In 2017, Eddie Raymond Tipton, former information security director of the American Multi-State Lottery Association (MUSL), confessed to rigging a random number generator that he and two others used in multiple cases of fraud against state lotteries. He was sentenced to 25 years in prison.
[0]: https://www.nytimes.com/interactive/2018/05/03/magazine/mone...
Even a cursory glance of Powerball frequency charts shows no discernible pattern.
Looking at the last winning numbers, they certainly seem clustered at the high end. Still uniform random for a given sample. But certainly not evenly distributed.
Question you really want to be asking is: does my likelihood increase if I select the most frequently picked numbers? Advantage is probably minuscule.
Although, I believe there is a strategy in table roulette that exploits "runs" in which the same number is drawn consecutively. Which for small sample sizes has a much higher probability of occurring than a long non-repetitive sub-sequence.
It would be the scandal of the century if the entire lottery were faked. Centralized database of numbers played. And then a drawing that results in a "lottery actor" winning for show.
Of course the true scandal is that the real winner of every jackpot is the IRS!
http://www.chicagotribune.com/news/nationworld/ct-lottery-ri...
"predictable numbers only on certain days" is not subtle. (I had known of this or a similar case when I wrote.) What I'm thinking of is much less traceable - just an RNG function that happens to leave say, 10% of the numbers as quite rare. There are easy ways to do this that can plausibly explained as mere programming errors. (Meaning you won't be convicted, since there's no code that's definitely tampered with, that couldn't possibly be there unless someone had the intention of cheating. Just a logic error.) You or your confederates buy tickets with those rare numbers, with a very positive ROI, until you're rich. Takes a while.
Putting this on the QuickPic machine at the till means most customers will be competing for common numbers, so you can scoop up the rare ones.