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It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of rankable applicants for a position.The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant.If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end.Under it, the interviewer rejects the first r − 1 applicants (let applicant M be the best applicant among these r − 1 applicants), and then selects the first subsequent applicant that is better than applicant M.
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An easy analysis implies that the optimal win probability is always at least applicants that are interviewed (where e is the base of the natural logarithm) and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.
Terminology: A candidate is defined as an applicant who, when interviewed, is better than all the applicants interviewed previously.
A major drawback for applications of the solution of the classical secretary problem is that the number of applicants (Presman and Sonin, 1972).
For this model, the optimal solution is in general much harder, however.