Calculating Expected Value

Understanding value and knowing how to act on it appropriately is an important element of playing winning poker – this is why you need to know Expected Value. In this article, I'll teach you how to calculate it, and how to act based on the outcome.

Expected value (EV) is the sum of money you can expect to win or lose on average when you act a certain way in a given play.

Every time you make a decision in poker, be it to check, call, raise or fold, your action carries with it intrinsic value. Understanding how to assess this value and knowing how to act on it appropriately is an important element of playing winning poker– and this is why it is so incredibly important to know about expected value. 

Obviously, not all plays are going pan out and pad your bankroll, which is why expected value is expressed in terms of positive (+EV) and negative (-EV) outcomes.  It probably comes as no surprise that your objective is to lean towards plays that yield the highest expected values.

The EV Equation

Working out your expected value is very simple; just figure how much you stand to win and then subtract how much you stand to lose:

EV =$ to win – $ to lose.

Easy, right? Sure - as soon as you know how to calculate those win/lose amounts. To do this, you are going to need to calculate pot equity

Let’s walk through it.


You: T♠, T♥
Opponent: A♦, K♠
Pot: $200
Flop: J♠, T♦, Q♣

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By either calculating your pot equity on your own or by simply using an online equity calculator, we can determine that your equity at this point in the draw is only 32.55%. In other words, calling is not looking that profitable - but let's go on anyway. (There's a point to be made here!)

Pot equity is not the final say on whether or not you should make a play. Use your EV. 

Let's say your opponent decides to move all-in with $10, and you’re stuck on whether to see his bet. The pot is now $210 and, as we’ve noted, the odds are not in your favour.

However, using EV we can determine exactly how much you actually stand to lose or win by taking action and as such, we can see if you should call or fold. Yes, your lackluster pot equity may make it look like the answer to this question is obvious, but, as mentioned, pot equity is not the only way to tell if your hand is worth playing.

Here's what we mean: 

You will win the whole pot ($210) 32.55% of the time, which translates to $68.35

You will lose your call ($10) 64.65% of the time, which translates to $6.47

EV = $68.35 - $6.47

EV = $61.88

So, if EV = amount we stand to win - the amount we stand to lose, you actually come out ahead here with an EV of +$61.88. In other words, it is actually worth it for you to make this call on average, despite less than ideal pot odds because - in the long run - you stand to make money due to your very low investment (i.e. a $10 call). 

For the sake of perspective, we'll also look at the same example, but change one variable; namely, the amount your opponent bets into the pot. Let’s say he bets $400 instead of $10, bringing the pot size to $600.

EV = $600(32.55%) - $400(64.65%)

EV = $195.30 - $258.20

EV = -$62.90

In this case, you are going to want to sit this hand out. Your opponent’s bet size combined with your poor equity make the call too risky. 

Pot equity and expected value, while not the same, can both be used in tandem to give you a clear picture of when it’s best to act and when it’s best to sit this one out. Of course, in the beginning it can be tough – if not agonizing – to do these calculations in your head at the table. This is why there really is no substitute for experience. Play enough hands and you’ll begin to get a ‘feel’ for the best way to play your hands in particular situations. However, to do this you’ll also have to look back at the hands you have played in the past, work out your EV and your equity and learn from their hits and misses. Eventually the math will begin to feel like second nature. 

Photo Credit: Michael Dorausch | Flickr