This is definitely mostly true.
It does breakdown some when every new deck has the same starting order, and people frequently shuffle poorly. Those 52! possibilities shrink massively.

What’s fun is how often this principle is used every day. For example, when you upload a video to YouTube, you’re assigned a unique URL, but it would be too slow to simply add your URL to a list to make sure nobody else uses it. There are millions of videos uploaded every day, and thousands of servers spread all over the world.

Instead, YouTube just generates a truly random URL and depends on the odds of two videos having the same URL being effectively zero.

The same is true for Bitcoin. If you could guess a Bitcoin private key for any currently used wallet, you’d have full access to the funds within that wallet. This can even be done offline. Even if you could guess trillions of private keys per second, the odds of you hitting even one that’s already been used is low enough to be totally secure.

Since cards start in order and the majority of shuffling is done the same method, there will be a bell curve of repeated combinations.

Or you could go with it either is or it isn't, that way it's 50%.
That's the principle I use for gambling, although for some reason I've had an insanely long streak of bad luck?
/s 😂

V-Sauce had an incredible video on this, outlining exactly how unfathomably colossal the number 52! actually is. If I remember correctly:

Stand at the equator and set a timer for 52! seconds, press start, then stand still and wait for 1 billion years. Then, take one single step forward, and wait another billion years.

Continue walking at this pace until you've made your way around the Earth and back to your original starting position, then remove one drop of water from the Pacific ocean, and set it aside.

Repeat this process until you've completely emptied the Pacific Ocean drop by drop, then set a single sheet of paper on the ground beside you. Refill the Pacific Ocean again (instantly), and do it all over again.

Continue this process, setting each sheet of paper on top of the last, until the stack of papers reaches the sun. Then tear it all down and do the whole thing over again, 999 more times.

At this point, the timer would be about a third of the way to 0 seconds.

The video continues with an alternative mind-boggling process to kill the rest of the time while you're waiting for the timer to reach 0, which involves dealing yourself 5 cards from a well-shuffled deck once every billion years, and buying a lottery ticket for each royal flush you deal yourself. If that lottery ticket hits the jackpot, you'd (EDIT: throw a grain of sand into the grand canyon, repeating until it's full - forgot this step) then remove 1 ounce of rock from Mount everest, and repeat all of this until Mount Everest is completely leveled.

After doing this 256 more times, then the other two-thirds of the timer will have elapsed, and it would finally reach 0.

That's how long 52! seconds would be.

This looks a lot like AI slop to be honest

This isn't true in practice since we don't shuffle cards well enough for it to be true but at least this isn't AI Slop haha.

Thanks to auto-capitalization, that factorial looks like the end of an exclamatory sentence with very unremarkable odds.

Incorrect, if it was a true random shuffle from an already true randomly shuffled deck you are would have these odds or possibly even better since the majority of all shuffles were not random, but if wo could know I think we would be surprised how poorly randomized the average shuffled deck is.

I've shuffled so poorly that my discard hand ended up Identical the next round in MTG.

Sure

https://infosec.pub/post/43321667

How many cards from a 52 card deck does it take to have a 50% chance of a unique order?