This principle made a big difference in my own life. Years ago, when I was just starting my family, I saw a house that was perfect for us in every way. The problem was that it wasn’t on the market and everyone I asked told me the owner wasn’t interested in selling. To make matters worse, I was pretty sure I would be turned down for an adequate mortgage. But I figured that it wouldn’t cost me anything to call the owner to see if we could work something out. As it turned out, not only was he willing to sell, he was willing to give me a loan!

The same principle applies when the downside is terrible. For example, even if the probability of your having cancer is low, it might pay to get yourself tested when you have a symptom just to make sure.

To help you make expected value calculations well, remember that:

Raising the probability of being right is valuable no matter what your probability of being right already is. I often observe people making decisions if their odds of being right are greater than 50 percent. What they fail to see is how much better off they’d be if they raised their chances even more (you can almost always improve your odds of being right by doing things that will give you more information). The expected value gain from raising the probability of being right from 51 percent to 85 percent (i.e., by 34 percentage points) is seventeen times more than raising the odds of being right from 49 percent (which is probably wrong) to 51 percent (which is only a little more likely to be right). Think of the probability as a measure of how often you’re likely to be wrong. Raising the probability of being right by 34 percentage points means that a third of your bets will switch from losses to wins. That’s why it pays to stress-test your thinking, even when you’re pretty sure you’re right.
