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It's the class in school that you either loved or hated, most likely the latter. We're at the point where math anxiety is a common condition that can be so severe that being presented with a math problem triggers the same area in the brain as physical pain.
Countless articles are written about how best to teach math, and while I won't be writing about that pedagogical debate, I do think it gets to an issue that Magic players can learn about: the nature of mathematics.
What is math? What is it well-suited for and what is it not?
We all like to think of Magic as a highly mathematical game. After all, Richard Garfield holds a doctorate in the field. And when we describe Magic as such, it's more than just the basic arithmetic we all do keeping track of life totals and figuring out combat. At a fundamental level, mathematical tools help us to develop the theoretical underpinnings of the game as we advance our knowledge of Magic.
I firmly believe that my background in mathematics was the single greatest contributor to my leveling up from PTQ grinder to someone who makes their living off the game, and there are many other high-level players who rely on a similar educational background, all the way up to Hall of Fame member Frank Karsten.
But again, the way in which math has helped me isn't in an ability to calculate my odds of drawing my third land on time or any other calculation, which strikes at the root of the problem of math anxiety. The common view of mathematics is that it's based in numbers and calculation. Whether you're adding numbers together or evaluating a complicated probability function, that's what people think about when they think of math, so being "good at math" gets turned into "being able to carry out those calculations quickly and accurately."
A Small Piece of the Pi
This is a superficial understanding of a subject that has so much more to offer and is much more flexible than most people realize. If this were all math is, then it would not be a very powerful tool for Magic players because there's a limit to what we can calculate efficiently, especially if you're trying to calculate something in the middle of a game.
At its heart, mathematics is an exercise in logical reasoning and problem solving. You make certain assumptions and attempt to deduce conclusions from those assumptions. This definition is necessarily vague, but in that vagueness lies great power. In math, you get to make the rules that define the universe in which you want to live. If you want 3+3 to equal 0, then you can make it so and see what happens. You have total control. But with great power comes great responsibility. That is to say, the trick in doing good math is in making assumptions that are reasonable and drawing conclusions that are useful in solving your problem.
In many cases, reasonable assumptions are those that make your invented universe align with the real world so that we may put the conclusions to some practical use. The problem lies in how messy the real world is. Magic exemplifies this quite well with how many variables there are to account for. The questions that we want to answer, such as "How many lands is optimal for Temur Energy?" or "What is the best mana curve for Ramunap Red?" are very complicated, and the path to a solution is not at all clear. There is no simple formula that you can evaluate to get a clear answer to them. But this does not mean that mathematics has nothing to offer when we answer such questions.
Every theorem or formula in mathematics is a tool and any tool is designed to carry out a specific job. It's our job to pick the correct tool for the job at hand. If you try to use a hammer to open a glass bottle and end up smashing the bottle open, then it's not the hammer's fault. Similarly, if you try to use the Pythagorean Theorem to calculate the side lengths of a non-right triangle, you're going to come out with the wrong answer.