Now, this trick uses an ordinary deck of cards.
A fresh deck, still sealed in the package, which I’ll open in front of you.
A normal deck, as you can see: 52 cards, plus the two jokers, which we’ll remove.
We don’t need them.
Unless you want to keep them – it makes no difference, as you’ll soon see.
But I generally think it’s more elegant to take them out.
So, if you agree, I’ll leave them aside.
And shuffle the remaining 52.
I’ll give them a good, long shuffle.
A thorough shuffle.
But what is that, anyway?
A “thorough” shuffle.
It’s hard to tell.
There are so many ways to shuffle a deck of cards.
There are actually hundreds of shuffling techniques, at least known ones.
There’s the pile shuffle, the corgi shuffle.
There’s the zarrow shuffle, the spiral shuffle, and the mongean shuffle.
There’s the weave and faro shuffles.
There are shuffles originating from all over the world, from across history, derived from cultures both living and dead.
Techniques of varying degrees of complexity and finesse, and beauty, and effectiveness.
Techniques of varying degrees of fairness.
There are techniques that one can do by oneself, with just two hands.
And some that require two, sometimes even three participants.
There are techniques designed for one hand.
There are techniques designed for no hands.
There are techniques that require certain specific conditions or spatial arrangements.
That must be done outside, for example, or with one’s back to a corner.
And techniques that must be done using certain implements.
A common suggestion is that a shuffle be performed on top of a table.
For some, it’s a requirement.
For some, the height of the table is a requirement.
One technique specifies that it be performed under water, in the air bubble captured within an overturned bowl.
One technique specifies that it be performed in one’s sleep.
But the two most popular kinds of shuffles are the riffle shuffle and the overhand shuffle.
These are the kinds of shuffles you’ll most likely see in, say, a casino.
Or on TV or in the movies.
If you’ve played cards at home, you or a friend has probably executed something equivalent.
The riffle shuffle, or “dovetail” shuffle, is modeled by cutting the deck binomially so that half the deck is held in each hand with your thumbs pointed inward so that the cards arc against one another.
The cards are then released by the thumbs so that they rapidly drop, interleaved, from either half of the deck.
Here, I’ll demonstrate.
Here, I’ll do it again.
That last bit is called a bridge.
Some people call it a cascade.
It’s somewhat of a flourish to get the cards back in place.
I’ll demonstrate again.
This time, placing the halves flat on the table in front of me with their rear corners touching, then again lifting the edges with my thumbs while pushing the halves together.
You’ll notice I didn’t cascade them this time.
That’s to minimize the chance of you, or myself, or anyone else seeing any of the cards mid–shuffle.
It’s pretty effective.
That relative effectiveness at keeping the card faces hidden is why this method is usually standard for casinos.
Here, I’ll do it again – try and see if you can catch a peek.
Cards on the table – riffle, cut.
Cards on the table – riffle, cut.
Now, the overhand shuffle is more rudimentary.
For this shuffle you hold the deck in either hand, either right or left, then gradually transfer it to the other by shaking out small packets of cards, like so.
The smaller and more rapid the packets, and the more times the shuffle is performed, the more random the final shuffled deck’s arrangement of cards.
Or so they say.
In reality, it’s a very unreliable shuffle, prone to sleight–of–hand and manipulation, or even error, with cards sometimes falling into their new hand in the exact order they’d left the previous, or with variations so minor as to be useless for legitimate games of chance.
So we won’t use it.
We’ll just use a riffle shuffle, for now.
It seems like the most thorough method.
Or at least the most commonly recognized thorough method.
Interestingly, there’s in fact an exact number of riffle shuffles that, once performed, thoroughly randomizes a deck of cards.
It’s seven.
One, two, three, four, five, six, seven.
The mathematicians Persi Diaconis and Dave Beyer proved this in 1992, in a paper entitled “Trailing the Dovetail Shuffle to Its Lair.”
The paper was based on a model of probability distribution for riffle shuffle permutations known as the Gilbert-Shannon-Reeds model, named after the mathematicians Edgar Gilbert, Claude Shannon, and J. Reeds, who, over a period of nearly 40 years of combined research, developed the mathematical infrastructure to experimentally observe the outcomes of human riffle shuffling.
Diaconis and Beyer analyzed the total variational distance between two probability distributions: the uniform distribution in which all permutations are equally likely, and the distribution generated by repeated applications of the Gilbert-Shannon-Reeds model – repeated riffle shuffles, essentially, analyzed according to this model.
Their calculations showed that, for n = 52 (as in 52 cards), seven riffles give total variation distance 0.334.
(You want to get as close to 0 as possible.
0 is the absolute in the measure of randomness, in this model.)
After that, the cards can continue to be randomly mixed, but never to a degree smaller than the variational distance of 0.334.
That’s the transition point, as well as the threshold.
It’s the most finely distributed fact of unpredictability possible for a deck of cards.
Seven sets of one riffle shuffle plus one random cut.
And then the deck is reset as a mystery, uncertain.
Assuming, of course, that the shuffler is proficient.
Which I am, so don’t worry.
I’m quite proficient.
I’ve been doing this a long time.
But, of course, despite being proficient, I’m not perfect.
Because nobody’s perfect.
And that’s important.
Perfection would be a problem.
Here’s another interesting fact.
Over the course of this study, Diaconis became obsessed with executing a “perfect shuffle.”
A “perfect shuffle” is an exact interlacing of the cards in a riffle shuffle.
One pile braided seamlessly into another, at a one-card-to-one-card ratio: one card from one pile on top of another card in the second pile, and so on, and so on, for the entire deck.
Diaconis assumed that this consistency would create the ultimate stable baseline for his investigations into probability.
And it did, kind of.
But maybe not in the sense he was thinking.
You see, in applying this standard, he found that, rather than perfecting randomness, the “perfect shuffle” in fact eliminated it.
If a deck is perfectly shuffled eight times, for the first seven times the cards will appear to deviate and confuse themselves.
But with the eighth shuffle, the cards will (without fail) end up in the same order as they were before the shuffling began.
Thus signaling a loop.
What Diaconis discovered was that in order to achieve randomness in the final order of cards, there needed to be a randomizing aspect to the shuffle itself.
The shuffle had to be accurately executed – the cards couldn’t just be flying all over the place – but it also had to be imperfectly executed.
Describing this phenomena to the New York Times, Diaconis mused: “When you take an honest description of something realistic and try to write it out in mathematics, usually it's a mess.
We were lucky that the formula fit the real problem.
That is just miraculous, somehow.”
I try to keep this conclusion in mind when I’m developing a trick.
I thought about it a lot when developing this trick.
I think it gets at something fundamental within the practice of magic.
That we perceive imperfectly.
We’re easily distracted.
We’re often manipulated.
We observe using sensual patterns ingrained from years and years of repetitive use, tics of attention and awareness, easily identified and influenced.
And on top of that, our minds, despite their extraordinary and beautiful capacity for thought and analysis, remain incredibly limited when it comes to the degrees of information they can immediately process within a given moment.
That limitation is the opening through which any trick must pass in order to be effective.
A magic trick has to live in those unobserved spaces that are the consequence of our own finitude.
However – and this is the paradox – at the same time, they must remain, themselves, observable.
One must be able to witness a trick without also seeing how it is possible to witness it.
It’s a strange problem.
And one that leads us to a second, correlative principal: that, in addition to our own perceptions, we also perform imperfectly.
We are fallible in our movements.
We’re dependent on a host of complex, interdependent mental and physical factors that must fall perfectly into place to properly translate a technique into action.
And so we’re inconsistent, and occasionally clumsy.
We take the cards in our hands and shuffle the piles into one another.
But not without divergence.
Say a couple of cards stick.
Or our thumbs can’t maintain the exact same levels of tension between themselves.
Or the air is more humid on one side and prevents those cards from falling evenly.
It’s an imprecise process.
But if it weren’t, the shuffle couldn’t exist.
Because the predictability of its materials would prevent any mystery as to its outcome.
It’s the same with a trick.
A trick can never be truly predetermined if it is to actually exist – instead, it needs to accomplish itself, every time, through the hazard of a performance.
Every magic trick needs to exploit that delicate balance between the fallibility of the spectator and the fallibility of the performer, where the risk of failure rears itself up.
Think about it.
Think about most skilled card controller you can.
Say, someone with an absolute understanding of the deck’s operations.
Someone with a clear mental map of every card’s position, and the practiced expertise to produce them at will.
The only way for that person to be a magician is for them to place those extraordinary abilities at the mercy of a performance.
They have to actually do the trick.
And in so doing, they must risk catastrophe.
They must risk the catastrophe that, even when whittled down to the tiniest chance (a 0.334 out of 100 chance, say) the spectator might not be fooled.
The methodology of the trick might be revealed.
It might be seen.
The secret process of the trick might be seen and discovered.
This risk – the risk of discovery – is what I believe we actually witness when we witness magic.
It is what allows the trick to be observable, despite the invisibility of its process.
That risk is the shadow the trick casts from outside the edge of our sight, which signals to us that it has a form.
Which is why, when we’re able to figure out an act – when we catch a magician mid-palm, or recognize whatever contraption is making an effect possible – the magic disappears.
Because the risk has disappeared.
And now the trick is just like anything else: just a handshake, or the turning of a gear.
Diaconis, in addition to being a mathematician, was, unsurprisingly, a magician himself.
He grew up in New York.
At 14 he dropped out of school.
He dropped out to travel with and apprentice under a magician by the name of Dai Vernon.
This was maybe 1959.
Vernon was traveling around the country, performing magic and researching sleight–of–hand.
He was interviewing and observing card cheats, con artists, pickpockets, and other assorted criminals.
People working with much higher stakes in their efforts to fool people.
He was developing a unique focus on up-close performance that would come to define his career, cemented by a star-making residency at the Magic Castle in Los Angeles, at this time still a few years away, but that, once begun, would continue on for the rest of his life, introducing his work to millions and cementing his legacy as one of the great masters of the art of illusion.
But in 1959, Dai Vernon wasn’t a legend yet: he was established and well respected, but still somewhat of an insider.
He had a reputation as a preternaturally skilled and creative card magician, and enjoyed a certain insider’s notoriety in the magic community.
This notoriety had been earned through a singular and impressive achievement, made all the more unlikely considering how young Vernon was when he did it.
Now this is a famous story, so if you’ve heard it I apologize.
But it’s important for the trick, so I hope you’ll indulge me.
For anyone who does not know, as a young man Vernon accomplished a feat deemed by many in his field to be impossible: he had fooled Harry Houdini.
This supposedly took place on or around February 6th, 1922.
Houdini, at that time, was the most famous magician in the world.
He was a superstar, a seemingly inexhaustible talent.
He was a master card manipulator, a daring escape artist, and a keen and ruthless critic of magic.
Houdini would often boast that he could figure out any card trick presented to him by any magician, so long as it was presented to him three times.
The day that he met Vernon, in Chicago in 1922, he was actually in town debunking spiritualists, who he held a personal grudge against after having been the victim of a predatory seance scam following the death of his mother two years previous.
Houdini was basically a debunking machine at this point in his life.
It was almost the entire focus of his career.
And he was killing it – he was debunking mediums to sold out crowds at the fucking Majestic Theater for weeks on end.
Vernon, comparatively, was making a modest living cutting silhouette portraits out of black construction paper on the Coney Island boardwalk, practicing magic in his spare time.
He was 20 years younger than Houdini.
So, when they were introduced that night at the Great Northern Hotel, at a gathering of the Society of American Magicians, Houdini reportedly rolled his eyes.
He was utterly incredulous.
He had never heard of this guy, never seen him in his life.
But Vernon was unintimidated.
He presented Houdini with a deceptively commonplace setup: a fanned deck of cards, and then politely asked him to pick one – “pick any card,” he said – and then to write his name on it.
Houdini, reaching in, chose the ace of clubs, and with his own pen, wrote his initials, “HH,” across its face.
Vernon then took the card back, flipped it over, and slowly slid it, face-down, underneath the top card in the deck.
Calmly, he set the deck down on the table between them.
He squared it up – everything visible, nothing hidden.
He snapped his fingers over it, and then – without a flourish, as if it were the least remarkable thing in the world – he turned over the top card.
It was the ace of clubs, with Houdini’s initials clearly visible.
Houdini stared at the card.
He asked Vernon to do it again.
Again Vernon took the ace of clubs and slid it gently under the top card.
Again he snapped his fingers.
And again, once the top card was turned over, it was the ace of clubs.
“HH” written on it in black ink.
The ace of clubs had seemingly risen through to the top of the deck.
As if the top card had simply vanished, or had never been there to begin with.
Houdini asked Vernon to do it a third time.
And then a fourth.
And then a fifth.
And then a sixth, this time for his wife Bess.
Finally, he asked Vernon to perform it a seventh time.
Which Vernon did.
And then Houdini gave up.

Josef Kaplan is the author, most recently, of Poem Without Suffering (Wonder). His new book, Loser, is forthcoming from Les Figues Press in 2019.