(Roughly) Daily

… though that law can sometimes be less than obvious. Erica Klarreich reports on one creative mathematician’s efforts to help us learn…

In late January, Daniel Litt [pictured above] posed an innocent probability puzzle on the social media platform X (formerly known as Twitter) — and set a corner of the Twitterverse on fire.

Imagine, he wrote, that you have an urn filled with 100 balls, some red and some green. You can’t see inside; all you know is that someone determined the number of red balls by picking a number between zero and 100 from a hat. You reach into the urn and pull out a ball. It’s red. If you now pull out a second ball, is it more likely to be red or green (or are the two colors equally likely)?

Of the tens of thousands of people who voted on an answer to Litt’s problem, only about 22% chose correctly. (We’ll reveal the solution below, in case you want to think it over first.) In the months since, Litt, a mathematician at the University of Toronto, has continued to confound Twitter users with a series of probability puzzles about urns and coin tosses.

His posts have prompted lively online discussions among research mathematicians, computer scientists and economists — as well as philosophers, financiers, sports analysts and anonymous fans. Some joked that the puzzles were distracting them from their real work — “actively slowing down economic research,” as one economist put it. Others have posted papers exploring the puzzles’ mathematical ramifications.

Litt’s online project doesn’t just highlight the enduring allure of brainteasers. It also demonstrates the limits of our mathematical intuition, and the counterintuitive nature of probabilistic reasoning. As Litt wrote, there’s “nothing more exhilarating than posing a multiple-choice problem on which 50,000 people do substantially worse than random chance.”…

The answer to this puzzle, other puzzles, and Litt on what makes a great puzzle, and why simple probability questions can be so deceptively difficult: “Perplexing the Web, One Probability Puzzle at a Time,” from @EricaKlarreich in @QuantaMagazine.

Vaguely related (but also very interesting): “The Bookmaker,” via @annfriedman, who observes: “Leif Weatherby and Ben Recht on Nate Silver and the addiction to prediction: ‘Silver insists that viewing all decisions through this lens of gambling is the underappreciated characteristic of Very Successful People,’ they write. ‘But what Silver willfully ignores is that the successful players in this world aren’t the bettors. They are the bookies and casino owners—the house that never loses.'”

* Boethius, The Consolation of Philosophy

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As we contemplate chance, we might send confirmatory birthday greetings to Carl David Anderson; he was born on this date in 1905. An experimental physicist, he shared the 1936 Nobel Prize in Physics for his discovery (that’s to say, confirmation of the existence) of the positron, the first known particle of antimatter… which had been predicted by mathematician and physicist Paul Dirac, whose “Dirac Equation“– in part a product of its author’s application of probability theory– had predicted (among many other features of quantum theory as we know it) the existence of the particle (and antimatter).