When to Stop
Twenty candidates will pass before you, one at a time — flats, hires, suitors, exits; the mathematics does not care which. Each holds up a score, on a scale that changes from street to street and that nobody tells you. Say yes, and the door opens for them. Say no, and no is forever: passed candidates do not return. Reach the last, and you take the last. Your goal is not a good one. It is the best one.
Now watch the mathematics
If all you can judge is how each candidate ranks against the ones before, there is a provably optimal strategy, and it is beautifully blunt: look, then leap. Spend the first 37 per cent of the field looking — choose nobody, remember the best you saw — then take the very next candidate better than everyone so far. Below, the exact odds for every possible looking phase. As the field grows large the best looking phase converges on exactly 1/e of it — 36.8 per cent, 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 curve finds it: watch the peak. Blind luck manages 5 per cent.
The rule carries over to many irreversible choices made in sequence, when they come in random order and only the best will do, and its deeper lesson is a kindness: some failure is the fee, not the fault. Even played by the rule, 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; and for the other kind of stopping, where the question is whether a machine will let you, try The Stop Button.