In fact, 99.999999% is an extremely low estimate. The number of ways that a deck of cards can be shuffled is 52! Which is equal to 8065817517094387857166063685640376697528950544088327782400000000000 possibilities.
If you shuffled cards every second from the birth of the universe until now, you still wouldn’t even come close (statistically) to getting the same arrangement twice.
cross-posted from: https://lemmy.world/post/42773245
When considering a full deck you don't really need to estimate the number of dealt hands, because any estimate that is anywhere close to realistic is completely negligible compared to 52!
We're talking: If every person that ever lived became 100 years old and shuffled one deck of cards every minute of their life, the number of shuffled decks in history is still in practice indistinguishable from zero when compared to 52!