How many shuffled decks of cards would it take for any two to have a 50%+ probability of being in an identical order?

I heard this morning the statement that "no two shuffled decks of cards have ever been the same." I know that this discounts the fact that all decks come presorted and humans shuffle cards non-randomly, so there are plenty of instances in practicality where you'll have matching decks after a single shuffle from a fresh deck, but I'd also like to leave those out of my equations and focus on the purely theoretical solution, given they're all random shuffles.

While I can easily grasp that the shuffle I just did will not match any other shuffle that has ever been done, it's hard to believe that no two have ever been the same. Then it got me to thinking about the birthday "paradox", where it turns out that you only need about 23 people in a room for a >50% probability for two birthdays to match, even though comparing any one birthday to any other one birthday is a 1 in 365 chance.

So in that same line of thinking, would it take trillions of shuffles to get any two to match? Quintillion? Septillion? Or would it shock me and be only a few million? The birthday paradox's match confuses me and that's only 365 days. I couldn't begin to do that math with 52!, but if any of y'all are smart enough to figure it out, I'd sure appreciate the answer.