> 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...
But that assumes the model is only tracking cards’ arrivals in the left and right piles, not their ordering relative to one another. I only got that from the article.
Am I missing something? Is it that the left/right split is actually only informative about the amount of mixing that has occurred under the assumption that the interleaving was perfect, and therefore if imperfect interleaving is possible then one must weaken that guarantee - which then requires a more complex tracking system?
Would that get us closer to "random enough", quicker?
Also the new result is cool! (14 semi bad riffle shuffles are sufficient to mix)
I had understood that seven "typical" riffle shuffles produce good randomness.
Nick Scarne is an interesting name to look up, and his writings are almost on a level with his facility to manipulate cards.
https://en.wikipedia.org/wiki/John_Scarne
Whenever someone acquires a morally-neutral skill (like "card manipulation" or "martial arts") that can be used for "good" or "evil" and chooses the former, that's almost always a good story... especially if they flirted with the latter...
There's the general belief that all magical tools develop significance for the user over time, something that my wife who is a "secular green witch" who doesn't believe in psi at all would tell you all about.
Scientifically though, if somebody isn't a good shuffler their deck is not going to be well shuffled and they'll get readings that deviate from what you'd get from a well shuffled deck. It's harder to shuffle a tarot deck well because it has more cards and these are frequently larger. (Personally my riffle shuffle is awful and probably not much better than an overhand)
A new deck usually has the major arcana together and in order and other cards might be sorted by suit and then number. We do a 5 card spread and if your have a new and poorly shuffled deck of course you are going to have more spreads where you get both the Emperor and the Empress or the 4 of Swords and the 7 of Swords.
I found the tarot readings were infinitely better to the person getting the reading when I just forced the results. So I did.
I still did all the things you're indicating about talking about specific personality, etc, as the patter to the concept.
I got into the tarot group because it's not so easy to find a therianthrope's guild!
From a scientific perspective there is a lot to say for randomness. Like the theory that the I Ching was a version of game theory from bronze age China. I recently created A System of Blessings with 13 selected characters from the I Ching because I wanted to give people something nice but didn't want to give everybody the same thing.
My job was to heighten their experience, and to essentially act as a mini therapist enabling them to feel confident in their own decisions.
But I feel you. I did things entirely differently to everyone else. Which is why I thought it was an interesting story.
Also see Magic players being fond of pile shuffles, which, of course, do very little randomization, and guarantee a good mana weave. Without a few shuffles of your own, most Magic decks ever presented are not sufficiently randomized, and it's even worse in Commander, where we are talking 100 card decks.
If anyone actually cared, and really learned the moves, it would be imperceptible, even on camera, but instead regularly players get caught doing the dumbest of obvious things, even while on camera.
The most interesting feature of it for me is that the carefully-developed bridge bidding systems don't work properly as they're implicitly based on a normal random distribution of cards. With a goulash it's likely that both sides have hands with 7+ cards in one suit, and the game is to pre-emptively bid high in "your" suit before they can do so in theirs. So you would ideally like different signaling arrangements that indicate suit length rather than quality.
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?
You would need sloppy ones to introduce randomness.
>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.”)
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).
as a magician, I'm always still impressed when I see perfect faros.
Now, all these decades later, I don't regret giving up on the Faro and a burnable 2nd. I got along just fine without either one as there's so many ways to reach the same destinations. It's weird how some moves just 'speak to you' right away and others never seem to sit right. Best advice I ever got was to not force it. If progress stalls out, just move on.
You going to Magic Live this year?
That’s a thing where when you know how hard the trick is, it makes it better.
Very cool your training.
And same on poker plots. I can do them infinite other cooler ways, so what’s the point?
The burnable 2nd I have. But it’s not the traditional 2nd. I have practiced and still practice the Richard Turner style 2nd, but I never do it in a performance. I use another path to get to the same result.
Wasn’t planning on Magic Live, but I should see where it is and when.
That's not a bug, it's a feature! Just do a "new deck order restore" with the selected card out of seq. :-)
> when you know how hard the trick is, it makes it better.
Totally! A few years ago I shared my view on "The Progression of Close-up Magic" (pardon the paste):
1. When you're 12, you're happy if a trick fools anyone.
2. Once you get older and have practiced a lot, you start to feel cocky that almost all your tricks fool almost everyone.
3. Then you keep practicing obsessively, start sessioning with good magicians and get humbled all over again. But in their work you start to realize there are levels of depth beyond just fooling people. You can finally see the path and your journey begins.
4. If you keep no-lifing it, eventually those magicians you respect, start respecting a few of your moves back. And that feels better than the loudest applause from any audience.
5. If you're a public performer, you're now probably working regularly. You fool all non-magicians all the time, and even other magicians some of the time. All your years of practice and study have finally paid off. Then you realize, most nights the valets make more than you do. :-)
6. But you keep doing it because you love it, except now the only audience you're working to impress is yourself. Non-magicians love it just as much whether you do easy tricks the easy way or hard tricks the hard way. In competent hands, they all look identical.
But you keep looking for even harder stuff, and then spend hours reworking the methods, exploring how to create the same effect in new ways. You sweat the meta stuff - structure, timing, flow. You pick up new subtleties by studying ancient VHS videos of the old masters. How Slydini's body language made his lapping transcendent. You contemplate how Goshman put that goddamn coin under a clear water glass, in the middle of an empty table, under a spotlight, with 80 year-old arthritic hands. And no one saw him do it. No trick, no move, just pure Jedi misdirection. And no audience will ever know the hours you waste obsessing on this. To everyone else, the tricks look exactly the same, but you do it your own weird, much harder way simply because you think it's neat, elegant, clever or sometimes just because it feels a little more right.
7. At that point, whether you keep working as a pro or even still perform magic at all becomes irrelevant. It's just a day job like any other. You do magic for yourself and maybe handful of others who 'get it'. The tech equivalent is kind of like the time I realized I'd spent more time (and had more fun) reading Doom's source code than I ever had playing the game.
> I can do them infinite other cooler ways, so what’s the point?
One cold deck is worth a thousand perfect Faros :-).
> Very cool your training.
I'd been obsessed with magic since I was 7 and was lucky enough to live in Los Angeles. When I was 16 I heard about the Magic Castle Junior program, then just in it's third year. When I auditioned, Vernon himself (then in his late 80s) was one of the three judges. No pressure, kid - it's just the guy that book you've had since you were 12 titled World's Greatest Magic says is "the greatest magician of the 20th century." The Castle Juniors was the hardest audition in magic because they lose money on (and have to mentor) every kid they let in. Three tricks, 10 minutes. I was so nervous, I blew two of my three tricks. Complete fail. I was so naive and stupid, all three tricks I picked were originals with insanely high difficulty. I had zero chance of nailing them under the pressure and lights of the Castle close-up gallery. :-)
I was shocked when I found out I'd gotten in on my first audition (the avg was 3). Vernon was at my first meeting, took me aside and made it very clear he'd voted against me because I "sucked." He blamed the other two other judges for being 'softies' who gave partial credit to my failed tricks because they were "mildly interesting" twists. Vernon stayed tough on me for all my years in the Juniors, but I did learn a lot from the cranky old bastard. Once when I was classic palming a coin, he slapped my hand and snorted "you palm like a girl!" Offended, I replied "At least the coin didn't fall out when you hit my hand." He rolled his eyes, and sighed "Kid, if you're doing it right, it should fall out!" Vernon passed away a few years after I turned 21 and became a regular member. It wasn't until I was invited to be a judge for regular member auditions that I learned Magic Castle auditions require that all three judges vote "Yes" to accept anyone. Vernon had lied to me! That was the moment I began to suspect maybe he didn't believe I was completely hopeless! I think he just saw how arrogant and cocky I was and knew I needed to be humbled before I could learn anything he had to teach. At best, Vernon seemed to find all the Juniors annoying, and at worst, insufferable. We used to wonder why he bothered showing up to every meeting since we were so hopeless. Only in later years did I appreciate the gift he was giving us and the legacy he was creating. That first decade of graduates from the Juniors created a shocking number of the top magical performers, creators and teachers in the world (although I don't count myself in that lofty company).
I 'dropped out' as a performer after 4 years working full-time as a pro to become a serial tech startup entrepreneur. A few years ago, Stan asked me to give the opening keynote at Magic Live to reflect on how, in my case, so much early magic potential and world-class mentoring "had gone so horribly wrong." :-) My conclusion was that learning the centuries-old craft, rigor and discipline of inventing all-new ways to make the impossible seem possible, and then the showmanship to present it well - was the best training possible for a successful career in tech.
> The burnable 2nd I have.
I'm envious. Mine's just ugly. I kept playing with it on and off over the years but when I saw Lennart Green do his (face up!) I officially gave up on it forever. :-) Of course, Vernon was one of the few humans ever to master a perfect burnable middle. But that's a god move beyond us mere mortals. (Excellent book on Vernon's years long journey to get that 'perfect middle': https://www.amazon.com/dp/0805074066).
> Wasn’t planning on Magic Live, but I should see where it is and when.
First week of August in Vegas (usually the same week as Blackhat). I go every year just to hang out with friends from the old days. Ping me if you go.
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.
Sloppy shuffles have a much lower average displacement and thus need more shuffles to get to a random state.
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.
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.
To be fair, sure most of those marking strategies are approximations designed for a specific trick or a specific gambling game and so don't always need to be 100% of the state information (suit and rank of every individual card). But there are certainly close up magic reasons to have a deck you can find exact cards by marks. Though also to be fair, many (but not all) of those do move the marks to the back of the card with the assumption that you can at least spread the backs of the cards.
... 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)
Isn’t that where the randomness comes in?