Once in 737,000 times. That's how frequently happens what I saw yesterday evening, playing poker with my kids.
We were playing with eights and up since we were three, so 28 cards. And Filippo got served off the deck a straight flush. Even waiving the fact that it was a maximum flush (10-J-Q-K-A), there are only 16 such combinations in a 28-card deck, out of 12-some million possible hands.
Small-probability events do happen from time to time, and we usually give too much importance to them. I will most probably never see another straight flush at my table in my life, but maybe one day I'll die in a plane crash (an event which has similar odds).
Or maybe not; what is certain is that I will see many, many more 5-sigma "discoveries" of new particles and new effects in particle physics experiments, which later turn out to be flukes.
While the odds of a straight flush are very hard to mess up, the odds of a 5-sigma discovery depend on whether the tails of the error distributions you evaluate are Gaussian or not.
And guess what ? They never are.
