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

llayer8 about 7 hours ago 26 commentsRead Article on quantamagazine.org

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vessenes•13 minutes ago

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)

RNanoware•about 3 hours ago

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.

brookst•about 2 hours ago

Games that sort the cards are the worst / most interesting for this. Gin rummy, etc, where the end result of a game is sorted groups of same-numbers and runs. You can really tell when then shuffling has just transposed a few cards.

soared•about 3 hours ago

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_•about 4 hours ago

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

You would need sloppy ones to introduce randomness.

jtbayly•about 2 hours ago

A "perfect shuffle" according to the article:

>The riffle shuffle has to follow a realistic but strict model where 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. This means that the cards don’t simply alternate between left and right, which would result in a predictable structure; instead, the order might go “left, right, right, left, right, left, left.”)

myrmidon•about 3 hours ago

You misunderstood because the title is ambiguous.

This talks about seven consecutive riffle shuffles ("cut the deck and interleave the piles"): Those are not a "perfect shuffle" (i.e. same probability for every permutation) by themselves, only after doing them several times consecutively (which is kinda suprising by itself).

HPsquared•about 3 hours ago

It's modelled with randomness, each card is taken from left or right with a probability, it's not a deterministic model.

soared•about 3 hours ago

I don’t know on perfect shuffles but for the sloppy shuffles, the deck is cut at a random location between each shuffle.

empath75•about 1 hour ago

Yeah, a "perfect" shuffle is known as a faro shuffle and it's the basis of a lot of magic tricks, but it's a weird looking shuffle and it sort of ruins the tricks once you can recognize it.

aureate•about 3 hours ago

See the paragraph beginning "Yet terms and conditions also apply."

fartcoin67•about 3 hours ago

shouldn't a perfect hackernews rtfa?

ecolonsmak•about 2 hours ago

"...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.

layer8•about 2 hours ago

They didn’t do this practically, the “tracking label” is just an analogy to convey what they did mathematically. The word “barcode” is also only used because it might be more accessible to the layperson than “bit sequence”.

hdndjsbbs•about 1 hour ago

This is just the authors explanation to explain how to encode where a card ends up. The cards don't actually have barcodes, they have a binary-encoded number where a 0 indicates the left pile and 1 indicates the right pile during a specific round of the shuffle. The number encodes the journey that card makes during the shuffle. It's not an actual barcode.

empath75•about 1 hour ago

There are actually "marked" decks you can buy that come with an iphone app that tell you exactly where every card on the deck is by looking at the side.

chadgpt3•about 2 hours ago

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

zeroonetwothree•about 1 hour ago

Username checks out

have_faith•about 4 hours ago

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

brookst•about 2 hours ago

So just do -1 shuffles and save yourself a lot of effort?

HPsquared•about 3 hours ago

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)

fwlr•about 2 hours ago

If there is one card in this pile and no cards in the other, the probability of dropping the card from this pile is one. If instead there are some cards still in the other, a) the probability is less than one, and b) we move one step closer to the first state. So by construction it must be proportional - perhaps a poorly behaved proportionality, but that is still enough for the math to work.

tobr•about 3 hours ago

> But not perfectly and continuously

Isn’t that where the randomness comes in?

HPsquared•17 minutes ago

The randomness comes from sampling the probabilities. The strange assumption is that the probabilities are exactly proportional to number of cards currently in each stack.

layer8•about 7 hours ago

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

mrbluecoat•about 3 hours ago

TL;DR "roughly 14"