Poker EV – Learn How to Calculate Expected Value of Your Hand
When you are first learning poker, you will often hear the more experienced players or your coach talk about how the result of a hand does not matter and how it’s all about the long run.
But what does it actually mean, and how do you determine if you are playing well in the long run if you end up just losing a hand and the pot with it?
To determine this, we use a poker concept of expected value, which tells us the average result of our play if we were to do it many times over.
In this guide, I am going to talk about the expected value in poker, how to calculate it, and how it will help you improve your overall poker game.
Learning how to calculate your poker EV and how to apply it to your decision-making is one of the important steps you will have to take in taking your game to the next level.
Let’s start out by explaining what poker expected value actually is on a simple example.
What is EV in Poker?
Expected value is a mathematical concept that can be useful in poker in other gambling games where money is on the line, and there are probabilities of winning and losing.
Poker expected value is the amount of money you stand to win or lose each time you make a certain play, as calculated by playing (or simulating) the play many times over.
The result of the poker hand will never correspond to your poker EV exactly because there is variance at play, and you can either win or lose the hand each time you play it.
Yet, if you play the same hand many times, your EV will begin to even out, and you will win the amount you are supposed to, according to the math.
A simple example of this is being all-in before the flop with AA against KK, which is a common scenario in Texas Hold’em.
You are going to win with aces about 80% of the time, and in the long run, this situation is going to be massively +EV.
Yet, each particular time you play the hand, you are either going to win or lose the whole pot, never just 80% of it.
For that reason, poker expected value is a long-term concept that only works over many hands but one that will define your poker success or failure over the course of a lifetime.
How to Calculate Poker EV
You now have a general idea of how poker expected value works, but you still don’t know how to calculate it or how to apply it in your poker game.
Before we move on to any practical applications, it’s important to be able to calculate EV properly, and we will do this by using a mathematical formula.
The formula you want to use is:
EV = (%W * $W) – (%L * $L)
In this formula, the variables have the following meaning:
- %W – Percentage of the times you win the pot
- $W – Money won when you win the pot
- %L – Percentage of the times you lose the pot
- $L – Money lost when you lose the pot
If we take an example of a $100 pot where we invested $50 and have an 80% chance to win, the formula plays out as follows:
- EV = (%80 * $50) – (%20 * $50)
- EV = $40 – $10
- EV = $30
This simple equation leads us to the conclusion that by calling a $50 all-in shove before the flop with AA against KK, we will win approximately $30 each time the scenario goes down.
While some people might expect this number to be higher, it really is not. About 20% of the time, we are going to lose the whole pot, allowing our opponent to keep some of his money in the long run.
With an expected value of +$30, this situation is amazing for us, and it is probably one of the best situations you can get into in poker.
Most other spots in Texas Hold’em are much closer, and our EV is far lower than this. Yet, being a successful poker player is all about making as many positive EV plays as possible.
How EV Works in Actual Poker Games
Of course, calculating the expected value in poker after the fact is of little value, as it does not help us make better plays in-game.
Instead, what we want to be doing is calculating the EV of all possible lines we can take before we make the play so as to make the most profitable play possible.
Sitting in the big blind with AA and facing a shove is a situation that does not really give us many options. We are always going to call, and the play will always be +EV.
On the other hand, there are countless other scenarios where we are facing bets or looking to bet ourselves, where there are many options possible.
Remember that betting and raising are not the only aggressive options we can take. In fact, since we can size up our bets and raises as we choose, there are almost countless different options we can take.
Each time the action is on us in a poker game, our goal should be to make the play that offers the most +EV result.
This means we want to be making the play that will bring us the highest long-term profit, and this is not always an easy thing to determine.
Of course, we cannot do all the poker expected value calculations on the spot while playing the hand, so we will need to practice in the lab and run calculations for common spots ahead of time.
On top of that, we don’t know what exact hand our opponent is holding at any point in time, so we will have to do poker EV calculations against the entire range of hands our opponent could be holding.
All of this may sound daunting right now, but as you run many simulations and play many thousands of hands, the concepts of expected value are going to become a lot clearer.
+EV versus –EV, What Does it Mean?
If you often visit poker forums, you are going to see people often talk about a play being +EV or –EV, but what does that actually mean?
Well, it’s very simple. +EV means that a play has a positive expected value, while –EV means that a play has a negative expected value.
As a general rule, we always want to try and make a play that has a positive EV, or at least one with a neutral EV, which means we aren’t winning or losing money with it in the long run.
Regardless of how good at poker you are, you are going to make some –EV plays as well, but as long as most of your plays are +EV, you will be coming out on top in the end.
It is also important to realize that in certain spots, there may be many different plays that are +EV.
In this case, it is your job to pick the one that has the best EV potential, the so-called optimal solution.
For instance, you may be on the river and have a very strong hand. Your options will be to bet small for value, bet big for value, or overbet shove.
While each of these plays is +EV (considering you are sure you have the best hand), you will need to decide which play is the most +EV.
To determine this, you will need to think about the possible hands in your opponent’s range and which percentage of the time they would call each of the bet sizings.
This is a kind of calculation you cannot do on the spot, but you can run all the possible sizings and potential call percentages while analyzing the hand after the game.
These types of analysis will help you recognize spots in which you can extract more value in the future and will make your play overall more +EV.
Understanding Variance, +EV Plays Won’t Always Win the Pot
When talking about expected value in poker, it is very important to also discuss variance and how it affects our perceptions of expected value.
As I already said, EV is a concept that only makes sense to talk about in the long run, while in the short run, every hand will end in you either winning or losing the entire pot.
There are situations in poker that are definitely +EV but will end up costing you a large amount of money in the short run at times.
For example, you may decide to run a big river bluff that your opponent will only call off with the nuts.
Once in a while, your opponent will have the nuts, snap call you, and you will lose the entire bet and the pot in the middle.
While this bluff might end up working 90% of the time, you will lose big 10% of the time and may feel bad about the loss at the time.
If you want to be a truly great poker player, you need to learn that it’s all about making the +EV play, that the player won’t always have the nuts, and that they will mostly end up folding their cards in the spot.
However, also remember to make your expected value analysis unbiased and realistic. Give your opponents reasonable ranges and calling frequencies if you want your simulations to give you any useful data.
cEV versus $EV, Understanding the Difference
In poker cash games, the concept of poker expected value is not too complicated to explain. However, it becomes a bit more complex when it comes to tournaments.
Because players in tournaments can’t win all the money in the prize pool, the chip count does not correspond to the monetary value of the player’s stack.
For that reason, it is important to understand a tournament concept known as the independent chip model (ICM) if you want to be a professional tournament poker player.
This model helps you understand the relation between your stack and the prize pool, allowing you to make plays with the positive expected value.
Because the amount of money you can win in poker tournaments is limited, the ICM often dictates that you are forced to make tighter calls and looser shoves in many situations.
A play that may be slightly +EV in a cash game may end up being significant –EV in a poker tournament.
In tournament poker, you will need to understand the concepts of cEV (chip expected value) and $EV (dollar expected value), which are not equal.
Simply winning chips is not enough to win money in poker tournaments, and there are many times when making a play just to win a few chips is not the optimal play.
Learning how to apply ICM in your tournament game will help you make +$EV decisions, which will make you a big tournament winner in the long run. ‘
Putting it All Together: Expected Value Will Make You a Better Poker Player
Expected value is easily one of the most important poker concepts that you will need to master on your journey to poker glory.
From now on, every time you are about to make a play at the poker table, don’t think about winning or losing the pot at hand, but rather about which decision makes the most sense in the long run.
Making +EV decisions at the poker table is what’s going to make you a big winner in the long run and allow you to beat your opponents consistently.
You will need to constantly keep in mind that variance is at play as well, which means the results of particular hands don’t matter, and that it’s all about what’s going to happen after you play a certain hand many times over.
As you keep playing, you will notice that similar scenarios come up a lot, which is exactly why you can use sure your EV will even out, and you will win money in the long run if you keep making +EV plays.