The chance of ending up with the single best applicant in this full-information version of the secretary problem comes to 58%—still far from a guarantee, but considerably better than the 37% success rate offered by the 37% Rule in the no-information game.

If we were hiring at random, for instance, then in a pool of a hundred applicants we’d have a 1% chance of success, and in a pool of a million applicants we’d have a 0.0001% chance. Yet remarkably, the math of the secretary problem doesn’t change. If you’re stopping optimally, your chance of finding the single best applicant in a pool of a hundred

We know this because finding an apartment belongs to a class of mathematical problems known as “optimal stopping” problems. The 37% rule defines a simple series of steps—what computer scientists call an “algorithm”—for solving these problems. And as it turns out, apartment hunting is just one of the ways that optimal stopping rears its head in dail

even a very good applicant in the hopes of finding someone still better than that—but as your options dwindle, you should be prepared to hire anyone who’s simply better than average. It’s a familiar, if not exactly inspiring, message: in the face of slim pickings, lower your standards. It also makes clear the converse: with more fish in the sea, ra

As we have seen, this Catch-22, this angsty freshman cri de coeur, is what mathematicians call an “optimal stopping” problem, and it may actually have an answer: 37%.

If you can recall previous applicants, the optimal algorithm puts a twist on the familiar Look-Then-Leap Rule: a longer noncommittal period, and a fallback plan. For example, assume an immediate proposal

science, the tension between exploration and exploitation takes its most concrete form in a scenario called the “multi-armed bandit problem.”

Surprisingly, not giving up—ever—also makes an appearance in the optimal stopping literature. It might not seem like it from the wide range of problems we have discussed, but there are sequential decision-making problems for which there is no optimal stopping rule.

For instance, let’s say the range of offers we’re expecting runs from $400,000 to $500,000. First, if the cost of waiting is trivial, we’re able to be almost infinitely choosy.