Do you want to do something historic? To accomplish something that’s never been done before? It’s actually not as difficult as you might think.

Simply shuffle a deck of cards.

You see, every time you shuffle a deck of cards, the resulting sequence of cards has almost certainly never been seen before. Ever. So when you shuffle a deck of playing cards, you are making history. You are likely the first human in the history of the world to hold that particular configuration of cards. Sound absurd? Let’s think for a moment about card configurations.

Imagine that you have two cards—say, the ace of spades and the queen of diamonds. In how many different ways could those cards be arranged? Obviously, the answer is two. Either the ace comes first and the queen comes second, or vice versa. Similarly, three cards can be arranged in six different ways. Four cards can be arranged in 24 different ways. Five cards in 120 different ways. And so on.

How do we calculate these numbers? Well, we could of course take the cards and carefully arrange them in all their different possible sequences. But a much faster and easier way to do it involves something called a factorial. A factorial, represented by an exclamation point, is the product of a number and all the numbers below it. So, for example, the factorial 4! equals 24, because 4 x 3 x 2 x 1 = 24. Factorials allow us to calculate the number of different possible configurations for a given number of items (in this case, playing cards).

Turns out, factorials get big very quickly. 10! equals 3,628,800. So if you had 10 playing cards and a ton of free time, you could arrange them in exactly 3,628,800 different ways. Or, if you had 20 cards, you could find approximately 20 quintillion unique configurations, because 20! is approximately 20 quintillion (20 followed by 18 zeros). Impressive, right?

However, those number look itsy bitsy compared to 52!, which is the number of possible configurations for a full deck of 52 cards. Here’s what 52! equals:


That’s an astoundingly, staggeringly, mind-bogglingly huge number.

Think about it this way. If every star in our galaxy was orbited by a trillion planets, and each of these planets had a trillion people living on them, and each of those people had a trillion packs of cards and somehow managed to make unique shuffles one thousand times per second, it would take over 10 billion years before they’d start consistently repeating sequences. That illustrates just how enormous 52! is.

Here’s another illustration. Find a really big, powerful timer. Plug in 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 seconds and start the countdown. Then pick your favorite spot on the equator. With the timer running, take one step every billion years. Every time you complete a lap around the entire earth, remove one drop of water from the Pacific Ocean. Then do the same thing again, walking around the world at one step per one billion years, removing one drop of water from the Pacific Ocean once you circle the globe. Continue repeating that cycle until the Pacific Ocean is empty. At that point, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time the Pacific is emptied. Do this until the stack of paper reaches from the Earth to the Sun. Then start all over again. By the time you repeat that entire process (circling the globe at a pace of one step per one billion years, draining the Pacific one drop at a time, stacking the sheets of paper all the way to the Sun) one thousand times, your countdown timer will only be about a third of the way done. That how big 52! is.

Truly, the number of possible configurations for a full deck of cards is immense.

So, what are you waiting for? Find a deck of cards. Make history.

H/T for illustrations: and Tim Urban


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