When visiting a new city, deciding when to stop searching for a better restaurant can be tricky. Now researchers have uncovered a mathematical equation devised by physicist Richard Feynman that addresses this conundrum, at least when the range of options is known.
Professor Tom Griffiths of Princeton University, a co-author of the study, explained that the problem involves balancing exploration and exploitation: “The value of exploring decreases the opportunities you’re going to have to make use of that information.” The team notes the dilemma is a form of “stopping problem,” with the added feature that one can return to a previous restaurant.
Feynman’s interest was sparked by a lunch with his friend Ralph Leighton at a Thai restaurant in California in the 1970s. Leighton debated whether to stick with his favourite meal or try something new. Feynman turned the issue into a mathematical problem, but his handwritten notes remained inscrutable for decades until the researchers deciphered them.
According to Feynman’s solution, people should try a different restaurant each night until they find one exceeding a threshold that reflects desired quality. This threshold declines more rapidly as the number of days left reduces, meaning less motivation to hunt for an amazing spot when time is short. The approach assumes equal possibility of finding any restaurant within a fixed quality range.
The researchers also explored other scenarios. If most restaurants are awful with a few gems, the threshold starts higher, making it worth exploring longer. If most are of similar above-average quality, the threshold is lower. In tests with 2,520 participants, people decreased their threshold linearly with remaining nights rather than following Feynman’s exact curve, but this simpler strategy still worked well.
