> The deck has to be cut more or less in half before shuffling.
"More or less" is doing some heavy lifting here. The original GSR shuffling model cuts the deck at a point that is binomially distributed, so that for example about one-fifth of the time the cut may be at least as asymmetric as a 21-31 card split, which I think most would agree is nowhere near "the precision of a professional magician."
Also note that the theorem in the paper really focuses only on relaxing the cutting model; the model of subsequent interleaving of the resulting piles is the same, dropping a card from a pile with probability proportional to the size of the pile. (Equivalently but perhaps less intuitively, for the original GSR model with the binomial cut, imagine flipping a fair coin for each card in the deck, then "de-interleaving" by sliding the "heads" cards out, preserving their relative order, and placing that pile on top of the remaining "tails" cards.)
> But with that seventh shuffle, the deck suddenly tips into a highly unstructured state.
More accurately, the total variation distance from a uniform distribution first drops below 0.5 at seven shuffles[0]. The actual cutoff phenomenon's asymptotic result would suggest 3/2 lg n shuffles for a deck with n cards, which for n=52 would be closer to nine shuffles.
Unrelated but the animated photo of the magician performing a shuffle really shows how advanced, efficient, and deliberate our limbs are.
I randomly came across a 1979 bbc documentary on "Word Processors" on YouTube yesterday. Even though I wrangle terabytes of data using AI agents everyday now, it still felt like magic to imagine myself seeing the documentary for the first time in 1979.
vessenes
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)
show comments
RNanoware
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.
show comments
soared
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?
capitol_
Shouldn't a perfect shuffle just reorder the cards without adding entropy?
You would need sloppy ones to introduce randomness.
show comments
vanderZwan
Does this new proof have any practical consequences for determining if a PRNG algorithm is any good?
ecolonsmak
"...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.
show comments
have_faith
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 article deserves several clarifications:
> The deck has to be cut more or less in half before shuffling.
"More or less" is doing some heavy lifting here. The original GSR shuffling model cuts the deck at a point that is binomially distributed, so that for example about one-fifth of the time the cut may be at least as asymmetric as a 21-31 card split, which I think most would agree is nowhere near "the precision of a professional magician."
Also note that the theorem in the paper really focuses only on relaxing the cutting model; the model of subsequent interleaving of the resulting piles is the same, dropping a card from a pile with probability proportional to the size of the pile. (Equivalently but perhaps less intuitively, for the original GSR model with the binomial cut, imagine flipping a fair coin for each card in the deck, then "de-interleaving" by sliding the "heads" cards out, preserving their relative order, and placing that pile on top of the remaining "tails" cards.)
> But with that seventh shuffle, the deck suddenly tips into a highly unstructured state.
More accurately, the total variation distance from a uniform distribution first drops below 0.5 at seven shuffles[0]. The actual cutoff phenomenon's asymptotic result would suggest 3/2 lg n shuffles for a deck with n cards, which for n=52 would be closer to nine shuffles.
[0] https://possiblywrong.wordpress.com/2018/09/02/arbitrary-pre...
Unrelated but the animated photo of the magician performing a shuffle really shows how advanced, efficient, and deliberate our limbs are.
I randomly came across a 1979 bbc documentary on "Word Processors" on YouTube yesterday. Even though I wrangle terabytes of data using AI agents everyday now, it still felt like magic to imagine myself seeing the documentary for the first time in 1979.
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.
Does this new proof have any practical consequences for determining if a PRNG algorithm is any good?
"...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.
And 8 perfect shuffles resets it back to starting order (perfect being cards interlaced 1 by 1)
The paper: https://arxiv.org/abs/2510.22783
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)
AI written? Em dashes, it's not X it's Y
TL;DR "roughly 14"