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37 Percent Rule Calculator

Result

36.8%

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.

Worked examples

Case 1
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 values
Case 2
Which model
With a known number of candidates
Start of the window
18
End of the window
35
Number of candidates
10

39.8%

Open with these values
Case 3
Which model
With a known number of candidates
Start of the window
18
End of the window
35
Number of candidates
30

37.9%

Open with these values

How it's calculated

P = (k/n) · Σ 1/i, k = round(n/e)

  1. StepChoose the time model or the candidate-count model.
  2. StepFor the time model, enter the start and end of your window.
  3. StepFor the count model, enter how many candidates you expect.
  4. ResultRead your chance of ending up with the best of them.

What this number means

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.

Small pools beat the limit

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.

It optimises one narrow goal

The rule maximises the chance of landing the single best candidate. It does not maximise average satisfaction, and it does not minimise regret.

The two phases must stay separate

During the looking phase you commit to nobody, however good they seem. Blurring the phases removes the guarantee the whole rule rests on.

Commonly misread

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.

Reference table

CandidatesReject firstChance of the best
5243.3 %
10439.8 %
20738.4 %
1003737.1 %
Open windowfirst 37 %36.8 %

Questions

What is the 37 percent rule?

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.

Why 37 percent when 1/e is 36.79?

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.

Why does the age window not change the answer?

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.

What does the number with a known candidate count mean?

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.

Does it apply to real decisions?

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.

Sources and last check

  1. projecteuclid.org

Information, not professional advice.