I remember being enraptured by David Copperfield’s television specials as a child, but neither the larger-than-life illusions nor perfectly coiffed hair has remained as vivid in my memory as his interactive tricks. These illusions, with use of props like a deck of cards or even the TV screen itself, seemed like an impossible shattering of the fourth wall: a magician reaching into my quiet living room to create something amazing. David would ask me to pick a card from my own deck, or trace my finger on the screen, and he’d reach out and solve it as if he were in the room. As an adult, it’s clear enough that these were essentially elaborate logic puzzles, but that doesn’t make the feat any less impressive. Instead of a magical effect, the beauty is in the meticulousness of creating it.

“These became so popular,” Copperfield said in a commentary on one of his most famous interactive tricks. “You know, we’d spend all this time and money and choreography and lighting and writing on other pieces, and these very calculated and tested interactive things were the pieces that people remembered the next day. So it’s not like we didn’t work hard on them but the impact these had really was remarkable to us.”

In the same commentary, Copperfield claims that his organization consulted with the television data firm Nielsen and found that 90% of the audience participated in the interactive tricks. But when Copperfield said these tricks were calculated, he meant it very literally.

“All of them come back to some sort of mathematical calculation,” magician Kevin Spencer told GeniiOnline. “All of these interactive effects are taking these calculations and using them in a way that’s surprising and interesting. I think because there’s multiple steps to them, it’s much more difficult for the audience to go back to recreate it. You could DVR or, at the time, tape it, and go back and look at it and try multiple possibilities.”

To dissect the puzzle of interactive magic, I did just that with Copperfield’s famous destination trick. In it, he presents a clock-like grid and has the participant choose a number between five and 15, and then moves back and forth a few times, ultimately landing on the Moon at the 10 o’clock position. Unbeknownst to the audience, the trick actually converges every participant into one space relatively early.

The first move begins from outside the clock face, adding three extra spaces just for the first move. Since the first move is to pick a number between five and 15, this effectively hides the similarity to a clock face from the beginning. The trick would be the same if it started from the 12-o’clock position and told you to pick a number between two and 12, but by adding a few extraneous spaces that are quickly removed after the first instruction, Copperfield is able to pick a range that seems less tied to the familiar, even numbers of a clock. Either way, the result is the same: players can land anywhere but the Clouds at 11 o’clock. Then, by having the viewer repeat their previous move in reverse, everyone will land on the same piece: the City at the 3 o’clock position. From there, Copperfield simply eliminates a few pieces on each side, seemingly at random, and instructs viewers to move four times in either direction. Due to the precise elimination of moves, and the fact that by this point all participants have converged in one space, they’ll always land on the Moon for the final reveal.

Crucially, the instructions tell the viewers at home to pick one volunteer to participate. If two or more people did it at once, they would easily see the paths converge on the second move.

That isn’t to say that interactive tricks can never benefit from multiple participants, however. Spencer said he did a similar illusion called Final Destination in his stage show, with an audience of participants keeping track in their heads instead of tracing their movements with a finger. In a live setting, the reveal was two-fold: first that he knew which landmark you had landed on, and then as the audience of up to 3,500 people realized they all did it together despite their wildly varying choices.

“You had this double response,” he said. “One you had a singular response from them, ‘oh he knew I was going to be in Rome,’ and then a second wave where they look around the theater, and that’s when it’s really powerful.”

To give another example, Spencer walked me through a brief interactive card trick over the phone. And while I could dissect the steps somewhat, he was sure to throw in several extraneous steps: putting some cards to the side, tossing one away, and so on. These steps, which didn’t actually impact the outcome of the trick, were interwoven with the ones that did, which helps hide the puzzle even more.

“How do you take these things and make them appear magical, this thing that’s very logical?” Spencer said. “It’s because of those diversions, the impossibility of what you’re asking them to do.”

Copperfield’s destination illusion was tightly timed for a television audience, and as a result didn’t include any extraneous steps. It’s easy to see how a live version could add more moves to obscure the effect, and interactive tricks often have at least a few meaningless pieces added to the calculations for just this reason. In a way, the Copperfield illusion is the perfect mousetrap of the interactive trick: the exact minimum parts needed to achieve the goal.

Inversely, the moves the magician makes to limit your options serve two crucial purposes. The first is the function of the logic puzzle itself, to limit options and narrow the possibilities so that players are forced to move in certain ways. The second, though, is a bit of magical flourish found across all types of tricks. By exposing which pieces of the game board aren’t in use, the magician adds a slow-burn of constant delightful surprise.

“In magic we call those proofs,” Spencer said. “The more proofs you can have as part of a trick, the more incredible it is, the more impossible it is. With each proof it becomes more and more powerful.”

In a more traditional illusion, the proof may be planted to make the trick seem more visceral or even life-threatening. A sword box might open midway through to show the assistant’s side still in the box, or a giant fan might shred a stack of newspaper to prove the blades are deadly-sharp. The more times a magician can anticipate your skepticism and take steps to debunk it, the more astounding the final effect. A participant in an interactive trick might be trying to puzzle out the possible moves, when the magician reveals that some of those options aren’t even on the table.

Meanwhile, interactive magic leaves room for lots of different stage personas. While Copperfield played up the mentalism aspect by suggesting he was “finding” the participant through miles of separation, Spencer pointed out that another magician could suggest he’s actually controlling your movements with the power of his mind. On the other end of the spectrum, a magician could casually point out your location with a “shucks, isn’t that neat” charming tone.

“There are a lot of magicians but there are only a few magic tricks,” Spencer said. “What each magician brings to it with their own personality is what makes it uniquely their own. We all draw from the same magic catalog and it’s what you do that lets you own that trick. The patter, what you’re going to say, the moves you’re going to make.”

Copperfield, ever the showman, acknowledged the logic puzzle aspect of the trick in his commentary, but kept a little of his mystical edge intact. It wasn’t the math that made the magic, he claimed. It was his precise tuning of every aspect of the instructions.

“To make that work we had to test it, and we tested it everywhere–inner city schools, rich areas, poor areas, we tested in other languages,” he said in the commentary. “We found when we were testing this all around, the intonation of my voice, how fast I gave instructions, how I said it, if I changed one word it wouldn’t work. But if I said it a particular way with a particular tone of voice, the illusion would work, so it had to be just, exactly perfect.”

Spencer suggested that the popularity of interactive magic has helped feed the advent of street and close-up magic, as a new generation uses the same tools to replicate the effect on a more personal level.

“People began seeing these big audience responses to these interactive tricks. I think David Blaine was the first one to kind of key in on this,” Spencer said. “So let’s take this to the street and get this from a one-on-one or two-on-one perspective, and that feeds back into the stage performer. Maybe it’s more circular than it is evolutionary.”