Researchers have deciphered a mathematical equation devised by the late physicist Richard Feynman to solve the dilemma of when to stop searching for a better restaurant while on holiday. The study, published in the Proceedings of the National Academy of Sciences, reveals that Feynman’s approach can help optimise dining choices when the range of options is known.
Feynman’s interest in the problem was sparked during a lunch with his friend Ralph Leighton at a Thai restaurant in California in the 1970s. Leighton was debating whether to stick with his favourite ginger chicken or try a new dish. Feynman turned the issue into a mathematical problem, but his handwritten notes remained inscrutable for decades until the research team deciphered them.
According to Feynman’s solution, people should try a different restaurant each night until they find one that exceeds a certain quality threshold. This threshold declines more rapidly as the number of days left in the city decreases, reflecting the diminishing value of finding a great restaurant when there is less time to enjoy it. “If you have a long time to look, finding something amazing has a lot of value because you can go back many times,” said Prof Tom Griffiths of Princeton University, a co-author of the study.
The researchers also tested how people behave in such situations by recruiting 2,520 participants for an online task. Participants were asked to choose restaurants for each day of a stay in a city, with varying quality distributions. The team found that people used a simpler strategy than Feynman’s: they decreased their threshold linearly with the proportion of nights remaining. “It’s a little bit simpler than Feynman’s solution, but it actually turns out to be quite good,” said Griffiths.
The study highlights that the optimal strategy depends on the distribution of restaurant quality. In cities with many poor restaurants and a few gems, the threshold should start higher, encouraging longer exploration. Conversely, where most restaurants are of similar, above-average quality, the threshold is lower, making it not worth exploring for long.
