The Maths of Tarot: How Many Tarot Spreads Are There (Really)? And How Long Would It Take To See Them All?

Every time you lay out a 10-card tarot spread, you’re arranging a tiny paper universe. But just how many possible universes are there? And what are the chances of ever seeing the same one twice?

It turns out that there are so many possible variations on a 10 card spread like the Celtic Cross, the odds are no one else has ever had your exact spread before, anytime you do a pull. Which honestly blows my mind. Each 10 card reading is probably unique to you (and to your reader if someone else is reading for you). A message from the cards just to you, one they’ve never given to anyone else.

Which is wild, right?!?

As a (mostly) secular reader, one thing I always second guess myself with in Tarot is all the super spooky ‘coincidences’ that you see when you read a lot (which I do now I’m on the market stall 2 days a month). Weird sequences (stalker cards, mother and daughter getting the same 4 card spread with the signifier card swapped over to refer to each other etc.) happen all the time, and the inside my of my head is a constant battle between OK, this is some Twilight Zone stuff vs. sure, but you know that probability does looks weird from the outside, and that humans are crap at distinguishing expected statistical anomalies from fate, right? But until recently, whenever I spotted the same cards coming up over and over, I mostly leaned on the side of maths-doing-its-weird-maths-stuff.

However, last year I had one client who said they’d had the exact same Celtic Cross spread I drew for them a few months prior (from another reader). I was obviously skeptical, but then they showed me a photo on their phone, and yeah… The exact same 10 card spread. Now, I’m by no means an expert mathematician, but as a social scientist who analyses quantative data, I’ve been dragged kicking and screaming into a rudimentary understanding of statitsics. And this case struck me as so improbable I decided to do a little number crunching (particularly as I teach second year research methods, and am always scrabbling around for any weird bit of statistics that makes quant more interesting for a bunch of bored 19 year olds sitting in a stuffy windowless lecture theatre! If they paid as much attention to my stats classes as they pay to my Tarot readings at the student Halloween Party they’d be employed by NASA straight after graduating 😂)

And this is how I figured out that each Celtic Cross spread is probably unique in all the world.

In the history of all the world.

Sounds unbelievable, right? But 10 cards out of a deck of 78 has approximately 1.17 trillion combinations. That’s… a lot. If you dealt out 10 cards a time every 15 seconds it would take you around 555 million years to get all possible combinations – to have seen them all by now, you’d have to have started dealing before the first fish evolved lungs.

But even that doesn’t account for how super unlikely it is anyone’s ever had your exact spread before. In a classic 10-card Tarot spread like the Celtic Cross, the position of the card matters. Anyone with even a passing interest in Tarot can tell you that the Ten of Swords as your signifer card is not the same as having the Ten of Swords as the likely outcome of your situation.

So if you want to know how likely it is someone has had your exact spread before – with the same ten cards in the same ten positions – you need to look at permutations. So – provided my maths is correct – which it may not be, but the students haven’t called me out on it yet, lol! – you end up with 4.55 quadrillion possible combinations. If you dealt a Celtic cross spread once every fifteen seconds, it would take over 2.17 billion years to see all the possible versions of those spreads (and that’s if you never got any repeats). That’s longer than life has existed on Earth.

However, IRL you’d definitely pull some repeat spreads, so to figure out how long it would actually take to see every combo at least once you’re now in the realm of the Coupon Collector’s Problem, a classic and FUN probability conundrum (hey, you can take the cheesy professor out of the lecture hall, but you can’t take the… I dunno… something something… basically, I’m a nerd, OK). So, the number of draws you’d need to reasonably expect to encounter every possible spread at least once is even more staggering: over 80 billion years of continuous 15-second draws.

For context, the universe is about 13.8 billion years old. So you’d need more than 5 universe’s worth of time.

So: if you ever see the exact same 10-card spread twice, even my cynical little heart thinks that same universe is probably trying to tell you something. Loudly. And you’d be well minded to listen!

He deals the cards as a meditation
And those he plays never suspect
He doesn’t play for the money he wins
He don’t play for respect

He deals the cards to find the answer
The sacred geometry of chance
The hidden law of a probable outcome
The numbers lead a dance

I know that the spades are the swords of a soldier
I know that the clubs are weapons of war
I know that diamonds mean money for this art
But that’s not the shape of my heart

‘Shape of my Heart’ by Sting (Miller / Sumner)

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