Imagine you’re playing a coin flipping game.

You will win a dollar for every correct guess, and lose a dollar for every incorrect guess.

Since the odds of a coin being heads is 50% and the value of guessing heads correctly is $1, then the expected value of that guess is 50 cents. The expected value of guessing tails is the same.

This means that on average you will win 50 cents from guessing heads and 50 cents from guessing tails. It’s an average proposition by definition.

But what if you were faced with a new situation in which it was 60% likely that heads was to be flipped and 40% likely the coin would come up tails. Now the expected value of guessing heads is 60 cents and the expected value of guessing tails is 40 cents. Obviously you should guess heads every time.

This concept seems straightforward in this example, but the theory of expected value can be applied in countless situations in life. When you’re contemplating entering a raffle and the prize is worth $100 and tickets cost $1, how do you know if you should buy a ticket? Well, if they sell exactly 100 tickets, the expected value of buying a ticket is $1. So you lose a dollar and “gain” a dollar. On the other hand, if there have been 500 tickets sold, then your expected value is only 20 cents. Don’t buy a ticket.

Graphically, you should stop buying tickets when the expected value becomes equal to or less than the cost of a ticket.

While expected value is used a lot in betting, you can apply it to general decision making and how you invest your time. Say you’re trying to land a new client who is interested in a $10,000 contract, but the chances of you winning that contract are only 10%. Investing in that scenario has an expected value of $1,000. On the other hand, if you have a client who wants to engage in a $2,500 contract but you’re 90% you could land it, your expected value is $2,250. While the upside is lower, the expected value is higher and you should probably prioritize that client.

These situations get complex in real life because the probabilities are not exact, but you can see how this theory can be applied not only in betting, but in investing time and other resources. Expected value is a way of seeing the world and it’s not taught in schools. Top performers use mental models like this to make critical decisions on a daily basis. It’s time we all start understanding the tools to making great decisions. What’s a decision you are contemplating and how could you view it from this lens?