Expected Value Calculations Made Simple

June 13, 2014


Expected value is the average amount of money you stand to gain or lose on any type of wager, and being able to figure out the expected value of different types of bets is a pretty big deal. All you need to know to do an expected value calculation, or EV calculation for short, is know the mechanics of the wager in question or know the payout rate or house advantage of the wager. We're going to look at some simple and more complicated examples here and show you how they can all be made simple.

The first thing you need to do is list out all of the possible outcomes, how likely each outcome is to happen, and what the profit (or loss) is for each outcome. For example, suppose you're taking a corner bet for $3 in European roulette. The outcomes are winning or losing. You win 4/36 of the time, and you profit $21 when you win. You'll lose 32/36 of the time, and you'll have a loss of $3 (or a profit of -$3) when you lose. Multiply the chance of each outcome happening by the profit of each outcome to get the EV of each outcome, then add together those individual EVs to get the EV of the bet as a whole.

For the win outcome, you multiply 4/36 by $21 to get $2.33 as the EV of the win outcome. For the loss outcome, you multiply 32/36 by -$3 to get -$2.67 as the EV of the loss outcome. Add these two values together to get $2.33 – $2.67 = -$0.33. So your EV of the $21 bet is -$0.33. That's all it takes to do these EV calculations, and you can make them as complicated as needed with as many possible outcomes as you want.

In games like video poker or blackjack where some skill is involved, computers often go through each hand to calculate the EV of every possible play to figure out which play has the highest EV. This is how they figure out which play is the best. When you look at what the computer decides about similar types of hands, you can extrapolate to figure out general strategies that give you the right play most of the time. This is where most general principles for these types of games come from, and they're all based on this simple mathematical calculation.