Why in a new city we first look for the best restaurant before returning to a familiar one

It turns out that this is not just a household habit, but a mathematical problem. It was invented and solved back in the 1970s by physicist Richard Feynman, when his friend at lunch was choosing between his favourite dish and something new. For a long time, the solution remained in handwritten notes, but now researchers have deciphered them and checked how a similar problem is solved by ordinary people.

The work is published in Proceedings of the National Academy of Sciences.

The main idea is simple: while there are many days ahead, it's advantageous to look for a better place. If you're lucky, you can go back there many more times. But when the trip is almost over, the search loses its meaning - there is little time to enjoy a new find. That's why people more often choose the tried and tested option.

Details

This task belongs to the dilemma "to search or to use what you find". In English it is often called explore-exploit dilemma. In ordinary life it occurs all the time: to try a new restaurant or to go to your favourite one, to watch a new TV series or to switch on a familiar one, to look for a new job or to stay at the one you are already satisfied with.

In Feynman's version, a person comes to a city for a limited number of evenings. Each night he can either try a new restaurant or return to the best one he has already found. If he keeps looking, there is a chance of finding a better place. But each new search takes away one evening that could have been spent at an already good restaurant.

Feynman proposed a strategy with a "quality threshold." Simply put, you only settle for a very good restaurant at first. If the place you find doesn't reach that threshold, you keep looking. But as the days get shorter and shorter, you have to lower the bar. Otherwise, you could spend the whole holiday looking for the perfect place and never get the best find.

The scientists didn't just take apart Feynman's old notes. They moved the task from choosing a meal to choosing restaurants in a new city and tested people's behaviour in an online experiment. 2,520 people took part. Participants were asked to imagine they were in a city for a different number of evenings, and to choose a restaurant from a virtual grid each time. After making a choice, the person would find out how good the place was.

People didn't follow Feynman's exact formula. Their strategy was simpler: they gradually reduced their requirements for new restaurants as the end of the trip approached. But this simple scheme worked almost as well as an optimal mathematical solution.

That is, the brain uses an understandable rule of thumb: search first, then consolidate a successful find.

Why it matters

This story shows that maths can describe very ordinary solutions. We don't think about formulas when we choose a cafe, a film or a walking route. But there is still logic behind such decisions: time is limited, and each new choice can be either a good one or a wasted one.

At the beginning of a trip, a mistake costs less. If the restaurant turns out to be bad, there are still evenings ahead. You can try another one. But on the last day the risk is higher: if the new place disappoints, there is nothing to fix. Therefore, returning to a familiar good restaurant is not boredom, but quite a sensible strategy.

This principle explains not only restaurants. We behave the same way with shopping, holiday destinations, itineraries, apps and even habits. First we taste, compare and search. Then we choose what has already proven its value.

Background

Richard Feynman was a Nobel laureate in physics, but liked to turn everyday situations into challenges. In this case, the occasion was lunch with his friend Ralph Leighton at a Thai restaurant in California: the latter was choosing between his favourite dish and a new option. Feynman wrote down the mathematical solution but did not publish it.

Decades later, researchers transcribed those notes and showed that Feynman's solution was indeed optimal for the problem at hand. They then extended the problem and tested how people choose under similar conditions.

Interestingly, the human strategy turned out to be simpler, but not stupider. People didn't calculate a perfect curve, but used an almost straight line: the fewer days left, the lower the demands on the new option. This reduces the mental workload and still gives a result close to optimal.

Source

Research: Brian Christian, Evan M. Russek, Thomas L. Griffiths, "Resolving Feynman's restaurant problem reveals optimal solutions and human strategies", Proceedings of the National Academy of Sciences, 2026.