Unexpected Value

Higher mathematics may be an unlikely arena from which to draw cogent parenting advice. Simple arithmetic, on the other hand, is the poster child for good sense. Expected value—even if you don’t know the name—is a transparent concept that we all take advantage of on a daily basis.

I’m going to flip a coin. If the coin lands on heads, you will give me a dollar. If the coin lands on tails, I will give you two dollars. This is a great game for you. The more we play, the more you will win. Sometimes, the coin will land on heads and you will have to pay me a dollar. (Bummer!) But half the time the coin will land on tails and I will give you two dollars. (Awesome!) What a great game!

If only it existed in real life--where so many of have taken up residence.

(If you are not an arithmetic person, you can skip the following two paragraphs. I’ll get back to parenting young adults with DUIs in a sec.) Expected value is the likelihood that something good will happen multiplied by how much you win if that good thing happens minus the likelihood that something bad will happen multiplied by how much you lose if it does. In our game, the likelihood that you win is 1/2 times what you win, two dollars, minus the likelihood that you’ll lose, again 1/2, times how much you lose, one dollar. 1/2×2 -1/2×1 equals .5. On average, you win half a dollar with each coin flip. If you flip the coin 100 times, chances are you will be \$50 ahead.

Of course, nobody is going to offer you a game like this, a game where you’ll win. Real games—the ones in casinos—have an expected value that is negative. Typically gamblers lose an average of a few cents on each bet. A few cents doesn’t sound like much, until you consider that you can invest your money in the stock market for a year hoping to earn a double digit return. Losing 3% on each spin of the wheel or roll of the dice adds up in a hurry. Did I say, “adds”? “Subtracts” is more like it.

Imagine your young adult son has been arrested for impaired driving. Here are some options: Believe him when he says that the drugs in the trunk did not belong to him, that he was just holding them for a “friend.” Hire a criminal defense attorney. Bail him out of the pokey. Pretend the whole embarrassing incident never occurred.

Here’s what you win: temporary gratitude of your substance use disordered son plus his promise never to drink and drive again, he really means it this time, cross his heart and hope to die, honest and for true. What you lose: the likelihood that your adult son subsequently does indeed drive under the influence again and does serious, long lasting harm to himself or someone else. The likely expected value here is--what's the word I'm looking for? Oh, yes: "bad." Chances are something bad will happen.

Which brings us to the crazy billionaire. The crazy billionaire offers you the same flip a coin game described above. You’re going to flip a coin only this time you lose a billion dollars for heads, but you win TWO billion dollars if the coin comes up tails. This is a great game for you! You will win, on average, \$500,000,000 with each flip. The problem—there’s always a problem, even with imaginary games of chance—is that the billionaire will only play one time. One flip of the coin and he’s through.

Even though the expected value of each coin toss is half a billion dollars in your favor, you can’t play. You can’t take advantage of the crazy billionaire because you can’t afford to lose the one time. You don’t have a billion dollars.

I’m not saying you should leave your son in detention. I’m not suggesting that there is anything to be gained from your adult son experiencing the food, milieu, ambiance, or sensitivity* that is our criminal justice system. I’m just pointing out that rescuing, enabling, and denying the need for effective treatment is a bad bet. The smart money is on digging your well before you get thirsty--insisting that your young adult child get the help he--very likely--desperately needs.

* For the chronically irony impaired, let me state unequivocally that our jails are known for none of these characteristics.