The math of choosing a restaurant meal is revealed in Richard Feynman’s notes

A famed physicist’s scribbles reveal the answer to a quintessential dilemma: When dining out, is it better to stick with an old favorite, or try something new?

Nobel Prize–winning physicist Richard Feynman, known for his love of problem-solving, pondered this question with a lunch companion in the 1970s. Feynman turned this into a math problem and solved it on the spot — in his inscrutable handwriting.

Feynman, who died in 1988, never formally published his solution. It remained undeciphered until a team of researchers recognized, in Feynman’s scrawl, a solution to a class of mathematical questions known as stopping problems. That allowed them to make sense of the scribbles. Feynman — living up to his reputation — found the optimal solution, computational cognitive scientist Brian Christian and colleagues report in the June 2 Proceedings of the National Academy of Sciences.

Feynman framed the problem around choosing dishes at a single restaurant; Christian and colleagues recast it as choosing among multiple restaurants, though the underlying math is the same. Each restaurant is assigned a score to indicate its quality. The aim is to maximize the score added up over a given number of nights of dining.

Feynman found an equation for a threshold against which you compare the best restaurant you’ve tried so far. Each night, you check your favorite against it. If your fave scores above, return to it for the remaining nights; if not, try somewhere new. The threshold isn’t fixed: It starts high and falls as your remaining nights dwindle. Early on, with many nights left to enjoy a great find, it pays to hold out for something extraordinary. By your last night, you have little to gain from searching, so you should settle for anything better than average.

Quality also matters. Feynman had assumed that a given dish (or restaurant) is equally likely to be good as it is bad or mediocre. Christian and colleagues found that the equation for the threshold changed if, for example, most restaurants in an area are crummy but a few have food that is downright delectable.

To test how people actually decide, the researchers surveyed more than 2,500 people online. Participants didn’t use the ideal strategy. But they used a simpler one that approximated it — resulting in similar scores without the full mental gymnastics.

People don’t always do the optimal thing, says Christian, of the University of California, Berkeley. “They use these heuristics and shortcuts. But the heuristics that they use are strikingly, or uncannily, good.”