Actually, the probability that all decks ever shuffled are unique is also very high. We can approximate the probability that any two of the n decks shuffled in human history were identical as p=1-n^2/52!
Using the same estimate as the OP for n (1.56x10^23) gives p=3.02x10^-22. Still fantastically low.
Using the same estimate as the OP for n (1.56x10^23) gives p=3.02x10^-22. Still fantastically low.