Statistical auditing and randomness test of lotto k/N-type games

TL;DR

This paper develops statistical methods to audit lotto k/N games by comparing historical results with hypergeometric models, and also proposes testing pseudorandom number generators using these techniques.

Contribution

It introduces a statistical auditing approach for lotto k/N games and adapts it for evaluating pseudorandom number generators.

Findings

Derived mean values and covariances for drawn numbers

Proposed a method for testing the consistency of historical data with hypergeometric models

Suggested application to pseudorandom number generator testing

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.