Here's something for math people who like to do statistical analysis on lottery data
Tests of uniformity for sets of lotto numbers (Harry Joe)
https://www.sciencedirect.com/science/article/pii/0167715293901415 (sorry, the full text of the article is behind a paywall but you might have institution access)
Chi-square and the Lottery (Christian Genest, Richard A. Lockhart, and Michael A. Stephens)
http://lstats0.tripod.com/_TheLottery.pdf
Here's the gist of it:
Pearson's test statistic Σ (Oi - Ei)2/Ei has a chi-squared distribution with N-1 degrees of freedom assuming that the observations of categorical data don't overlap. If you're analyzing the frequencies of numbers in lottos like 6/49 (or any k/N lotto), or the white ball portion of lotteries like Mega Millions and Powerball, this assumption doesn't hold because numbers are chosen without replacement. So this test statistic doesn't follow a simple chi-squared distribution with N-1 degrees of freedom, which makes finding the p-value a little harder.
The author of the second paper seeks to find the actual distribution of the test statistic (which turns out to be a more complicated distribution). The author of the first paper seeks to alter the test statistic so that it does fit the well-known chi-squared distribution with N-1 degrees of freedom. Although the first paper is hard to access, one of its important results is cited in the introduction of the second paper.
