The problem
You are hiring for one position and will interview a known number of candidates, one at a time, in random order. After each interview you must decide on the spot: accept this candidate and stop, or reject them permanently and move on. You cannot recall a rejected candidate. You can rank the candidates you have seen against each other, but you cannot know how the later ones compare. Your goal is to end up with the single best candidate.
This is the secretary problem, also called the marriage problem or the optimal stopping problem in its general form. Optimal stopping is the broader field of deciding when to stop and act on a sequence of opportunities. The same structure appears in choosing a flat to rent, selling an item to offers as they arrive, or picking a parking space on a road.
The strategy
The best simple rule has two phases:
- Look. Reject the first group of candidates, no matter how good, but note the best of them.
- Leap. After that, accept the first candidate who is better than everyone seen so far.
If no later candidate beats the early group’s best, you end up with the last candidate by default.
The question is how large the “look” group should be. For a large number of candidates n, the best choice is about n divided by e, where e is roughly 2.718. That is about 0.368 of the total, which is why it is called the 37 percent rule. With 100 candidates, you would look at roughly the first 37.
A small example checked by hand
With three candidates the numbers are small enough to list. Rank them 1 (best), 2 and 3 (worst). They can arrive in 6 equally likely orders. Use the strategy: reject the first candidate, then accept the first later candidate who is better than the first, or the last one if none is.
| Order | What happens | Result |
|---|---|---|
| 1, 2, 3 | First is 1, nobody beats it, so you take the last (3) | Fail |
| 1, 3, 2 | First is 1, nobody beats it, so you take the last (2) | Fail |
| 2, 1, 3 | First is 2, then 1 beats it and is taken | Success |
| 2, 3, 1 | First is 2, 3 is worse, 1 beats it and is taken | Success |
| 3, 1, 2 | First is 3, then 1 beats it and is taken | Success |
| 3, 2, 1 | First is 3, then 2 beats it and is taken | Fail |
That is 3 successes out of 6, or 50 percent. For comparison, picking at random succeeds one time in three, about 33 percent. For three candidates, this strategy is actually the best available, and it beats random choice.
Why the chance falls as the list grows
As the number of candidates grows, the success chance of the best look-then-leap strategy settles at about 1/e, roughly 36.8 percent. So with many candidates you still pick the single best only a little over a third of the time. That sounds modest, but random selection from 100 candidates succeeds just 1 time in 100. The strategy matters most when the list is long.
The intuition for the 37 percent figure is a balance between two risks. If you look for too short a time, you have too little information, and you may stop on a mediocre candidate. If you look for too long, the best candidate may already be among the rejected ones, and you are left with no way to get them back. The 37 percent point is where those two risks balance for a long sequence.
The strategy also fails in a recognisable way. If the best candidate happens to be in the look group, you will not choose them, and you will end up with the last candidate. That happens about 37 percent of the time, which is exactly the share of the sequence you rejected.
What the rule assumes
The result is a mathematical idealisation, and it holds only when the assumptions do:
- The number of candidates is known in advance.
- The candidates arrive in a uniformly random order.
- You can rank each candidate relative to those already seen, but have no numerical scores.
- You only care about getting the single best, not a good-enough one.
- Rejected candidates are gone for good.
Real decisions rarely fit all of these. If you care about a good result rather than the very best, or if you can recall earlier options, other rules do better. If the options have measurable values, a threshold based on the values often does better than a ranking-based rule. So the 37 percent rule is best treated as an illustration of the trade-off between exploring and committing, not as a rule for real hiring, housing or relationships.
Links to other ideas
The problem is a clean case of decision-making under uncertainty. It connects to risk under uncertainty in strategy games, where a player must commit to a plan before all information is available, and to the broader theme of informed decisions, where the quality of a decision is judged by the information available at the time and not only by the outcome. A good decision can still turn out badly.
You can test the rule yourself with a simple Monte Carlo simulation: shuffle the numbers 1 to 100, apply the rule with a look phase of 37, and record how often the best number is chosen. Over many thousands of repeats the success rate should be near 37 percent, though small batches will vary.
This is a puzzle about choosing, not about games of chance. It offers no method for beating a casino game, where the house edge and independence of each round decide the long-run outcome.