N candidates arrive one by one. You can accept or reject each -- but you can't go back! What's the optimal strategy?
The optimal strategy: reject the first N/e (~37%) of candidates, then accept the first one better than all you've seen.
This gives a ~37% chance of picking the absolute best -- far better than random guessing (~5% for 20 candidates). The same math applies to house-hunting, dating, and hiring!