Randomness tests for large samples of Keno numbers

Abstract

We describe a study in which a comprehensive set of statistical tests verify the randomness of a large sample of pseudo-random numbers. These were derived from random electronic noise produced by a hardware random number generator used by Jupiter's Network Gaming in their state-wide Keno game. The procedure developed is suited to testing large samples of supposedly random numbers under various conditions. The procedure incorporates, for nine different aspects of randomness testing, probability and frequency calculations in Borland's Delphi, as well as test statistic structure and significance calculations in Excel or SPSS. A brief description and summary table of results illustrates the customisation of each test conducted to the particular set of supposedly random numbers under consideration. A user-friendly interface implemented the application of all nine tests in Borland's Delphi. We developed algorithms suitable for dealing with the special problems concerning potential overflow due to large samples and large numbers of outcome categories as well as for the calculation of large Stirling numbers.