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The problem with choosing too soon—or too late

Many decisions must be made before all the options are visible. A driver needs gas but does not know the prices at stations farther down the highway. A company interviews applicants one at a time and must decide whether to hire each person before meeting the rest. Someone searching for an apartment may have to sign immediately or lose it to another buyer. In each case, gathering more information improves the comparison—but waiting too long can mean letting the best option disappear.

Mathematicians call this the best-choice problem, or sometimes the secretary problem. Its classic form imposes strict rules: the number of candidates is known; they arrive in random order; each can be ranked against those already seen; rejected candidates cannot be recalled; and the goal is to select the single best candidate, not merely a good one. Under those assumptions, a remarkably simple strategy gives the highest possible chance of success.

First, reject roughly the initial 37 percent of the options while using them as a reference sample. Then choose the first later option that is better than every one seen so far. If no such option appears, accept the final candidate. The method feels wasteful because it deliberately discards the early possibilities, including any that may be excellent. But accepting too early provides too little information, while waiting longer increases the chance that the best candidate has already passed. The 37 percent cutoff balances those risks.

Why 37 percent keeps appearing

The fraction is not an arbitrary rule of thumb. It is approximately 1/e, where e is Euler’s number, about 2.718. The same constant appears throughout mathematics, and here it describes both the optimal sampling fraction and, approximately, the probability of actually selecting the best option.

That probability is surprisingly durable. With 1,000 candidates, choosing randomly would find the best only 0.1 percent of the time. The optimal strategy raises the success rate to almost 37 percent. Even with a billion candidates, it remains above one third because the result does not depend on the size of the pool. Certainty is impossible—the best candidate might appear in the rejected sample—but a disciplined strategy substantially improves the odds.

The problem circulated informally among mathematicians in the 1950s before Martin Gardner presented a version called Googol in his February 1960 Scientific American column and published the solution the following month. It has since grown into optimal stopping theory, a field that studies many variations: allowing several selections, letting an adversary control the order, or accepting a second- or third-best outcome instead of insisting on first place.

A useful model with narrow assumptions

Real decisions rarely match the textbook problem perfectly. Mathematics-curriculum designer David Wees estimated that he could view 26 apartments during a six-month search. He rejected the first 10—about 37 percent—then signed the first later apartment he preferred to all previous ones. He could not know whether it was truly the best of all 26, but he had maximized his chance under the model.

A more cautionary example comes from Michael Trick, now a Carnegie Mellon University dean. In his 20s, he treated ages 18 through 40 as his dating window and decided at 26 to propose to the first woman he liked more than all his earlier dates. She rejected him. His experience exposes a major mismatch: the classic model assumes that selecting an option is enough, whereas jobs, homes and partners can reject the chooser.

Other departures matter just as much. Wees and Trick did not actually know how many candidates they would encounter, so both substituted estimates. If every option can be reviewed before a decision, there is no need for an optimal stopping strategy at all. If the goal is a satisfactory result rather than the absolute best, the optimal cutoff is typically lower than 37 percent. And changes to the arrival order, recall rules or number of allowed selections can produce different solutions.

The best-choice problem therefore offers less a universal life hack than a lesson in modeling. People often stop searching too early, and the 37 percent rule can counter that impulse—but only when the decision resembles the mathematical setup. Its real value lies in making the tradeoff explicit: explore long enough to learn what quality looks like, then be ready to act when a genuinely superior option appears.