So for a long time, mathematicians believed that, given 100 choices (each of which has to be chosen or discarded after the interview) you should discard the first 50 and then choose the next best one. (The assumption also is that if you don't choose the first 99, you have to choose number 100, which, again, seems rather realistic to me. I know so many people who have chosen the last resort out of perceived necessity rather than, say, happiness.)

The "Discard 50 then Choose the Next Best" method apparently gives you a 25 percent chance of choosing the best candidate.

However, then along came John Gilbert and Frederick Mosteller of Harvard University. I do not believe they were married. However, they came upon the idea that the magic number is, in fact, 37. Yes, you should stop after 37 candidates and choose the next best one. This number was apparently derived by taking the number 100 and dividing by e, the base of the natural logarithms (around 2.72). And it apparently increases your chances of the best choice to 37 percent.

Link via The Corner

Image: U.S. Department of Energy

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)I think the idea is that if you estimate you will have n options in your lifetime, you should reject the first n/e options, then choose the best one after that.

Estimating n is the hard part.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)http://www-abc.mpib-berlin.mpg.de/users/ptodd/publications/todd97/todd97a.htm

Testing 9 to 12 candidates and then taking the next better one gets you into the top 75 to 90% of the pool, whether the pool is 100 or 1000.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)"Um. Thirty-seven."

"I'm THIRTY SEVEN?"

Abusive comment hidden.(Show it anyway.)Anyway... Interesting article, good to know. Now I have to count up the number over crushes/lovers I've had and see if I'm close... I think I'm almost there.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)I believe what you're seeing tested empirically in figures 2 and 5 of that paper is this ...

http://en.wikipedia.org/wiki/Secretary_problem#Cardinal_payoff_variant

For that problem, the optimal skip pool, given N candidates, is sqrt(N):

http://dx.doi.org/10.1016/j.jmp.2005.11.003

So for N=100, it's 10, and for N=1000, it's ~32.

Abusive comment hidden.(Show it anyway.)Okay- so should I now acutely divorce my wife that I 've been with harmoniously for the past 20 years to date some 34 ladies more...?

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Even so, as stated, you're only a little better than 1-in-3 by this method, a bit worse than 'real-world,' where the marriage breakup rate is ~ 1-in-2

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