How this calculator works
The secretary problem assumes you will meet a fixed number of candidates one at a time, in random order. After each meeting you must accept or reject on the spot, and a rejected candidate is gone for good. You only learn how good someone is relative to the people you have already met. The optimal rule is surprisingly simple: reject a fixed opening share of candidates without committing, then accept the first person who is better than everyone so far. The opening share approaches 1 / e, about 37 percent, as the number of candidates grows. That leaves the remaining 63 percent as the window in which to act. The chance of ending with the single best candidate is also about 37 percent, which is the best any strategy can guarantee under these assumptions.
Formula
For a total of n candidates, reject the first r and then accept the first candidate better than all previous ones. The success probability is (r / n) x the sum of 1 / m for m from r to n - 1. The page evaluates every r and reports the one with the highest probability. For a top-k target the same stopping point is used and the probability is estimated by simulation, because the exact top-k optimum uses a different rule.
Worked example
With 20 dates, the best rejection point is 7. The chance that the next person better than everyone before is also the best of all 20 is about 38 percent. Rejecting only 3 gives a slightly different chance, and rejecting 17 leaves too few candidates to choose from. With 100 dates the best point is about 37 rejected, and the chance of finding the best is about 37 percent.
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Frequently asked questions
Is this a real dating strategy?
It is a mathematical model, not advice. The assumptions are strict: a known number of candidates, random arrival order, no going back, and a clear ranking. Real dating has repeat meetings, changing preferences and no fixed pool, so treat the result as an illustration of optimal stopping rather than a rule for your life.
Why reject so many people?
The early dates are used as a sample to calibrate what a good match looks like. Committing early risks choosing someone who seems good only because you have met few people. The 37 percent rule balances the cost of learning against the risk of running out of candidates.
What if I would be happy with someone in the top five?
The best stopping point does not change much, but the chance of success rises a lot because there are more acceptable outcomes. The page uses the same rejection point and estimates the chance by simulating many random orderings, so the figure is an estimate rather than an exact probability.
Does the calculator account for people rejecting me?
No. The classic problem assumes you make the decision. A variant with a chance of rejection changes the optimal rule and lowers the success probability. This page keeps the standard assumption so the arithmetic stays transparent.