Think of every decision as a bet with a probability and a reward for being right and a probability and a penalty for being wrong. Normally a winning decision is one with a positive expected value, meaning that the reward times its probability of occurring is greater than the penalty times its probability of occurring, with the best decision being the one with the highest expected value.

Let’s say the reward for being right is $100 and its probability is 60 percent, while the penalty for being wrong is also $100. If you multiply the reward by the probability of being right you get $60 and if you multiply the penalty by the probability of being wrong (40 percent) you get $40. If you subtract the penalty from the reward, the difference is the expected value, which in this case is positive (+$20). Once you understand expected value, you also understand that it’s not always best to bet on what’s most probable. For example, suppose something that has only a one-in-five chance (20 percent) of succeeding will return ten times (e.g., $1,000) the amount that it will cost you if it fails ($100). Its expected value is positive ($120), so it’s probably a smart decision, even though the odds are against you, as long as you can also cover the loss. Play these probabilities over and over again and they will surely give you winning results over time.

Though we mostly don’t carry out these calculations explicitly, we constantly make them intuitively. For example, when you decide to take an umbrella to the store even though there’s just a 40 percent chance of rain, or you check your phone to confirm the directions somewhere, even though you’re almost certain you know the way, you’re making expected value calculations.

Sometimes it’s smart to take a chance even when the odds are overwhelmingly against you if the cost of being wrong is negligible relative to the reward that comes with the slim chance of being right. As the saying goes, “It never hurts to ask.”
