When to Stop

Twenty candidates will pass before you, one at a time — flats, hires, suitors, exits; the mathematics does not care which. You see each one's quality, you say yes or no, and no is forever. Passed candidates do not return. If you reach the last one, you take the last one. Your goal is not a good one. It is the best one.

Candidate 1 of 20 quality is out of 100; each score unique

Now watch the mathematics

There is a provably optimal strategy, and it is beautifully blunt: look, then leap. Spend the first 37% of the field looking — choose nobody, remember the best you saw — then take the very next candidate better than everyone so far. Below, ten thousand simulated choosers try every possible looking phase. As the field grows large the best looking phase converges on exactly 1/e of it — 36.8%, with Euler's number hiding in your love life — and succeeds just as often. With a field of twenty the discrete optimum lands on seven candidates, and the simulation finds it: watch the peak. Blind luck manages 5%.

As a table

The rule generalises to anything with irreversible sequential choice, and its deeper lesson is a kindness: some failure is the fee, not the fault. Even played perfectly, you lose most of the time — so a bad outcome does not prove you chose badly, and the looking you did before leaping was not waste. It was the strategy.

More play on the Playground