What strategy should you adopt? Well, if you wait to the end, the odds are only 1/100 that the last person is the optimal choice; ditto if you choose the first person. The modeler then asks: what strategy should you adopt for optimum results? A little bit of mathematics involving infinite series gives the answer. You can prove mathematically that the best strategy is to look at (approximately) the first 36.787944117144235 people (rounding it to, say, 37 people) and then you should choose the first person from that point on that is ‘better’ then the previous 37 people. This increases the odds of your finding the best match from 1% to about 37%- roughly a 37 times improvement. (In the pre-politically correct literature this model was called “The Sultan’s Dowry Problem,” or “The Secretary Problem”; now, alas, it is usually called simply an example of an “Optimal Stopping Problem.” )
Is this a good model for how we behave? Is this a strategy that one can realistically adopt? Certainly, 100 possibilities seems like a lot of choices to have if one is not the current day equivalent of a sultan — a movie star or an athlete. But the model is intriguing, if not totally realistic and applicable.
Models that spring from modification of the rules of the Sultan problem have always been one of my favorites in this area. This makes Chapter 3 my favorite chapter: it is chock full of goodies with lots of interesting variations of the original problem, and thus even more interesting models. Some may be far more applicable. For example, if you get to play the cad and can keep potential mates ‘stockpiled,’ then, by stockpiling seven potential mates, there’s a strategy that you can use to increase the odds of finding the best one to 96% or so!
Now, the notion of relying on mathematicians for romantic advice seems sketchy at best, but there seems to be an element of truth to what the author of MATHEMATICS AND SEX posits, especially when it comes to stockpiling. Women, being somewhat more ruthless than the average man when planning for the future, have a strong tendency to do this “stockpiling”; this is the sort of thing I’ve described before when I referred to the “posses” of quasi-friends that many women keep about them.
Whereas men like to create love stables, a sort of harem-by-telephone to keep them provided with a dependable variety of casual rides, women’s posses ensure that they’ll have several fall-back options in case Mr. Perfect doesn’t materialize by a certain point of time. And as the numbers suggest, this is the mathematically optimal strategy.
So, keep that in mind the next time she “just wants to be friends” but confuses you by calling you up all the time and stirring up your interest in her. The good news is that there is a small chance in the long term. The bad news is that you’re nothing but a stashed man, held in pocket for a rainy day.