H050

When should you stop apartment hunting and pick one?

You can see one apartment at a time, and each must be accepted or turned down on the spot. Stop too early and you miss better ones; wait too long and the best is already gone.

Look first, without choosing
37%
of the options you can reasonably see
Then take
the next best-so-far
the first one better than everything you've seen
Chance it's the very best
≈37%
versus 1% for taking the first of 100

How long to look before leaping

Chance of ending up with the single best of 100 options, by how many you pass on first

0% 10% 20% 30% 40% 0% 20% 40% 60% 80% 100% Share of options you look at first without choosing Look at 37%, then pick: best one 37% of the time Pick the first one: 1%

Spend the first 37% of your search learning what "good" looks like, then commit to the first option that beats it. If you choose too soon, you have no benchmark; too late, and the best option has likely passed. Looking at the first 37% (1/e) without choosing, then taking the next one better than all of them, finds the single best option about 37% of the time, no matter whether there are 10 options or 10,000. Mathematicians call it the secretary problem, or optimal stopping.

The rule fits any one-way decision made in order: hiring, house hunting, choosing a parking spot as you drive toward a building. It also explains why "the first one I saw" so rarely turns out to be the best.

Try it somewhere else

You're driving toward a concert and want a parking space as close as possible. You can't turn around once you pass one.

When should you stop looking and take a space?

Where the rule bends

The 37% rule assumes you can't go back to an option you passed, you only care about getting the very best, and you know roughly how many options you will see. If you can go back, or if second-best is fine, you should look for a shorter time and settle sooner. For a 30-day apartment search, the rule says to look for about 11 days, then sign for the first place better than everything you saw.

Related exhibits

Sources: Optimal stopping and the 1/e (about 37%) rule: Thomas S. Ferguson, "Who Solved the Secretary Problem?" Statistical Science, 1989; Brian Christian and Tom Griffiths, Algorithms to Live By (2016). Curve computed for 100 options.