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Hate math? You’ll still love this cornucopia of simple-yet-seductive math games

Amusing hand-drawn instructions for pen-and-paper game.
Enlarge / Ultimate Tic-Tac-Toe is at heart a game of fractal structure, per math teacher Ben Orlin, author of Math Games with Bad Drawings. Players must balance two levels, an element that requires them to “Think globally, act locally.”

Ben Orlin

In 1974, a geneticist named Marsha Jean Falco devised an ingenious research tool to help determine whether epilepsy in dogs was an inherited trait. She drew a series of symbols on index cards, where each card represented a dog and each symbol represented a DNA sequence, to create her own coding system. But as she shuffled and reshuffled the index cards over time, she began seeing the deck in terms of pure abstract patterns and combinations.

Eventually her personal coding system became the game of Set—just one of the many math-y games included in math teacher and bestselling author Ben Orlin’s new book, Math Games with Bad Drawings. (You can read an excerpt and try your hand at a game of Quantum Go Fish here.)

Orlin’s first book, Math with Bad Drawings, after his blog of the same name, was published in 2018. It included such highlights as placing a discussion of the correlation coefficient and “Anscombe’s Quartet” into the world of Harry Potter and arguing that building the Death Star in the shape of a sphere may not have been the Galatic Empire’s wisest move. We declared it “a great, entertaining read for neophytes and math fans alike, because Orlin excels at finding novel ways to connect the math to real-world problems—or in the case of the Death Star, to problems in fictional worlds.”

In 2019, Orlin took on the challenge of conveying the usefulness and beauty of calculus with tall tales, witty asides, and even more bad drawings in Change Is the Only Constant: The Wisdom of Calculus in a Madcap World. That book is a colorful collection of 28 mathematical tales connecting concepts in calculus to art, literature, and all manner of things human beings grapple with on a daily basis. So a third book collecting a wide variety of math-y games was a natural progression—illustrated, as always, with Orlin’s own distinctively bad drawings.

Math Games with Bad Drawings isn’t really designed to be read cover to cover; rather, readers can browse randomly at their leisure to find the games best suited to their particular tastes and skills. (Wordle fans should enjoy Jotto, a similar logic-oriented word game invented in 1955.) There are 75.25 games in total, at least by Orlin’s idiosyncratic count. “I wanted a non-integer number of games,” he told Ars. Technically, there are around 51 full games, plus several he counted as 11/12s, because, even though they are full games, they didn’t merit more than a brief mention in the book. Variations of existing games counted as one-quarter games, while very tiny rule variations counted as 1/57th of a game. Add it all up and you get 75.25.

<em>Bullseyes and Close Calls</em> is a classic code-breaking game, where players must guess their opponent's secret number before their opponent does. It was hugely popular in the 1970s under the trade name <em>Mastermind</em>.
Enlarge / Bullseyes and Close Calls is a classic code-breaking game, where players must guess their opponent’s secret number before their opponent does. It was hugely popular in the 1970s under the trade name Mastermind.

Ben Orlin

The games can all be played with just a few common household items: pencil and paper, coins, colored pens, standard dice, Goldfish crackers, paper clips, your hands, and occasionally an Internet connection. There are five sections focused on five different categories of games: spatial games, number games, combination games, games of risk and reward, and information games. For each, Orlin outlines the basic rules of play, a few “tasting notes” about the subtleties of the gameplay, where the game came from, and why it matters. He also lists any variations and related games.

For instance, Ultimate Tic-Tac-Toe involves two players navigating nine smaller (“local”) tic-tac-toe boards in a 3×3 grid, and the choices made determine the positions on a larger (“global”) board. Quantum Tic-Tac-Toe is even trickier, whereby players must place their “entangled particles” (Xs or Os) in such a way that when the “wave function” collapses, the winning player will be left with three in a row. (The wave function collapses when various pairs of boxes form an “entangled loop”: Box 1 is entangled with Box 2, which is entangled with Box 3, which is entangled with Box 1.)

“I tend to like the party games, the ones that actually work well for a group, more than the very intricate two-player, abstract strategy,” said Orlin, although he admits to having a soft spot for Ultimate Tic-Tac-Toe, the game that inspired this book. Among his favorites is Sequencium, a game of pure strategy, which, like chess, tends to favor the player who moves first.

“You’ve got this little grid, and you start with some numbers coming out of the corner, and then you just keep adding one to the number and putting it into the next box,” said Orlin. “You’re trying to grow this little vine of numbers as you move around the board. It’s a very simple ruleset but makes for a really surprisingly rich game.” Bonus: Per Orlin, there’s one surefire way for the second player to ensure a draw. Simply rotate the board 180 degrees and copy the first player’s moves symmetrically.

Orlin is already hard at work on his next book: How to Speak Math: A Guide to the Universal Language for Native and Non-Native Speakers. Unlike his prior books, where he carefully avoided most mathematical notation, this one will teach readers how to read and interpret mathematical symbols, proofs, and mathematical diagrams. “Mathematical notation is off-putting for a lot of people, and you can discuss what is exciting and intellectually rich about mathematics without getting into the notation,” he said. “But there are also certain things about math that you can only access through that notation.”

Ars spoke with Orlin to learn more.

Math teacher Ben Orlin is the author of a new book (his third), <em>Math Games with Bad Drawings</em>.
Enlarge / Math teacher Ben Orlin is the author of a new book (his third), Math Games with Bad Drawings.

Rayleen Tritt

Ars Technica: Why math games?

Ben Orlin: There’s this thing that math does for people who enjoy math. You hear a setup to a problem and you just get pulled in. “Ooh, what is that going to create? Those choices of axioms or assumptions, what is going to emerge from that?” But other people don’t respond to math that way. You give them the setup of a problem, and they shrug their shoulders. It’s not an exciting prompt.

But most people want to try games. They want to see what happens when you start playing around in the space created by these rules. So I wanted to give people the experience of that kind of thinking, when you get into a ruleset and start messing around and seeing what possibilities it allows. Where do you have freedom, where are you constrained? It’s all very logical thinking and to me, that’s a very mathematical kind of thinking. Games are a great backdoor into that thinking because people just intrinsically enjoy it. With a more austere or abstract mathematical setting, they might not dive in as readily.

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