Expected Utility

Imagine I offer you a gamble. I will spin the wheel that looks like this:

And you win the amount of money that it will choose. If it hits a negative number you owe me that much. Should you play or not?

This is the kind of problem you are solving every time you are trying to decide whether or not to take any risky action.

It comes down to figuring out whether the action has a positive or negative value to you, so called Expected Utility, whether it’s benefits outweigh the potential risks.

To find out the answer, you need to know the sum of all the potential benefits multiplied by their probability, and compare it to the benefits and probability of the risks.

So first we estimate probabilities of each outcome:

And then we calculate our upside:

$20 * 0.3 + $15 * 0.2 + $5 * 0.2 = $10

And the downside:

-$10 * 0.2 - $30 * 0.1 = -$5

So now we can see that the expected utility of playing this game is

$10 - $5 = $5

So now we know that if you play this game many times, on average, you will be making $5 every game, so that’s a good deal.

This is a very useful concept, because when you think like that about every action you take, you end up making much better decisions. You don’t take dumb risks, and you don’t miss great opportunities.

In life, we need to make decisions under uncertainty. When you know your values, and take actions with maximum expected utility, you can take the optimal way towards achieving your goals.