## Monday, August 17, 2009

### Gambling as a way to choose a spouse?

I was reading an article in New Scientist titled 'What's luck got to do with it? The math of gambling', and enjoying it, when a section caught my eye. The author maintains that one can calculate the odds of choosing the best potential husband or wife, and make one's selection accordingly.

Suppose you are told you must marry, and that you must choose your spouse out of 100 applicants. You may interview each applicant once. After each interview you must decide whether to marry that person. If you decline, you lose the opportunity forever. If you work your way through 99 applicants without choosing one, you must marry the 100th. You may think you have 1 in 100 chance of marrying your ideal partner, but the truth is that you can do a lot better than that.

If you interview half the potential partners then stop at the next best one - that is, the first one better than the best person you've already interviewed - you will marry the very best candidate about 25 per cent of the time. Once again, probability explains why. A quarter of the time, the second best partner will be in the first 50 people and the very best in the second. So 25 per cent of the time, the rule "stop at the next best one" will see you marrying the best candidate. Much of the rest of the time, you will end up marrying the 100th person, who has a 1 in 100 chance of being the worst, but hey, this is probability, not certainty.

You can do even better than 25 per cent, however. John Gilbert and Frederick Mosteller of Harvard University proved that you could raise your odds to 37 per cent by interviewing 37 people then stopping at the next best. The number 37 comes from dividing 100 by e, the base of the natural logarithms, which is roughly equal to 2.72. Gilbert and Mosteller's law works no matter how many candidates there are - you simply divide the number of options by e.

It's a fascinating thought . . . selecting one's spouse through probability theory! The whole article is very interesting, particularly if you partake in games of chance of any sort, or just want to understand them better. Recommended reading.

Peter

#### 1 comment:

Stranger said...

Well, the article is good for a chuckle, anyway. Before WWII there were still many groups that insisted parents had the right to choose mates for their children. I still run into couples who married at 14 or 15, 70 or more years ago. Still together, still best friends, and still doing fine.

As are the several couples I keep in touch with who met at "play parties" in the dirty thirties, picked an elopement date as they skipped to the caller, and stuck to it. Also doing fine.

And I used to know several dozen couples who "married for love." And got hourly rations of hot tongue and cold comfort for their troubles.

While there are women a man cannot live with, and vice versa, it seems to be more a case of a couple deciding "we are going to make this work" than anything else. Substitute wife for brother in "Bare be back without brother behind" and choose someone you would trust with your back.

Stranger