A mathematical model sometimes used for shuffling cards is that after the cut, as you joke N cards in one hand and M in the other, the next card to fall has N/(

A mathematical model sometimes used for shuffling cards is that after the cut, as you joke N cards in one hand and M in the other, the next card to fall has N/(N+M) chance of calling from the hand with N, and M/(N+M) chance from the band with M. This is used to come up with results like 8 riffle shuffles being needed to randomize a deck of cards. I sometimes thing about how this model gives an extremely small but non-zero chance that you drop all the cards from the left hand before the right and end up with no shuffle at all. Or just one or two cards fall before the other hand. And I'm sure this has actually happened to people! But if you're counting your shuffles trying to get to 8 to call it randomized, nobody would count that shuffle. They'd redo it. I don't think anyone submitting HHHHHHHHHH or TTTTTTTTTT does so thinking they've generated a random sequence.