Magic Math Unleashed

Ryan Normandin
June 06, 2017

Today, I’m doing something a little different. I’m reaching into my mailbag to answer the Magic questions that readers are dying to know -- and I’m doing it with math. So brace yourself; this content is going to be pretty graphic. Let’s crunch some numbers!

Q: How good are people at evaluating cards during spoiler season?

            To answer this question, I first broke it down the way you might expect; I took every card I could find and created a scatterplot of actual playability (measured by the expected number of copies of the card in the average deck during the time it was legal in Standard) versus the average prediction of playability made by the card evaluation experts on Reddit. We then look for a trend.



            Strangely enough, it seems that there is absolutely no relationship between the predicted playability of a card and its actual performance.


TL;DR Answer: On average, people are about as good at card evaluation as they are at relationships – they try to make educated guesses based on previous, incorrect guesses until they eventually blunder their way into the right answer. Then, they take all the credit and claim that they knew what they were doing all along, only to get it wrong again three months later.


Q: How can I optimize my Marvel spins?

Once Marvel became the deck to beat post-Felidar Guardian ban, more and more people began to notice they were getting tired of Standard. Surprisingly (to naïve, non-Karstens), this was prominent especially among Marvel players themselves! However, observant players will note that this trend began with the release of Kaladesh, and the popularization of energy-based decks in particular. First it was RG Marvel cheating out Emrakul, then Copy Cat in an energy shell, and now back to Marvel.


But here’s the thing; everyone thinks they’re tired of Standard because of broken cards that weren’t developed properly, but they’re forgetting Ryan’s Golden Rule of Statistics: Correlation Shall Not Imply Causation. Do people hate Standard? Sure. Does this correlate perfectly with the printing of stupid cards? Absolutely. But it also correlates with my friend Joey getting with Vicki, which happened the day KLD was released. He broke up with her on the day of the cat ban, then got back with her again a week later. The correlation is undeniable, but Joey and Vicki rubbing their romance and happiness in my face certainly isn’t making me hate Standard – it’s only making me hate them.

But there’s one more correlation which I will try to show is, in fact, causal - the popularity of the energy mechanic. And if you think back to high school physics, you should remember Ryan’s Golden Rule of Physics: Energy Cannot be Created or Destroyed.

Whenever you add energy to your energy reserve, where do you think it’s coming from? You’re not creating it, as physics doesn’t let you do that! It must be coming from you! This is why everyone is getting so tired of Standard; they’re losing all their energy, becoming literally fatigued from playing games of Standard.

In a previous article, I advocated running some magic number of “hits” for Marvel in your deck, but honestly, that’s nonsense. If you want to have better hits than your opponent, you need to take advantage of the Law of Conservation of Energy. When you spin Marvel, that energy is not being destroyed; it’s simply changing forms, from a couple of dice on the table to an indestructible 10/10 on Turn 4 that eats your opponent’s library in two attacks. That, folks, is why physics is such a beautiful subject.

All of this is to say that if you want better hits than your opponent, you need to cheat by throwing in a little bit of extra energy when you spin Marvel. People who simply tap the card and, with a sigh of frustration at the stale, non-interactive, high-variance format that Standard has become, look through the top six cards of their library for a hit are going to hit Puzzleknots. Every time. People who spin with more enthusiasm are subtly inputting additional energy, making it more likely that they’ll hit some of that sweet, sweet 10/10 goodness. To spin Marvel optimally, you really need to spin it. One way to do this is by taking advantage of torque. Torque is, to use a scientific term, the spinny version of force. It is given by:

The fancy “t” on the side is torque, the “r” is the distance between the point of force and the point of rotation, and the “F” is the strength of the force. To summarize how to implement this equation to maximize your Marvel spins, you want to flick your Aetherworks Marvel very, very hard in the very, very corner of the card. I personally guarantee that if you do this, the top six cards of your library will positively leap off the top of your deck onto the battlefield. Those six cards, by the way, will be five Ulamogs and an Emrakul, the Promised End; if you’re going to use Marvel to screw the rules of Magic, you may as well ignore the rest of the game’s rules as well.

TL;DR Answer: Flick your Marvel into your opponent’s face. If you’re bad at flicking, get a fidget spinner; plenty of torque there!

Q: How do I fit all my playmats in a drawer?

This is a problem that plagues all Magic players, given sufficient time, as shown below.

You can see the exponential increase in playmats over time as players attend more and more events. Then, of course, you see the breaking point, when players snap, burning all but 2 ± 1 of their playmats and never again bringing one home with them. The burning of playmats is, of course, something we want to prevent. Luckily, a blend of math and physics can get us out of this tight conundrum!

First, you’ll note that I ignored significant figures; that is because I’m a badass. Second, this is a great size for your smushed playmat; it’s only slightly smaller than the upper limit for the size of quarks and electrons! And hey, you know that spring cleaning you’ve been putting off? With a black hole in your drawer, you won’t even have a house to clean! You’re welcome.

TL;DR Answer: Crush your playmat into a black hole.

Q: What’s the probability that, in a given year, a straight, white male writer will try to write an article about women in Magic and fail miserably?

Hmmm, this is a tricky one. First, we need demographic information on the writers that the major MTG content-producing websites choose to employ. After a quick scan of some webpages…

Intriguing, intriguing. And of those male writers, how many are white? Another quick scan…

Wow, fascinating stuff! Even if we account for the fact that my data-gathering method was skimming the front pages of a couple of websites, I’ve gotta say that this doesn’t look great. There are really two schools of thought on how to approach the problem from here: we can either go a couple levels deeper, divvy this problem up into a set of independent random variables, and check when all conditions become satisfied, or… well… we can go with the gut. And I know that you guys rely on me for hard-hitting statistical analysis that you can’t really get anywhere else, but those pie charts that I made and tweaked for maximum dramatic effect are pretty convincing; I’m going with my gut! In any given year, the odds of a privileged white dude shooting themselves in the foot with a preachy article absolving them of any responsibility are pretty damn good!

TL;DR Answer: Pretty damn good.


Isn’t math great? That’s all I have time for today, but I certainly had a fun time reading all of your questions and putting this together. If you didn’t see your question here, it could be because

  1. your question did not allow for me to demonstrate my expertise with the mathematical arts.
  2. you made fun of me.
  3. your name was Joey or Vicki. Sorry, but they’ve really been getting on my nerves recently.
  4. your question was stupid. There totally is a thing as a stupid question by the way. “I can’t find my keys, do you know where they are?” absolutely falls into that category and is not something you submit to a mailbag article. (They fell in the flowerpot. The blue one, by the ornamental cat sculpture next to your TV.)

If your question does not satisfy any of the four conditions above, then submit again next time! Until then, may all the random variables you encounter be Gaussian!