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