There is a magic number. It’s 37 per cent

Whatever you’re searching for, apartment, parking space, restaurant or spouse, there’s a point when you stop looking and say yes. But which is the best moment?

You just got married and you’re ready to move out of your one-room bachelorette into a proper dream house. You and the love of your life start checking out apartments for rent. Every weekend, you drive around inspecting prospective homes.

The first one gets no sunlight. The second is on a low floor and will have far too many mosquitoes. Another one has a giant kitchen and a closet-sized bedroom. The fourth one is perfect but - you decide to keep looking because you can’t just take the first best option, right? 

Here’s my question - if you’re looking for place to live, how many apartments good and bad will you reject before you get to yes, even though a little voice says something a little better might be just around the next corner?

On an average Mumbai day, you will go through variations of this problem again and again. You’re searching for a parking space at the mall. How many will you skip before deciding you’re not going to find anything better than the one you just found?

You’re searching for a good new restaurant to eat in. How many will you explore on Google before settling for one?

You’re looking for a soul mate. No one checks all the boxes but you definitely want Miss or Mister Perfect, so you keep looking. When will you say enough, the next one is the one? 

Turns out this very human predicament is known as the Optimal Stopping problem, and is one of the oldest problems of mathematics. Its more popular version, described in 1958 by the man who coined the word software, American mathematician Merrill Flood, is the Secretary Problem. 

You’re hiring a secretary; 100 candidates are waiting to be interviewed. After each interview, you must decide yes or no. Say yes, and the remaining candidates will disappear. Say no, and the one you just interviewed will go away forever. The 100th one is most unlikely to be the best. But when should you decide to go with the next best candidate who’s better than the ones that came before her?

Candidate #1 meets that criterion because there was no one before her. The second one has a 50% of being better or worse than the first. But alas, the first is gone forever since you rejected her, so you’re stuck with #2 for better or worse. So you go for the third interview. Except that this one has only a one in three chance of being the best. The more candidates you interview, the lower their odds of being the top pick as the pool gets larger.

When you finally choose, whether a secretary or a parking spot or a spouse, you know you might have found something better if you’d looked longer. Or not.

So - when to stop looking?

The good news is that if you postponed taking a decision until you’d explored 37% of your options and then jumped at the next one that stood out, you’d do just about as well as if you’d explored all the options. It’s called the Look-Then-Leap rule.

The magic number is 37%. You decide to search for a parking space for 20 minutes. Following the 37% Look-Then-Leap rule, you’d just look for the first 7 minutes, and then go with the next spot that met your criteria.

You decide to search for a soulmate till you hit 40 years. You’re 18 years old now, so you plan to search for 22 years. The 37% rule tells you to put off a decision till age 26 but date like hell. After that age, say yes to the next woman or man who gives you a nice buzzy feeling.

Of course, he or she might turn you down because she’s not reached her 37% line yet but hey, hard cheese.

Seen from the 37% perspective, arranged marriages begin to make a different sense. The spiking divorce rates worldwide tell us that endless searching doesn’t improve your odds of finding that perfect person or being happy ever after. In fact, you have the highest chance of getting a winner - 50% -when you just go for the next likely partner. Just like your ageing parents did. Hidden in all this is secret wisdom - in real life, we don’t search till we find the very best. We stop arbitrarily and settle for second best.

The difference between the Secretary Problem and real life is that sometimes you can go back to a better choice.

Johannes Kepler, the astronomer who showed that planets had elliptical orbits, became a widower in 1611 and started looking for a new wife. No one quite fit his checklist and he kept rejecting one after another, a total of 11 women. However, #5 - incidentally, the first woman he’d met after crossing the 37% line — had impressed him because “of her tall build and athletic body”. He went back and proposed to her and was accepted. 

Kepler and Susanna Reuttinger married and had six children. Their life was described as peaceful and joyous.

Here, viewed from there. C Y Gopinath, in Bangkok, throws unique light and shadows on Mumbai, the city that raised him. You can reach him at cygopi@gmail.com Send your feedback to mailbag@mid-day.com

The views expressed in this column are the individual’s and don’t represent those of the paper. 

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