Skip the first 37 of 100 candidates, then hire the next one who beats them all. You get the very best 37% of the time.

Candidates arrive one by one in random order. You see how each ranks against those you already met, and you must say yes or no on the spot. No going back. A random hire from 100 is the best one only 1% of the time. How well can you do?

First, your gut

If you follow the best possible rule, in what share of games do you hire the single best of 100?

Now interview them yourself

Pick how many candidates. Keys: H hire, N or space pass.

Your record: no games yet.

Test any rule on thousands of searches

Rule: look at the first 37 candidates without hiring, then hire the first one better than all of them. Drag to change how long you only look.

The curve rises fast, peaks at 37, and falls slowly. Skipping too few means you hire early and blindly. Skipping too many means the best one has probably already passed.

Does it depend on the pool size?

Barely. Drag the pool size and see the best number to skip and the chance it gives. Computed with the same exact formula.

The share converges on 1/e, about 0.368, and so does the chance. Both are computed here with Math.E, not copied from a book.

Why it works, in three lines

1. The best candidate is equally likely to sit anywhere in the line.
2. While you only look, you learn how good "good" is: the best of the first k.
3. The rule wins whenever the best of all comes after k and the runner-up before it is among the first k. That chance is (k/n) times the sum of 1/i for i from k to n-1, which is the formula behind the chart.

Caveats: this is the classic version. You want only the single best, ranks are never tied, and you cannot recall a rejected candidate. If any of these changes, the best rule changes. All numbers on this page are computed in your browser from the formula or simulated; none are taken from outside sources.