arXiv:0806.4595physics.data-an
Statistical auditing and randomness test of lotto k/N-type games
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Abstract
One of the most popular lottery games worldwide is the so-called ``lotto k/N''. It considers N numbers 1,2,...,N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.
Something interesting for the mathematically inclined. "Statistical auditing and randomness test of lotto k/N-type games", available freely at http://arxiv.org/abs/0806.4595v1 Powerball is not like a typical k/N lotto game though, but you might still want to skim the paper.
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