A Winner's Mean Earnings in Lottery and Inverse Moments of the Binomial Distribution

Abstract

We study the mean earnings of a lottery winner as a function of the number 𝑛 of participants in the lottery and of the success probability 𝑝. We show, in particular, that, for fixed 𝑝, there exists an optimal value of 𝑛 where the mean earnings are maximized. We also establish a relation with the inverse moments of a binomial distribution and suggest new formulas (exact and approximate) for them.