You see candidates in random order, must accept or reject each on the spot, and win only by taking the single best. Stop too early and the best is still out there; too late and you've already waved them through. The optimal rule is startlingly simple — watch a fixed fraction, then leap — and the fraction is 1/e, of all numbers.
The bar on a flipped card is the only thing you are told: how that candidate ranks among the ones you have already met. A full bar means “best so far”. Their standing among all twenty stays sealed until the round ends.
The looking phase is not waste — it is calibration. You are buying a yardstick. With no idea what “good” means, the first person you meet looks like a miracle; after seven you know roughly where the top of this particular pile sits, and every judgement afterwards is one you can actually make.
Two failure modes, pulling opposite ways. Look at almost nobody and the yardstick is a twig — you leap at the first person who clears a bar set by two strangers, which is to say you leap at mediocrity. Look at almost everybody and the yardstick is superb, but the best has already been shown the door and you spend the last interviews waiting for a ghost.
Between twig and ghost sits the best trade, and the striking part is where it lands: skip about 37% of the field, and about 37% of the time you walk off with the single best person in the room. The same number twice is no coincidence — it falls out of the algebra on the Formal tab.