24/10/2026
52 Playing Cards
A Number So Big, the Universe Starts Looking Small!
Here's something to think about the next time you're playing poker, blackjack or solitaire...A standard deck of 52 playing cards can be arranged in an absolutely ridiculous number of different ways.
How many?
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.
That's 52 factorial (52!), or approximately 8 × 10⁶⁷.
Now, unless you're particularly fond of mathematics, that number probably means absolutely nothing to you. So let's try to put it into perspective.
First, let's take a little trip through the universe...Imagine picking up a single grain of sand from a beach. That tiny grain contains an astonishing number of atoms, potentially tens of billions of billions of them.
Now imagine counting every atom in every grain of sand on that beach.
Then every beach in Australia.
Then every beach on Earth.
But why stop there?
Let's count every atom in every mountain, every ocean, every tree, every animal and every person on the planet.
. We're still nowhere near finished.
Now let's leave Earth and count every atom in the Moon, Mars, Jupiter, Saturn and every other planet in our solar system...Then the Sun. That huge Sun!!!
Then every other star in the Milky Way, along with their planets, moons, gas and dust.
And then let's do the same for the hundreds of billions, perhaps trillions, of other galaxies scattered throughout the observable universe. Every star. Every planet. Every cloud of gas. Every speck of dust.
Scientists estimate that the observable universe contains roughly 10⁸⁰ atoms...That's a 1 followed by 80 zeros.
Now here's the interesting part.
The number of possible arrangements of 52 playing cards is approximately 8 followed by 67 zeros.
That's an astonishingly large number, but there are actually around 1.24 trillion atoms in the observable universe for every possible arrangement of a deck of cards. Not that impressive...So the universe wins that particular competition.
But consider what we've just compared.
The entire observable universe, containing hundreds of billions of galaxies, each potentially containing hundreds of billions of stars, against a little cardboard box containing 52 playing cards.
And somehow, those 52 cards produce a number of possibilities that's "only" about a trillion times smaller than the estimated number of atoms in the entire observable universe.
But here's another way to look at it...Our own Milky Way galaxy contains an estimated 10⁶⁷ atoms, give or take.
That means there are roughly 8 times more ways to arrange a deck of 52 playing cards than there are atoms...
IN OUR ENTIRE GALAXY!!! get 8 galaxies together ... And then you will have approximately the same number of atoms, as there are ways to shuffle one deck of cards.
Every star, every planet, every moon, every cloud of gas and every speck of dust in the Milky Way...and 7 other galaxies.
All outnumbered by the possible arrangements of 52 little pieces of cardboard.
Not bad for something you can buy at Kmart!
Now, let's start shuffling.
Imagine you have a deck of cards and an enormous amount of spare time...You shuffle the deck once every minute.
Every hour, that's 60 shuffles.
Every day, 1,440 shuffles.
Every year, 525,600 shuffles.
And here's our one special rule:
Every shuffle must produce a completely unique arrangement. You're never allowed to repeat an arrangement you've already made.
We're going to work through every possible arrangement, one at a time, until we've seen all of them.
How long would that take?
Approximately:
15,345,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years.
That's roughly 1.53 × 10⁶¹ years.
Still means nothing? Fair enough. Let's make it a little more ridiculous.
The universe is approximately 13.8 billion years old.
Imagine you started shuffling cards at the very beginning of the universe.
Before Earth existed.
Before our Sun formed.
Before the first galaxies had even finished taking shape.
You shuffled once every minute, without sleeping, eating, stopping or ever repeating a previous arrangement.
By today, after 13.8 billion years, you'd have completed roughly 7.3 quadrillion shuffles.
Sounds impressive!
Except you'd have worked through only an unimaginably tiny fraction of the possible arrangements.
In fact, to finish the job, you'd need to repeat the entire 13.8-billion-year history of the universe approximately:
1,100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times.
And remember, that's assuming every shuffle is unique. No duplicates, no wasted attempts, and absolutely no tea breaks.
Now imagine every person who has ever lived shuffling cards every day of their lives.
Even with all those people, all those years and all those shuffles, the number of possible arrangements is so enormous that identical results would remain extraordinarily unlikely under ideal random shuffling.
But wait. There's a catch!
The enormous time we calculated earlier assumes we deliberately avoid every previous arrangement.
Real shuffling doesn't work that way...When you shuffle randomly, you have no idea whether the arrangement has appeared before...And here's where something called the birthday paradox comes in.
You don't actually need to work through all 52! arrangements before there's a reasonable chance of a repeat.
You ONLY need around 10,600,000,000,000,000,000,000,000,000,000,000,000 shuffles for a roughly 50% chance that at least two of those shuffles have produced the same arrangement.
At one shuffle per minute, that's approximately 20 octillion years.
Still more than a trillion trillion times the current age of the universe.
And that's just for a 50% chance!
So what does this mean for your next game of cards?
Whether you're playing poker, blackjack, solitaire or simply shuffling a deck because you're bored, you're handling something rather extraordinary.
In poker, there are 2,598,960 possible five-card hands.
In blackjack, there are 1,326 different combinations of two physical cards that can be dealt from a standard deck.
And in solitaire, the initial order of the deck is drawn from that same astronomical collection of 52! possible arrangements.
Of course, not every arrangement produces a different meaningful game, but the mathematics behind that little deck remains staggering.
And here's my favourite part.
The next time you thoroughly shuffle a deck of cards, there's an extraordinarily good chance that the exact arrangement you're holding has never existed before.
Not in a casino in Las Vegas.
Not in a dusty saloon in the Wild West.
Not during a poker game between soldiers a hundred years ago.
Not in someone's kitchen during a family game night.
Possibly not once, in the entire history of playing cards.
You could be holding something genuinely unique in human history.
52 ordinary pieces of cardboard, arranged in a way that nobody has ever seen before.
And all you did was shuffle them.
