So one of my good friends is starting to date again (after being out of the country for two years), and I think that it might be helpful, or at least fun, to keep track of her dates in a ranked fashion so that we can always be on the look-out for the optimum stopping point (i.e. who she should marry) in a semi-rigourous fashion (yes, we're nerding out about this). So I understand what the procedure is for the secretary problem with a known n, but since we're going to be doing this on the fly, how do we know when to accept the new best ranked guy as the one? Thanks!
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As asked, you should estimate how many candidates there will be, then divide by e. It is clearly not 1,000,000 and probably not 10, either. I think if you study it, the optimum is rather flat, so being off somewhat is not that big a deal. There are many "real life" things that modify the problem. The two largest that I think of are first, that as you meet candidates, you get an idea of the distribution, so can make a more informed decision and second, there is an opportunity cost of waiting, which should bias you early.