In fact, 99.999999% is an extremely low estimate. The number of ways that a deck of cards can be shuffled is 52! Which is equal to 8065817517094387857166063685640376697528950544088327782400000000000 possibilities.
If you shuffled cards every second from the birth of the universe until now, you still wouldn’t even come close (statistically) to getting the same arrangement twice.
cross-posted from: https://lemmy.world/post/42773245
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.
I’ve shuffled so poorly that my discard hand ended up Identical the next round in MTG.
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.
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.
it doesn’t need to be from an already randomly sorted.
Since cards start in order and the majority of shuffling is done the same method, there will be a bell curve of repeated combinations.
If the deck began its life randomly sorted, would the statistic be true then?
From a production point of view I think that it would be very difficult (which generally means expensive) to create a randomised deck while ensuring that the deck has all 52 cards in it (although I’m just thinking aloud and have no experience in this area so could be wrong)
However, if the starting deck is truly random then the output of the shuffle would also be random so there wouldn’t be a bell curve.
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 😂Don’t stop now. You’re obviously due for an equally long winning streak. Isn’t that how it works?
It absolutely is, any day now. 🤣
Thanks to auto-capitalization, that factorial looks like the end of an exclamatory sentence with very unremarkable odds.
Sure
