How many different ways can a standard deck of cards be sorted?

Think of your last card game – euchre, poker, Go Fish, whatever it was. Would you believe every time you gave the whole deck a proper shuffle, you were holding a sequence of cards which had never before existed in all of history? Consider how many card games must have taken place across the world since the beginning of humankind. No one has or likely ever will hold the exact same arrangement of 52 cards as you did during that game.

It seems unbelievable, but there are somewhere in the range of 8x1067 ways to sort a deck of cards. That’s an 8 followed by 67 zeros. To put that in perspective, even if someone could rearrange a deck of cards every second of the universe’s total existence, the universe would end before they would get even one billionth of the way to finding a repeat. This is the nature of probabilities with such great numbers. Though a long-time blackjack dealer might feel like they have shuffled thousands of cards in their lifetime, against a number this big, their rearrangements are irrelevant. There are simply too many ways to arrange 52 cards for any randomly organized set of cards to have repeated itself.

Don’t believe me? Consider how many ways you can order a deck of just four aces.
There are an estimated 8x1067 different ways a standard deck of cards can be sorted.