Scale economies of lotto once more

Abstract

Under the assumption of random number selection, higher moments of a lotto ticket payoff seem to exhibit a peculiar behaviour; variance (and probably skewness) rises up to some number of bets before approaching its limit from above. A close inspection of the ‘simplest’ expression obtained by means of a hypergeometric summation algorithm suggests that the payoff variance (and probably skewness) is unimodal and attains its highest at a realistic scale.

Acknowledgements

I want to express my gratitude to Marko Petkovsek for his invaluable help; in fact, the proof of Proposition 1 is entirely his.

Notes

¹A term borrowed from Forrest (2002).