- Which model
- Over a span of years
- Start of the window
- 18
- End of the window
- 35
- Number of candidates
- 10
36.8%
Open with these values36.8%
Result: 36.8 %Look without committing for the first 37 %, then take the first option better than everything you have seen. Over an open time window your chance of landing the best one is 36.8 % — and it stays 36.8 % however long the window is. Knowing the exact number of candidates does slightly better.
36.8%
Open with these values39.8%
Open with these values37.9%
Open with these valuesP = (k/n) · Σ 1/i, k = round(n/e)
This is the secretary problem, the classic optimal-stopping model: candidates arrive one at a time, each must be accepted or rejected on the spot, and none can be recalled later. The strategy that maximises your chance of picking the single best one is to look without committing through the first 1/e of the sequence — about 36.79 percent, usually rounded to 37 — and then take the first candidate who beats everyone seen so far. The number this calculator returns is that chance of success. In the time model it is the constant 1/e itself, 36.8 percent, however long the window: someone searching from 18 to 35 switches from looking to leaping at 24.25 years, roughly 24 years and three months. With a known number of candidates it can be computed exactly, and small pools beat the limit — 43.3 percent for five candidates, 39.8 for ten, 38.4 for twenty, 37.1 for a hundred, falling back toward 1/e as the pool grows. The caveat that matters most is how narrow the goal is. The rule maximises the probability of landing the absolute best candidate, not average satisfaction and not minimal regret. It also assumes you only ever learn whether someone ranks above or below those already seen, and that the two phases stay strictly separate.
With five candidates the success rate is 43.3 percent, with a hundred it is 37.1. The 1/e value is where a long queue settles, not a fixed figure.
The rule maximises the chance of landing the single best candidate. It does not maximise average satisfaction, and it does not minimise regret.
During the looking phase you commit to nobody, however good they seem. Blurring the phases removes the guarantee the whole rule rests on.
37 percent is how long the whole search should take.
It is where the looking phase ends. What follows is the deciding phase, and it can run to the end of the window.
The rule guarantees I end up with the best option.
It gives roughly a 37 percent chance of that. In the rest of the cases the best candidate was passed over in the looking phase, or never appeared.
| Candidates | Reject first | Chance of the best |
|---|---|---|
| 5 | 2 | 43.3 % |
| 10 | 4 | 39.8 % |
| 20 | 7 | 38.4 % |
| 100 | 37 | 37.1 % |
| Open window | first 37 % | 36.8 % |
Look without committing for the first 37 % of your options, then take the first one better than everything seen so far. It is the optimal stopping strategy for the secretary problem.
The name rounds the constant. The calculator uses 1/e unrounded, which is why the age model returns 36.8 % rather than a flat 37.
In the time model the probability is the constant 1/e whatever the window. Setting 18 to 35 or 30 to 32 both return 36.8 % — the independence is the result, not a bug.
It is the exact probability of ending up with the best one. With 5 candidates it is 43.3 %, with 20 it is 38.4 % and with 100 it is 37.1 %, falling towards 1/e as the count grows.
It answers a very narrow question: one choice, no going back, each option ranked against the ones before it. Real decisions rarely have all three properties at once.
Information, not professional advice.
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