It doesn't implement the algorithm but not for the reasons you described. The fundamental issue that this algorithm solves is whether to keep waiting for something better to pop up or accept what you have now. The fundamental constraint is maximum number of trials you are willing to do. So, if you are looking for rental apartment, you might say that you may keep looking for each day for N days. On day 12 when you find the best apartment you have seen so far, the question is if you should commit to it or keep waiting for better in coming days. One of the conclusion of Secretory Problem is that you should not commit to anything until sqrt(N) and then you should pick the one that is the best you have seen so far. This maximizes the goodness of the apartment you might select. If you want to select the best possible apartment then reject first 37% (also called 1/e rule) then select the best you seen so far. This maximizes the probability that you will select the best of the best out of N but this probability is only 37%. The problem with this approach is that there is much higher chance that it wouldn't beat the quality from square root approach.