Most people acted in a way that was consistent with the Look-Then-Leap Rule, but they leapt sooner than they should have more than four-fifths of the time.

The easiest way to understand the numbers for this scenario is to start at the end and think backward. If you’re down to the last applicant, of course, you are necessarily forced to choose her. But when looking at the next-to-last applicant, the question becomes: is she above the 50th percentile? If yes, then hire her; if not, it’s worth rolling th

a million, believe it or not, your chance is still 37%. Thus the bigger the applicant pool gets, the more valuable knowing the optimal algorithm becomes. It’s true that you’re unlikely to find the needle the majority of the time, but optimal stopping is your best defense against the haystack, no matter how large.

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

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.

Whence 37%? In your search for a secretary, there are two ways you can fail: stopping early and stopping late. When you stop too early, you leave the best applicant undiscovered. When you stop too late, you hold out for a better applicant who doesn’t exist.

The term connection has a wide variety of meanings. It can refer to a physical or logical path between two entities, it can refer to the flow over the path, it can inferentially refer to an action associated with the setting up of a path, or it can refer to an association between two or more entities, with or without regard to any path between them

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.

If your aim is finding the very best applicant, settling for nothing less, it’s clear that as you go through the interview process you shouldn’t even consider hiring somebody who isn’t the best you’ve seen so far. However, simply being the best yet isn’t enough for an offer; the very first applicant, for example, will of course be the best yet by d