EVERY VALENTINE'S DAY, I open the Journal of Mathematics to read how to make best choices. TL/DR: Take the square root of the choices and discard those from the initial batch.
This process is "an extension of the secretary problem in which the decision maker (DM) sequentially observes up to n applicants whose values are random variables X1;X2;...;Xn drawn i.i.d. from a uniform distribution on ½0;1. The DM must select exactly one applicant, cannot recall released applicants, and receives a payoff of xt, the realization of Xt, for selecting the tth applicant. For each encountered applicant, the DM only learns whether the applicant is the best so far. We prove that the optimal policy dictates skipping the first sqrt(n)-1 applicants, and then selecting the next encountered applicant whose value is a maximum."