What makes a good magic trick? (Part 1)

Earlier, my response to the question, "Is magic an art?" was "What an incredibly stupid question!" It may come as a surprise that I think "What makes a good magic trick?" is actually a very useful, practical question. If the twentieth century taught us anything it was that science (more specifically the methodology developed by science) is capable of measuring and quantifying many things that were previously thought to be unknowable.

I am skeptical that we would be able to find a single way to measure the quality of a trick and that any definition will have limited applicability. Ultimately, the best outcome we could expect would be "What is a good trick for X" where good and bad will change based on the performer, the audience and the environment. (This still allows me to retain the right to say, "What is the best version of Triumph?" is an incredibly stupid question.)

In this part, I want to describe one metric which can be used to measure the quality of a trick. I begin here mainly out of convenience. This one is the easiest to measure in practical terms.

Deceptiveness

After some trial and error, I propose a way to numerically measure the deceptiveness of a trick.

daum_equation_1367733363451

Where is the deceptiveness of the trick and p is the proportion of the population Φ who are fooled by a trick. It has three important properties that make it a viable candidate.

  1. It is increasing over its entire domain (more people fooled always means more deceptive)
  2. Its D-intercept is zero (if no one is fooled, the trick has a deceptiveness of zero)
  3. It has a vertical asymptote when p = 1 (the interpretation is either that a trick that fools everyone is infinitely deceptive or that it is practically impossible to fool everyone since at the very least, the performer has to know how the trick works.

Finding the inverse also gives some insight into making tricks more deceptive.

Solving for gives:

daum_equation_1367733279735

Even though is entirely an abstract notion at this point, it has an upper bound of p = 1 so that no amount of deceptiveness will ever fool more than 100% of the population.

Also note that is non-linear. So increasing from 0.95 to 0.97 requires D to approximately double. That's a lot of work to fool an extra 2 people out of a hundred.

Differentiating gives

daum_equation_1367733148229

So as D becomes large (you craft a better trick), further incremental increases in deceptiveness produce lower and lower results. This problem of diminishing returns is easy to verify through experience.

This leaves one very important question that should have been answered at the outset: What is Φ?

In his book Proving History, Dr. Richard Carrier (who looks  a lot like David Ben... go figure) uses Bayes' Theorem to reduce a rather muddy estimate of probability to something (more) concrete by reducing it to a set of simpler probabilities that are easier to establish and less controversial.

Similarly, I think that most debates about whether or not a certain trick is deceptive, are really arguments over who belongs in Φ. It doesn't matter what fraction of people in Φ are deceived by a trick, if none of those people are in the room when you perform, then you fail. So is really situation specific. This gets more confusing because the person you are having this debate will be a magician and can't represent Φ in any reasonable way.

There is also an issue that certain methods can be recognized by those familiar with them, such as the tell-tale sign of an Elmsley count or an illusion base. So in front of certain audiences, using these techniques reduces p.[1]

There are two approaches which both have merit. The first is a brute force approach based on large numbers. Behind it is the fact that magicians (from lifelong devotees to occasional visitors to magic shops)  make up such a small proportion of the population as a whole, it's most effective to treat them as though they didn't exist. In other words, to pretend, to a first order approximation that magicians don't exist. As an empirical calculation, I'm sure it wouldn't be that difficult to support.

This is extremely effective for practical purposes. Because even tricks which are considered banal, like the a thumb tip silk vanish would have p > 0.75 and certain modern classics like the Invisible Deck would easily have p > 0.95. Therefore you can learn, invent or purchase a huge number of tricks with a relatively high and turn yourself into a magic machine.

In this mindset, you would never object to using an Elmsley count because the people it fools outnumber the people who recognize it by orders of magnitude.

This approach brings rise to artistic objections, because it places a lower upper bound on p. To get up as high as possible, you have to predict accurately who will be in Φ for a given performance. And once you have committed to pursuing an above average p, it makes sense to try and carefully dissect the contents of Φ. Will they have nieces or nephews who were interested in magic? Would they have had magic kits as children? What concepts would that make them familiar with?

With the spread of the internet and the accessibility of information, these artistic objections may also develop into practical problems.

It depends on the amount of work you are willing to put in.

[1] Darwin Ortiz wrote extensively on this in Strong Magic and I can think of dozens of examples off the top of my head.