How a Richard Feynman formula could explain your dining habits in a new city

June 2, 2026 report How a Richard Feynman formula could explain your dining habits in a new city Paul Arnold Author Gaby Clark Scientific Editor Robert Egan Associate Editor One of the dilemmas facing anyone in a new and unfamiliar city is where to dine out. You might consult guides, speak to locals, check reviews, and ultimately, try your luck. But if you're there for a while, at some point you're going to be asking yourself whether to visit new eateries or stick to the ones you've already tried and liked. Feynman's napkin notes This is known as a classic explore-exploit dilemma and was something the late physicist and Nobel laureate Richard Feynman pondered during a restaurant meal with a friend in the 1970s. His companion was debating whether to order his favorite dish or try something new. Feynman turned the question into a math problem and solved it there and then, scribbling his workings on pieces of paper. Feynman, who died in 1988, never published his solution, but researchers came across his handwritten notes and not only deciphered them, but also put the solution to the test. Details of their research are published in the journal Proceedings of the National Academy of Sciences. Instead of focusing on which dish to choose, the researchers turned the problem into choosing between different restaurants. According to Feynman's approach, people should try somewhere new every night until they find one that exceeds a certain quality threshold. However, this threshold is not fixed and declines as the number of nights remaining in a city decreases. In other words, you may have high standards at the start of your trip, but you will lower them as you are near the end. The scientists also expanded the math to see how the strategy changes under different conditions, such as whether a city has mostly mediocre establishments or whether exceptionally good restaurants are relatively common or rare. How we actually choose To see how human behavior stacks up against the equations, the researchers conducted an online experiment with 2,520 participants. Each person was given a virtual version of the restaurant dilemma. The team found that, rather than following Feynman's optimal threshold, which changes nonlinearly over time, participants used thresholds that declined linearly with the proportion of nights remaining, as the study authors noted in their paper. "We definitively show that people do indeed use linearly decreasing thresholds for versions of the Feynman problem defined with different distributions over options, and that these linear functions share an identical slope but vary their intercepts in a manner consistent with the optimal solutions." Although this strategy differed from Feynman's, the results were nearly as effective as his solution. "People thus seem to follow a simple strategy that can be easily modified to accommodate differences in both total nights and distribution, allowing them to come close to optimal performance while minimizing cognitive effort." Written for you by our author Paul Arnold, edited by Gaby Clark, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive. If this reporting matters to you, please consider a donation (especially monthly). You'll get an ad-free account as a thank-you. Publication details Brian Christian et al, Resolving Feynman's restaurant problem reveals optimal solutions and human strategies, Proceedings of the National Academy of Sciences (2026). DOI: 10.1073/pnas.2509612123 Journal information: Proceedings of the National Academy of Sciences © 2026 Science X Network