Consider the problem: A committee interviews a stream of N candidates for selecting one. It has to accept or reject each candidate immediately after his/her interview. By rejecting the first half and accepting the first candidate thereafter who is the best so far, the committee can select the best person with a probability 1/4. Playing around with different cut-off times, one can increase this probability to 1/e. We'll use Optimal Stopping to show that 1/e is the best one can do (the material is borrowed from S.R.S. Varadhan's notes for a first Probability course).
