For most bets, calculating your expected value (or EV) is simple. It can become harder in games where you don’t have all the information you need to make the calculations; in games like that (such as poker or blackjack), expected value often requires a little estimation along with the hard math.
In order to make an expected value calculation, you’ll need to know four things: the probability of winning the bet, the amount you’ll win if you the bet is won, the probability of losing the bet, and the amount you’ll lose if the bet is lost. You can plug actual dollar amounts into the calculations if you want to know the expected win or loss on a particular bet (as we will do) you can just use “units” for more general calculations that cover bets of any size.
Here’s an example. Imagine you are flipping a coin with a friend. However, the payouts aren’t quite fair: you only have to bet $10 on each flip, while your friend has to bet $11. What is the expected value for you?
Well, we know that you have a 50% chance of winning, and when you win, you’ll win $11. We can multiply those numbers together to come up with a total of $5.50. We also know that you’ll lose half the time, and will lose $10 each time you lose. $10 multiplied by .5 is $5. We can then take those two figures, subtract the average loss from the average win, and find that you expect to make a profit of $0.50 on each flip. The math looks like this:
($11 * .5) – ($10 * .5) = $0.50
This is the same math used in any EV calculation, though things can get more complicated if you have to include the possibility of winning different amounts or that the bet could push.