Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet.
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.
This sum is obtained by noting that if applicant i is the best applicant, then it is selected if and only if the best applicant among the first i − 1 applicants is among the first r − 1 applicants that were rejected.
Letting n tend to infinity, writing , setting it to 0, and solving for x, we find that the optimal x is equal to 1/e.
This idea led to the following approach, the so-called unified approach (1984): The model: An applicant must be selected on some time interval of rankable applicants.
The goal is to maximize the probability of selecting only the best under the hypothesis that all arrival orders of different ranks are equally likely. The 1/e-law is sometimes confused with the solution for the secretary problem because of the similar role of the number 1/e.
Indeed, it is intuitive that there should be a price to pay for not knowing the number of applicants. Depending on the choice of the distribution of , the optimal win probability is typically much lower than 1/e and may even approach zero.