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
Unique against what? This almost sounded like the birthday problem, but there's only one deal?
Unique as in never having happened before in the history of cards.
We need to have an estimate of the number of hands ever dealt (I think), which isn't given in the infographic. I am suspecting you need a better estimate for the 50% calculation than a 99.999999% calculation, but I don't have the math to back it up.
The creator of this factoid doesn't have an estimate and is misrepresenting a basic permutation and assuming no hands have been dealt before.
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!