This, particularly the Chi-square test for randomness I have done with each data set that I have, from pick 2 through pick 5 in Pennsylvania... all fail, but not by much.
I ran them in both Python and using R Studio (the absolute Lamborghini of the stats programs... and it is open source free for anyone) and the results were the same. All game draw histories failed, but by tenths of a percent...
To be fair, I cleaned my data by eliminating any of their "double draw" promotional results (2 draws for the same game) and by deleting the infamous 666 draw.
The thing is, in PA, the day draws are done by an RNG, and the night games are still mechanical. There was no detectable bias between the methods.
When I started years ago I could barely write an Excel formula. The result of my exhaustive search for bias came up dry time and again.
The verdict... the results are random enough.
So the next journey should be to understand the very nature of the flimsy structural clues that exist in "random enough" data.
All histories of randomly drawn numbers are a special case of a uniform distribution known as a discrete uniform distribution. Discrete because there are only a finite number of possibilites. In the daily games, that is 0 through 9. They will never draw a 4.5 or an X.
You can see the nature of randomness itself when using frequency to classify, rather than trying to be concerned with the digits themselves. Hot and cold are the best examples. Treat them as outliers rather than targets. With this classification I had noticed that in the 16,800 draws of the PA pick 3 evening, a full 25% of results were the neutral numbers between hot and cold... when using a target of the next 7 draws, a draw consisting of 3 neutral numbers happens over 90% of the time. The best part is you only need 150 draws to train the model. The rolling back test proved it out... numbers tend to fill from the middle of the expectancy range, which is 10% for 0-9.
Funny part is it seems to hold for the pick 2 through the pick 5... draws comprised of all neutrals happen enough even in the pick 5 that it could be the start of a strategy of elimination.
It is a rabbit hole for sure, and I only figured out the first step... but it was exciting to see something actually hold up under back testing.
The parameters will change for the bigger games, such as expectancy is 10% in a pick N for each ball, while in a game like Power Ball, the expectancy drops to 1.449% for each ball... but that is a project for another day.
Their distributions may not be chi-square perfect, but they are random enough to work with.
