Imagine you are hiring a gardener. You have 4 people interviewing for the position. At the end of each interview, you have to decide immediately whether to offer the interviewee the job. If you proceed to the next interview, you cannot go back and make an offer to a previous candidate. At the end of every interview you can always clearly rank the candidates, and there are never ties in your preferences. Your goal is to choose the BEST candidate, second-best is as bad as fourth-best. Under these strict parameters, what is your optimal strategy?
Answer: Interview the first 2 candidates. If the second candidate is better, hire him. If the second candidate is not better, then hire the third candidate if he is the best of the first three, otherwise hire the fourth candidate. Such a strategy results in hiring the optimal candidate 11/24 of the time. See http://www.math.uah.edu/stat/urn/Secretary.xhtml for an excellent analysis.