Imagine you will meet a fixed number of potential partners one after another, can rank each against those you have already met, and must decide on the spot – once you move on, there is no going back. Choose too early and someone better may come later; wait too long and the best may already be gone. Mathematicians call this the secretary problem, and it has a famous answer: look at the first 37% (1/e) without committing, then choose the first person who is better than everyone so far. That gives about a 37% chance of ending up with the very best – far better than picking at random.
Real life is messier, so the calculator extends the model. You can aim for one of your top 5 or top 10 rather than the single best, which raises the chances a lot and moves the optimal stopping point earlier. You can allow for the risk that the person you choose says no, and decide whether you would settle for the last person if nobody suitable appeared.
It is an entertaining model, not relationship advice – people are not ranked on one scale and you rarely know how many you will meet. But the core insight holds: spend some time exploring before you commit.
How to use the Dating Theory Calculator
- I’m willing to go on dates with (number of people)
- I want to find a partner within (months, 0 = skip)
- I want to end up with
- Chance the person I choose turns me down
- If nobody suitable comes along
- Strategy for the detailed results and the bar chart
- Number of people I reject first
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
For every possible number of rejections r the calculator computes, exactly, the probability of ending with one of your top k candidates: each later candidate is a “best so far” with probability 1/i, you propose to such candidates and are accepted with probability p, and the best of the first i people is within your top k with probability 1 − C(N − k, i) ÷ C(N, i). The r with the highest probability is the optimum.
Worked example
You expect to date 20 people over two years and want the very best. The calculator checks every rule: rejecting the first 7 is optimal and finds the best with probability 38.4% (picking at random would give 5%). You would start choosing after 7 ÷ 20 × 24 = 8.4 months. The catch: the best was among the first 7 with probability 35%, and if so you end up alone.
Optimal rejections for the very best
| Candidates N | Reject first | Success |
|---|---|---|
| 5 | 2 | 43.3% |
| 10 | 3 | 39.9% |
| 20 | 7 | 38.4% |
| 50 | 18 | 37.4% |
| 100 | 37 | 37.1% |
Formula
Rule: reject the first r candidates, then choose the first one better than all before · classic optimum r ≈ N ÷ e ≈ 37% of N · P(stop at i) = (p ÷ i) · Π_{m=r+1}^{i−1}(1 − p ÷ m) · P(success) = Σ P(stop at i) · P(best of first i is in your top k)
Worked example
Inputs — I'm willing to go on dates with (number of people): 20; I want to find a partner within (months, 0 = skip): 24; I want to end up with: The best partner; Chance the person I choose turns me down: 0%; If nobody suitable comes along: I stay single; Strategy for the detailed results and the bar chart: The optimal number of rejections.
Results — Optimal number of people to date and reject first = 7; Chance of success with the optimal strategy = 38.42 %; Start choosing after (months) = 8.4 months; Share of candidates rejected = 35 %; Strategy analysed: reject the first = 7 people; Chance of success with this strategy = 38.42 %.
Key terms
- Optimal stopping
- Choosing the moment to act so as to maximise the chance of the best outcome.
- Secretary problem
- The classic optimal stopping puzzle of hiring the best of N applicants seen one by one.
- Exploration phase
- The first r candidates, met only to set a benchmark.
- Relatively best
- A candidate better than everyone seen so far.
Frequently asked questions
What is the 37% rule?
In the classic secretary problem you reject the first 37% (1/e) of candidates and then take the first one better than all before; this finds the very best with about 37% probability.
How many people should I date before choosing?
With 20 candidates and the goal of the very best, reject the first 7; your success chance is 38.4% versus 5% for a random pick.
What if I only want someone in my top 5?
The chances rise sharply and you should stop exploring sooner – with 20 candidates, reject the first 4 and the success chance is about 73%.
What happens if people can turn me down?
You should explore less: with a 50% rejection chance and 20 candidates the optimum drops and the chance of success falls, because each "yes" becomes valuable.
What is the risk of the rule?
If the best person appears in the exploration phase you reject them and may end up alone – with the optimal rule that happens about 37% of the time when you aim for the very best.
Is this really how to find a partner?
It is a mathematical model with strong assumptions (a known number of candidates, a single ranking, no second chances). Use it as a thought experiment about exploring versus committing.