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Expected value is definitely an advanced technique, but one that is critical to understand when to take a risk that even pot odds don’t necessarily support. There is reckless aggressive, and then there is smart aggressive. Expected value is one of those concepts that will take longer for most poker players to pick up, and it is a concept that is not used often, but it’s one of those little things that makes a gigantic difference in making a lot of money and making that next step in your poker game.

Expected value can be tricky because it is more theoretical than other concepts, but this is an underlying concept that every major poker player has to understand. The concept of expected value (often shortened to ‘EV’) is the expected return on a bet. What does this mean? Here is one of the most commonly used examples to explain expected value:

Suppose we made a bet on a coin flip. I tell you that if it is heads, I will pay you \$100. If it is tails, you’ll pay me \$1. Should you take this bet? Absolutely! The odds are 50-50, so to figure out your expected prize for winning, take the percentage times the total prize. So in this case (.5 * \$100) which makes it \$50. Your expected win is \$50.

On the opposite side, if the coin lands tails, you only lose \$1. So your expected loss is (.5 * \$1) which is fifty cents, or \$0.50. The expected profit, or the expected value of each bet, is the win minus the loss. So \$50-\$0.50 is \$49.50. So your expected profit by taking this bet is \$49.50 a bet, because in the long run if you take this bet every time, it should average out to \$49.50 up every bet.

Now the reason this is the expected value is that at no time do you actually win \$49.50. There is +\$100 and -\$1, but if you win once and lose once, then your total is \$99. That means you made \$99 off two bets, or \$49.50 a bet. That’s why this is your expected value in this situation. Now in real life, and in playing poker, the odds are never that mismatched, but using expected value is how to figure out when to chase, when to fold. Professional poker players know it doesn’t matter what happens in the short term, but making decisions based on the long term expected value is how they make a living at what they do and ride out bad luck.

The most common way expected value shows itself is through odds theories. Pot odds, implied odds, and reverse implied odds are all based on the overall concept of expected value. There are times where the cards and plays can be the same, but it’s right to call at one point, re-raise another, and fold in a different situation. Even basic odds are based on expected value. Why do you always call an all in pre-flop if you are one on one with another player and you have pocket aces? Because heads up you’re going to win almost 8 out of 10 times, so those eight wins will more than pay off the two losses.

Expected value also can help a player realized the difference between a big mistake and a small mistake. Big mistakes occur when a player makes a decision that has a very high negative expected value whereas a small mistake is when one gives up a small amount of expected value. In the long run, you want to make almost every play one that has a positive expected value for you, based on the information you have. Do this, and you’ll be on your way to taking your game to an entirely new level.