You need to hire a secretary from a pool of applicants, but you can only interview them sequentially. You can't go back to a previous candidate once you've moved on. What is the optimal strategy to maximize your chances of selecting the best candidate?
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To maximize your chances of selecting the best candidate, you can follow the "Optimal Stopping Rule" known as the 37% rule. Here's how it works:
1. Set a number n as the total number of candidates you plan to interview.
2. Initially, interview and reject the first √n candidates without making any decisions.
3. After the √n candidates are interviewed, note down the best candidate among them (let's call it B) without making an immediate decision.
4. Continue with the sequential interviews, ignoring any candidate that is worse than B.
5. Once a candidate is found who is better than B, immediately hire that candidate.
By following the 37% rule, you have a 37% chance of selecting the best candidate. Mathematically, this strategy helps you maximize your odds by balancing exploration and exploitation.