Since it was important to his business, probably no one in the world knows more about the vagaries of getting royals than Frank. A couple of years ago my wife and I played through a couple of royal flush cycles on a game in which the progressive had gotten very large. In the past, royals had come to us just as often as the naive person would suspect.
When after two royal flush cycles we hadn't gotten a royal, I became very suspicious and asked a friend of mine who was a statistician if he thought the rng in the machines had been gaffed. After a long explanation and a visit to Chi Square distributions, he convinced me that it was more of a miracle that we had been getting our royals with such regularity and going several royal flush cycles with nothing shouldn't be that unexpected.
My wife plays about 800 hands an hour and has not been surprised to get a couple of royals in a day. Like me, however, she was amazed to go two weeks without a royal, but that's just the other side of the distribution. It turns out that you can go a very long time between royals before you have good reason to suspect that the rng has been gaffed.
