Consider Statistical Sampling. This is the way polling companies predict winners from a very small number of interviews. It is also the way TV programming is determined. Remember Neilson?
OK, the problem with Neilson in the early years, was that they had a known group of samplers, who decided that they controlled the moral fabric of TV. Never mind that they were a small group of folks who could afford a color TV, and where of the ilk Neilson wanted. This ended up being a horrendous misuse of statistics.
Neilson changed, but not that much. They added a few minorities to the sampling group.
Enter the political polls. The truly independent political pols often run by big New organizations with no ax to grind, or news to make are probably the closest thing to pure stats for most of the 20th Century. They did pretty damn well at predicting voting outcomes, still do.
Enter the 21st century and we are privy to be part of the largest statistical test ever. Poker Hand distributions. These distributions were predicted and verified hundreds of times before this type testing could ever even happen.
The big picture shows little to no variance from predictions. Any one sample (session) or group of sessions (samples) will USUALLY be spread spectrum beneath the bell curve of possibilities. But a significant number will show abnormalities by having an unusual amount of hands that would be in the extremes under that bell curve. And with the enormous (gazillions) number of hands, and players and sessions, it would be rigged if any of those groups continually showed an even distribution. They must show deviation from the norm. That's normal!
All the hands you personally will ever play are not enough to prove an uneven distribution. But before long you will approach theoretically correct proportionality.
So there!