A scribble on paper at a Thai restaurant has turned out to be right.
Late US physicist Richard Feynman once responded to a friend’s dinner dilemma with a mathematical answer: when should you stop trying new dishes and stick with your favourite? Behavioural scientists have now revisited that solution and found that Feynman’s strategy was optimal.
The study was published in the Proceedings of the National Academy of Sciences on 1 June. It also found that people tend to choose meals in ways that closely match Feynman’s maths.
Behavioural scientist Shoham Choshen-Hillel at the Hebrew University of Jerusalem said the authors had written a “super creative article”.
“The restaurant example stands in for decisions in many settings,” she said.
The story dates back to the late 1970s, when Feynman, a Nobel prizewinning physicist at the California Institute of Technology in Pasadena, and his friend Ralph Leighton regularly visited a Thai restaurant in Glendale.
Leighton wondered if he should order ginger chicken, his favourite dish, or keep exploring the menu.
Feynman started writing and said he had a mathematical solution. In his simplified model, he worked out a threshold, a number of visits after which Leighton’s rational choice would be to always order his favourite dish.
The problem sits in decision theory, a field between economics and psychology that studies strategies in one-person games. It is also part of a broader group of decision theory questions known as stopping problems, which ask when someone should accept the option in front of them or keep searching.
Leighton kept Feynman’s notes and later partially transcribed the handwriting. He described his interpretation in an article he posted online in the early 2000s.
In 2013, Tom Griffiths, a cognitive scientist at Princeton University in New Jersey, became interested in the question while researching a book with collaborator Brian Christian, a computer scientist and cognitive scientist. Griffiths then fully transcribed Feynman’s notes for the first time.
Christian, now at the University of California, Berkeley, said the question then sat untouched for nearly another decade until the pair returned to it in 2021.
“We’d understood the meaning of Feynman’s notes, but there was all this work to be done,” he said.
The researchers found that Feynman had indeed reached the best solution. They also solved a generalized version of the problem.
With co-author Evan Russek, a cognitive psychologist at the City University of New York, the team then tested how closely people’s choices matched the maths.
They turned the restaurant problem into an online game and recruited 2,520 participants.
Participants were asked to imagine they were in a new city for between one and four weeks and had to pick a restaurant each night. They earned points based on the quality of the restaurant they chose, on a scale from 1 to 100, and were told to maximize their total score.
As the end of the visit got closer, participants became less willing to risk trying new restaurants. The researchers said that pattern followed logic similar to Feynman’s optimal formula.
The participants did not calculate the mathematical solution themselves, which includes a formula with square roots, but their behaviour came very close to it.
“The fact that, even in this simplified setting, they still find that people behave in a quite consistent, and pretty effective, way is quite impressive,” Choshen-Hillel said.
She said the problem could have uses in economics and marketing, but did not fully capture how people act in a restaurant.
Christian said one missing factor was boredom, because the optimal strategy in the model is to settle on one dish permanently. In real life, he said, someone might choose the same dish every second visit and keep trying other menu items on the remaining visits.
But the problem “does distil to its essential form this fundamental tension very familiar in every day: the decision between doing your favourite thing and trying something new,” he said.
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