The odds that a specific hand would be duplicated are exactly what would be predicted from that number.
The odds that two people in the history of the earth have had two random decks that are the same is a little smaller, it’s true. Pretty much completely immeasurably smaller, but a tiny bit smaller, yes.
The QI quote posted above is excellent:
If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they’d been doing that since the Big Bang, they’d only just now be starting to repeat shuffles.
