Copyright © 2010 Konstantinos Drakakis. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the mean earnings of a lottery winner as a function of the number of participants in the lottery
and of the success probability . We show, in particular, that, for fixed , there exists an optimal value of
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.