For a large number of candidates it ends up being approximately 1/e (37%) chance of picking the best candidate, 1-2/e (26%) chance of picking another top candid

For a large number of candidates it ends up being approximately 1/e (37%) chance of picking the best candidate, 1-2/e (26%) chance of picking another top candidate, and 1/e (37%) chance of picking a candidate of random skill. That last case occurs when the best candidate was among the first 37% of candidates, which are always rejected, then you run through the rest without finding a better one, and thus end up with the last one interviewed. If you somehow still have to immediately hire or reject all candidates and care about expected average, instead of just finding the best candidate. The optimal solution will have you reject fewer candidates outright, and then have the criteria for how good a candidate should rank to get hired lower gradually throughout interviewing, and drop sharply towards the end of the candidate list.