author/Creator ORCID
Date
2022-09-16Type of Work
5 pagesText
journal articles
preprints
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This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.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.