There Are More Ways to Shuffle a Deck of Cards Than Atoms on Earth

The sheer number of ways a simple 52-card deck can be ordered is a concept that pushes the boundaries of human imagination. The mathematics behind this is a function called a factorial. For the first card in the deck, there are 52 possibilities. For the second, there are 51 remaining, then 50, and so on. Multiplying all these numbers together (52 x 51 x 50...) gives you 52 factorial, a number so vast that it’s often used as a benchmark for incomprehensible scale.

To put this figure into perspective, the final number is an 8 followed by 67 zeros. By comparison, the number of atoms that make up our entire planet is estimated to be around a 1 followed by 50 zeros. This means you are more likely to pick a specific, pre-selected atom out of the whole Earth than you are to shuffle a deck into a specific, pre-selected order. Even if every star in our galaxy had a trillion planets, and every person on those planets shuffled a billion decks per second since the Big Bang, the chances of any two of those shuffles being identical would still be infinitesimally small.

This is why it is statistically guaranteed that a properly randomized deck of cards has produced an order that has never before been seen in the history of the universe. It takes approximately seven good riffle shuffles to achieve this state of mathematical randomness. The next time you shuffle a deck for a card game, you are, for all practical purposes, holding a unique arrangement of matter that has never existed before and will likely never exist again.