The idea you’re talking about is true and accurate, for a fully randomly shuffled deck of cards.
A newly opened (and therefore ordered) deck that has only been riffled a few times is not fully random.

Right. So these “interesting facts” you see online that claim that when you shuffle a deck of cards it’s never been like that before - are bullshit

I wouldn’t say BS. Just maybe a little misleading.

• This one specifies “randomly”
• This one says “completely at random”
• This specific the shuffles as “random”
• And this one is really clear, saying that “Card games tend to order decks in common ways, so you need to shuffle really well (about seven times using the "riffle" method) before you’re holding any deck which is truly one-of-a-kind. ”

Well, yes and no. You're definition of shuffle is much different than their definition of shuffle. You're thinking a shuffle could mean a small reorganization of some cards from a given starting point. A true shuffle will implement pseudo random number generation algorithm to sort a deck of cards. This is done by casinos. Otherwise a deck of cards that isn't reorganized between games of play and has seen substantial play would likely achieve similar results.

Wouldn't the part that has been shuffled still be part of the possible permutations? Like shuffling 10cards out of the bunch would still be 10! *1?

No really, more often than not, the same deck is used many times, most homes have a deck or two they use until they can’t, so after a single game, just putting the deck back together would possibly make it novel, then shuffling on top of that. The chance of shuffling a deck which has existed before, is less likely.

I don’t think I’m quite understanding.
The issue is thinking that one shuffle from an ordered deck is “as random” as one that has been shuffled 1000 times. They’re not. The first one is MUCH more likely to happen than the other (and thus is not truly random)

If you shuffle it like how you would with eg. a bridge, then yeah it isn't truly random. But if you were to do something more random--say, you throw them in a wind tunnel and pick them up off the floor--then it will be random, and this will likely be a permutation that no one has seem before.

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What i'm saying is even if you take 10 cards, shuffle them and put them back with the rest, that 52 card order is still one of the many possible orders that could happen if you shuffled all the cards( it would be a bad one but still ine of the possibilities.

Same as what are the chance the a 5 ball lottery winning ticket is X-Y- 48-49-50. Is it a bad sequence but it is still a ticket that has as the same chance of winning as a really random ticket like 9-23-29-36-42..