How to make perfect holiday choices? A Nobel winner’s math formula may help

For travellers arriving in an unfamiliar city, one of the most common dilemmas emerges almost immediately: should they continue trying different restaurants every evening in search of the perfect meal, or return to the best place they have already discovered?

A new study inspired by a decades-old mathematical puzzle devised by Nobel Prize-winning physicist Richard Feynman suggests there is an optimal answer.

The research, published in the Proceedings of the National Academy of Sciences on June 1, revisits notes written by Feynman in the 1970s and concludes that a carefully balanced strategy between exploration and commitment delivers the best results.

The work brings together researchers from Princeton University, the University of Oxford and the City University of New York.

More from Explainers

Suvendu government’s crackdown on illegal immigration is a strategic shock for Jamaat

Condemned before being heard: 403 students and the death of due process on Bangladeshi campuses

Beyond restaurant choices, the findings offer insights into a wide range of decisions people face throughout life, from buying a house and selecting a career path to choosing a romantic partner.

How a lunch at a Thai restaurant became a scientific puzzle

The origins of the study can be traced to a casual meal shared by Richard Feynman and his friend Ralph Leighton at a Thai restaurant in California during the late 1970s.

Leighton, who would later help Feynman write the bestselling memoir Surely You're Joking, Mr. Feynman!, was debating whether to order ginger chicken — his preferred dish — or experiment with another option from the menu.

For many people, such a question would end with a simple choice. Feynman, however, saw a mathematical problem.

As Leighton weighed his options, Feynman began sketching equations and graphs on paper. Within a short time, he claimed to have discovered a rational solution to the dilemma. Rather than treating the issue as a matter of taste, he framed it as a problem involving decision-making under uncertainty.

Leighton preserved those papers for decades. Yet despite their significance, the notes remained difficult to interpret because of Feynman's famously challenging handwriting.

“The notes remained inscrutable for decades, until we managed to decipher them and reconstruct Feynman’s original problem and solution,” the researchers wrote.

The documents remained largely unexplored until the early 2000s, when Leighton posted his own partial interpretation online. Years later, Princeton cognitive scientist Tom Griffiths became interested in the material while conducting research with author and computer scientist Brian Christian.

Griffiths eventually completed a full transcription of the physicist's notes. However, the work did not immediately result in a published study.

According to Christian, the project remained dormant for years after the notes had been deciphered. “We’d understood the meaning of Feynman’s notes, but there was all this work to be done,” he says.

The researchers returned to the problem in 2021, determined not only to understand Feynman's reasoning but also to verify whether his solution was mathematically correct and whether ordinary people naturally behaved in a similar manner.

What Feynman was trying to solve

Although the original question involved selecting dishes from a restaurant menu, researchers realised that the underlying problem was much broader.

Feynman had effectively converted a dining decision into what mathematicians and behavioural scientists call a "stopping problem" — a class of decision-making challenges in which individuals must determine the optimal moment to stop searching and commit to an available option.

Such problems occupy an important place within decision theory, an interdisciplinary field combining economics, psychology, mathematics and behavioural science.

At the heart of these situations lies a conflict between two competing goals. On one hand, continued exploration might uncover something significantly better. On the other, searching consumes time and opportunities that could have been spent enjoying a satisfactory option already discovered.

“The essence of the problem is that the value of exploring, of looking around and trying something new, decreases the opportunities you’re going to have to make use of that information,” said Prof Tom Griffiths of Princeton University, a co-author of the study, as quoted by The Guardian.

To make the problem easier to analyse, researchers reformulated it. Instead of choosing dishes from a menu, they imagined a traveller spending a fixed number of nights in a new city and selecting a restaurant each evening.

The traveller faces a repeating choice. They can continue sampling new establishments or revisit the best one found so far. The challenge is identifying the moment when additional searching no longer offers enough value to justify the risk.

What Feynman's mathematical solution proposed

Feynman's answer was based on a threshold strategy. Under this approach, travellers should initially devote time to exploration. During this phase, they gather information about the quality of available restaurants and learn what options exist.

Once they encounter a restaurant exceeding a certain quality threshold, they should stop searching and repeatedly return to that establishment.

The remarkable feature of Feynman's solution is that the threshold is not fixed.

Instead, the standard required to continue exploring changes throughout the trip. Early in a visit, when many nights remain, the threshold is high because discovering an exceptional restaurant can generate rewards over multiple future visits.

As the trip progresses and fewer dining opportunities remain, the threshold gradually falls. At that point, continuing to search becomes less attractive because there is insufficient time left to benefit from any new discovery.

“The thresholds are being guided by the best thing you might be able to find if you kept looking,” said Griffiths. “If you have a long time to look, finding something amazing has a lot of value because you can go back many times.”

The researchers found that Feynman's original calculations assumed restaurant quality was distributed evenly across a known range. However, they also extended the analysis to more realistic situations.

“We showed that if the distribution of restaurants varies, then the strategy you should follow will change too,” said Griffiths.

In destinations where most restaurants are poor but a handful are outstanding, exploration remains worthwhile for longer because the potential reward from finding one of those rare gems is substantial.

By contrast, if the majority of restaurants are already reasonably good, there is less benefit in continuing the search, making earlier commitment the smarter strategy.

What tests showed

To examine whether human behaviour resembles Feynman's mathematical predictions, the research team created an online decision-making experiment involving 2,520 participants.

Volunteers were asked to imagine visiting unfamiliar cities for varying lengths of time. Some participants undertook seven-day trips, while others experienced stays lasting 14 or 28 days. In another description of the experiment, participants faced visits ranging from one to four weeks.

Each participant viewed a grid in which every square represented a restaurant. The quality of each restaurant remained hidden until selected.

Restaurant scores ranged from one to 100 points, and participants were instructed to maximise the total value accumulated throughout their stay.

Each day presented a choice: visit a new restaurant and reveal its score or return to the highest-rated restaurant already discovered.

The setup closely mirrored the trade-off at the centre of Feynman's puzzle. Researchers also varied the distribution of restaurant quality so that participants would face different decision-making environments.

The objective was not simply to see whether participants found good restaurants. Instead, researchers wanted to determine whether their decision-making patterns resembled the mathematically optimal strategy.

How people's behaviour matched the mathematics

The findings revealed a striking similarity between human intuition and Feynman's calculations. Participants generally explored more aggressively at the beginning of their trips and became increasingly conservative as their visits approached an end.

As remaining opportunities diminished, people showed less willingness to risk discovering a disappointing restaurant and increasingly preferred returning to options that had already proven successful.

The pattern appeared consistently across different trip lengths.

Participants facing shorter stays lowered their expectations more quickly and committed to known restaurants sooner than travellers who had more time available.

Although people did not reproduce Feynman's exact mathematical formula — which includes square-root calculations — their choices closely approximated the underlying logic.

Researchers found that participants appeared to follow a simpler mental rule in which their threshold decreased roughly in proportion to the number 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 trick is having a threshold and then decreasing that threshold as you get closer to the end [of a trip]. And as long as you are doing something like that, that’ll actually work pretty well.”

The effectiveness of this intuitive strategy was evident in the results. Participants undertaking seven-day trips had a 98.4 per cent probability of locating an above-average restaurant before their holidays ended.

Those participating in the longest trips achieved success rates approaching 100 per cent.

Behavioural scientist Shoham Choshen-Hillel of the Hebrew University of Jerusalem, who was not involved in the research, said the findings demonstrated the effectiveness of human decision-making even in uncertain environments.

“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 told Nature.

What the restaurant problem says beyond holidays

Researchers argue that the importance of the study extends well beyond travel planning. The restaurant example serves as a simplified representation of countless decisions people encounter throughout their lives.

“The restaurant example stands in for decisions in many settings,” she adds.

House buyers must determine how many properties to inspect before making an offer. Employers and job seekers must decide when to stop searching for alternatives. Consumers routinely face choices between products already known to be satisfactory and potentially better options they have not yet explored.

The same logic can even apply to finding parking spaces, selecting investments or making long-term personal commitments.

Researchers noted that people frequently encounter situations requiring a balance between exploiting a good opportunity already identified and continuing to search for something superior.

“People must constantly balance finding new opportunities with good choices they have already experienced,” the researchers said. “This study shows that real-world decisions are being made in a much more rational way than expected.”

At the same time, the authors acknowledge that real-life decisions contain factors absent from their mathematical model. Human beings do not always seek a single best option. Variety, curiosity and boredom can influence choices.

For example, someone may continue experimenting with different dishes even after identifying a favourite meal. Likewise, travellers might alternate between a beloved restaurant and new venues simply for the experience.

Nevertheless, researchers believe Feynman's puzzle captures an essential feature of decision-making that affects people every day: determining when the search for something better is worth pursuing and when it is time to enjoy what has already been found.

Also Watch:

With inputs from agencies