Richard Feynman, the late physicist and Nobel laureate, devised a mathematical solution to the dilemma of when to stop searching for a better restaurant while visiting a new city, researchers have revealed. The work, published in the Proceedings of the National Academy of Sciences, deciphers handwritten notes from the 1970s that remained inscrutable for decades.
According to Feynman's approach, diners should try a different restaurant each night until they find one that exceeds a declining threshold of quality. The threshold drops more rapidly as the number of remaining nights decreases, reflecting the diminishing value of exploration when there is less time to enjoy a discovery. “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.
The researchers also tested how people behave in practice, recruiting 2,520 participants for an online task. Participants were asked to choose restaurants for a stay of varying lengths, with the quality of options revealed upon selection. The team found that people intuitively used a simpler strategy: lowering 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,” Griffiths noted.
The study highlights that the optimal strategy depends on the distribution of restaurant quality. In cities with many poor options 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 less worthwhile to search extensively.
