The (square) Root of Love

All right, fellas, huddle up.  We’re going to talk about the best way to find true love.  I mean, you can’t just go running around all willy-nilly hoping to bump into somebody great.  The world is a big place.  You need a strategy, man.  A dating plan of attack.

First, some ground rules, some general observations about romantic life, and a few restrictions in the interest of mathematical well-behavedness:

  1. You are only going to meet a finite number of datable women over the course of your lifetime.  It will be a depressingly low number.
  2. You are going to be an upstanding citizen and date only one woman at a time.
  3. You will date a woman for some finite period of time, at which point you’ll make a decision either to pull the trigger and propose, or cut her loose.  Or, more likely, she’ll dump you first.
  4. Once you propose, no takesies-backsies.  And once you cut a woman loose, you can’t ever reconsider her for marriage; she will hate you forever.
  5. You are able to perfectly rank the women you have dated according to a strict, unambiguous order of preference.  Tie goes to the blonde.
  6. You will encounter these women in random order.  That is, you are completely ignorant of where the next potential wife will stand in the overall rankings.
  7. You will date a certain number of women without really considering any of them for a proposal.  In other words, you’ll take some time getting a feel for who’s out there.  Setting the bar.

In the world of mathematics, this is what’s known as an optimal stopping problem.  You’re going to date, and date, and date…, and stop.  Hopefully on the woman of your dreams (hence the optimal part).  In fact, this is one of those problems that’s so famous it goes by several (mildly sexist) names: the secretary problem, the sultan’s dowry problem, the fussy suitor problem.  Because it’s Valentine’s Day, we’ll call it the marriage problem.

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