Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

Ironically seven perfectly interleaved riffle shuffles will return a deck to its original order, so the title is spectacularly wrong for one famous result.

Also the new result is cool! (14 semi bad riffle shuffles are sufficient to mix)

Anecdotally, I find that certain card games are more enjoyable with the imperfections of human shuffling: when clumps naturally arise after playing, packing, and unpacking the game several times. An element of organic personality arises when you see a sequence of cards from a previous game. That human element is lost when a computer perfectly shuffles a deck into a never-before-seen orientation.

Upper limit of 14. I’m curious then - when playing cards with friends we start with a semi -random, but definitely clumped, deck. It gets shuffled a couple times.

How random is that deck? How many “cold spots” does it have? Just how not random of decks are people playing with, and ultimately does that even matter if players lack the knowledge or skill to change their play because of that knowledge?

Shouldn't a perfect shuffle just reorder the cards without adding entropy?

You would need sloppy ones to introduce randomness.

"...unique tracking label for every card in the deck"

I'd like more details on how this was accomplished on a practical level. Got me thinking about how to embed trackers thin enough to go into a playing card that would operate like a mesh network then the deck could self report once it's properly randomized making a green light go off indicating play may begin.

AI written? Em dashes, it's not X it's Y

And 8 perfect shuffles resets it back to starting order (perfect being cards interlaced 1 by 1)

Quite the assumption here: "cards are randomly interleaved from the left or right pile one by one. (Each card gets dropped from either the left or the right pile with a probability that’s proportional to the number of cards remaining in that pile."

... Why would it be proportional to the number of cards in each pile? (Edit: I suppose the person doing the shuffling might adjust the rate of cards coming from each hand ... But not perfectly and continuously)

The paper: https://arxiv.org/abs/2510.22783

TL;DR "roughly 14"