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  • I thought about this for a very long time. For any given deck of cards, there is a coefficient of the average magnitude of displacement from their current order after a shuffle. This can be positive or negative, but we take the absolute value. Then, divide the total number of cards in a deck by this number to get the number of times you need to shuffle. A total of 7 shuffles implies an average displacement of about 7 cards. I think it's reasonable if you alternate the cuts in between shuffles.

    Sloppy shuffles have a much lower average displacement and thus need more shuffles to get to a random state.

    by kittikitti
  • This is a weird title, because what is a perfect shuffle? The word shuffle does not necessary imply a rifle shuffle, and does perfect mean "it mixes the cards well" or is it meaning "cards go down left-right-left-right". It the later, then "perfect" shuffles don't randomize at all, as evidenced by the fact that 8 faros return the deck to order consistently.

    I can do this when in shape, but like most mortal sleight-of-hand practitioners, only with in-hand faros. Actual table faros, what most people are thinking of with a rifle, are the domain of very very few, and even fewer can get that to a point of consistency. In hand faros are not impossible given fresh cards and enough practice.

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

    You would need sloppy ones to introduce randomness.

    by capitol_
  • Numberphile has a video with Persi Diaconis about the seven perfect shuffles. It gives a lot of insight and anectdotes in addition to the central theorem: https://youtu.be/AxJubaijQbI?si=ED7ufY4oPZnNxCbd
    by fisian
  • 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?

    by soared
  • 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.
    by RNanoware
  • 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)

    by vessenes
  • 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...

    by possiblywrong

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