The number of possible permutations of 52 cards is beyond astronomically large
If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they’d been doing that since the Big Bang, they’d only just now be starting to repeat shuffles.
To put it another way
There are 52 factorial (written as 52!) different ways to shuffle a pack of cards. 52! is just 52 x 51 x 50 x 49 … and so on down to 1.
This number is beyond astronomically large.
If you were to shuffle a deck of cards in a unique way every second, it would take you 52! - or 80658175170943878571660636856403766975289505440883277824000000000000 - seconds to cover all the permutations.
Let’s see how long that will take …
Go and stand somewhere on the Equator. Bring a good book. You’re going to walk at an extremely leisurely pace round the world while a timer counts down 52! seconds.
Start the timer and, after a billion years, take one step along the Equator.
Every billion years, take one more step.
When you’ve finally walked around the whole world, take a drop of water out of the Pacific Ocean.
Now do your slow walk round the world again, taking a step every billion years and a drop of water out of the Pacific every time you circle Earth … until the ocean is empty.
When it is, take one sheet of paper and place it flat on the ground.
Now, refill the Pacific and resume your circumnavigations of Earth: a step every billion years, a drop out of the Pacific when you get round the Equator and eventually emptying the ocean and placing another piece of paper on top of the first one.
Keep repeating the entire process, adding a sheet of paper to the stack each time you’ve emptied the Pacific.
Do this until the stack of paper reaches … the Sun.
Now you might be getting a bit bored, but you’re not even close to being finished yet.
So knock down the stack of paper and do that whole process again - still counting down from 52! seconds, step every billion years, drop of water out of the Pacific every Equator circumnavigation, empty Pacific, piece of paper, until the stack of paper reaches the Sun - one thousand times.
You’re not there yet. There’s still a very long time to go.
For a change of scenery, go to the USA and every billion years deal yourself a five-card poker hand.
Keep doing that until you get a royal flush and, when you do, buy yourself a lottery ticket.
If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon.
Keep dealing yourself a poker hand every billion years and buying a lottery ticket when you get a royal flush and eventually throwing another grain of sand into the Grand Canyon when you win the jackpot … and when you’ve filled up the Grand Canyon with sand, remove one ounce (about 28g) of rock from Mount Everest.
Now empty the Grand Canyon and start all over again.
Poker hand every billion years, lottery ticket when you get a royal flush, grain of sand into the Grand Canyon when you win the jackpot, fill up the Grand Canyon, remove one ounce of rock from Mount Everest.
Do that until you’ve levelled Mount Everest.
Still not there.
Do the whole poker deal every billion years, royal flush, lottery ticket, jackpot, grain of sand, fill Grand Canyon, ounce from Everest, level Everest thing 255 more times and you still have 3.024e64 seconds to go.
The timer would finally reach zero sometime during your 256th attempt.
(Original with more detail here.)