Cindy Lawrence, the director of the National Museum of Mathematics, in New York, put on her special Möbius-strip earrings when she was getting ready for a recent evening of math dinner theatre. The star of the show would be Peter Winkler, a Dartmouth mathematics professor and formerly MoMath’s Distinguished Visiting Professor of Public Engagement. Winkler has been leading his intimate “Probability and Intuition” sessions (as the dinner theatre is called) since 2019.
Winkler, who has a bushy salt-and-pepper mustache and sounds a little like Groucho Marx, is the author of three volumes of math puzzles. He picked up Lawrence at her apartment, before heading to meet their math-dinner guests at an Italian restaurant near Gramercy Park. “My mother was really good with crossword puzzles,” he said. “My grandmother was a Scrabble genius. I’m told she was sucked into a match with the mayor of Miami.” He went on, “I was the math kid.”
“You shouldn’t look sheepish when you say that!” Lawrence chimed in. “You should say it with some pride!”
At the restaurant, seated inside a sidewalk enclosure, Lawrence pulled from a tote bag a small whiteboard with a stand, along with several clipboards, each holding paper and a pencil—MoMath party favors. Six guests showed up, three with backgrounds in finance. “I’m really struggling with this week’s puzzle,” Saul Rosenthal, the president of Oxford Capital Funds, said. He was referring to the weekly “Mind Bender” that Winkler sends out, through MoMath, to thousands of puzzlers. That week’s puzzle: On average, how many cards does it take to get to a jack in a shuffled deck of fifty-two cards? “A bunch of guys in my office are working on it,” Rosenthal said.
Marilyn Simons, who has a Ph.D. in economics, said that her husband, Jim, a financier and a former mathematician, doesn’t like puzzles: “He says that if he works that hard he wants to get a theorem out of it.”
Winkler began the evening’s program. The first course of math, delivered during the first course of dinner (a scattering of salads), was a statistics starter called Simpson’s paradox, which explains how apparent biases in large samples can disappear in smaller ones. A famous example: For the University of California at Berkeley’s graduate programs in 1975, over all, men were admitted at a higher rate than women, but, program by program, women were admitted at a higher rate.
“I think that, to a lot of us who even think we know statistics, the way we process statistics is not deeply informed,” Simons said.
Winkler nodded and said, “Tell the story of the statistician who drowned in a river whose average depth was only two inches.” He laughed at his joke.
When the entrées came, Winkler moved on to puzzles: What’s the best way to use two coin tosses to determine which of two coins, one fair and one “biased,” is fair? And how can a biased coin be repurposed to produce a fair bet? (Hint: You can use sequences of flips to redefine a “toss”—it’s called “von Neumann’s trick.”) What’s the first odd number in the dictionary? (Hint: It starts with “eight.”)
Winkler let loose with the last official mind bender, a gambling thought experiment involving a fictitious couple named Alice and Bob, who are famous in math circles. Each of them has a biased coin—fifty-one-per-cent chance of heads, forty-nine-per-cent chance of tails. They each start with a hundred dollars, flipping the coin and betting against the bank on the outcome. Alice calls heads every time; Bob calls tails. The puzzle: Given that they both go broke, which one is more likely to have gone broke first?
Rosenthal looked thoughtful. “Every question that we were asked tonight,” he said, “the answer is never what it seems.”
Most of the diners guessed Bob, but the correct answer was Alice. John Tierney, a former Times columnist and a math buff (he once wrote that recreational mathematics was “oxymoronic”), thought it over. “But, the longer Alice plays, the less likely she is to go broke,” he said.
Winkler nodded and launched into a fuller explanation. “What’s a good example?” he said. “O.K.! What’s the probability that this dinner goes past eleven o’clock?” The attendees, whose eyes had started to glaze over, laughed. Winkler took the hint and decided to call it a night. ♦