My wife just pointed out that just as a dealt sequence of 52 playing cards is almost certainly going to be unique, since there are so many possible sequences, so humans are never identical (except twins), since the combinations are so many. Of course, none of them are intended, unless you are dealing off the bottom of the pack.
Actually, twins aren't identical. Even identical twins have different fingerprints.
Also, random mutations are extremely uncommon but there are so many base pairs in human DNA that if you sample the DNA of two identical twins, there is a good chance it will not be identical (because you are sampling cells that are a number of generations away from the original fertilised egg).
As for the playing card example, the probability of dealing thirteen spades to one player in a bridge game is low but it's four times higher than the probability that the top thirteen cards in the deck being spades. If I shuffle a deck and then examine it to see if I have 13 spades at the top and repeat until I do have 13 spades at the top, it's going to take a long time. The chance of getting it right is about 1/635,000,000,000.
Let's try a different process. I shuffle the cards and then I take another 100 decks and I arrange each one into the same order as my shuffled deck. I give the decks to Wigginhall and I say, one of these could have all the spades at the top.
Wigginhall examines all the decks and says "no, and, in fact, the decks aren't all the same so you must have made some mistakes in your arranging. However, I've measured the distance of each spade from the top of the deck for each pack and pack 53 is the best."
So I take pack 53 and I rearrange all the other packs and the original pack into the same order as pack 53.
Rinse and repeat. Gradually, the spades will migrate to the top of the best pack even though all the card position changes are completely random.