Why a “practice round” can help you choose
This is the classic secretary problem: candidates arrive in random order, you must decide on the spot, and a rejected candidate cannot be recalled. The aim is not to pick someone who is merely good; it is to pick the single best person in the whole pool.
The strategy separates learning from choosing. During the opening stretch, you hire nobody. Instead, you use those candidates to establish a benchmark: the strongest person you have seen so far. After that, you take the first candidate who beats the benchmark. That person is a new record in the sequence—the best encountered up to that point.
The probability hidden in the cutoff
Why stop observing after roughly 37 percent? If the best candidate appears in the later portion, the strategy can still find them: they will beat the benchmark, provided the strongest candidate from the practice round appeared before them. The longer the practice round, the better the benchmark tends to be, but the greater the risk that the overall best has already passed. A shorter round leaves more chances to act, but makes it easier to accept someone who only looks exceptional because you have seen too little.
The mathematical balance comes from weighing those two risks across all possible arrival positions. For a large pool, the optimal cutoff is about one divided by e—roughly 37 percent. Under the problem’s ideal assumptions, this strategy gives about a 37 percent chance of selecting the overall best. That may sound low, but no strategy can make success likely when the best person’s arrival position is unknown and a decision is irreversible.
What the rule does—and does not—promise
The cutoff is a probability-maximizing rule, not a guarantee or a universal hiring policy. It assumes candidates arrive in random order, can be ranked reliably, and that only the top-ranked candidate matters. Real decisions often allow interviews, negotiation, multiple hires, or revised judgments, so the assumptions may not fit.
Its lasting insight is narrower and useful: when you must choose once and cannot go back, a period of observation can be worth sacrificing—but only if you know when to stop observing.
