OtsoBet casino Poker EV, short for anticipated esteem, is the most fundamental numerical idea in poker. At the point when we say that something is +EV it implies the play is normal to be productive over the long haul. While a play that is - EV is supposed to lose us cash over the long haul.
The Poker EV Formula
The most simple poker expected value (EV) formula is this:
EV = (%W * $W) – (%L * $L)
Not sure what these variables mean? Either push play to watch this short poker video, or read the guide below, which will teach you everything you need to know.
EV is the most important mathematical concept in poker. Without a solid grasp of EV and the ability to create +EV plays, a player is doomed to fail. In this guide, I’ll show you what EV is, how to use it, and why understanding it is vital for poker success.
What Does +EV Mean?
Like I referenced before, EV represents anticipated esteem. It's the numerical approach to saying "over the long haul this play is supposed to net me X measure of cash". On the off chance that you've heard the terms +EV or - EV previously, these just depict assuming a line or play rates to make or lose cash in the long term.
Our goal in poker is to consistently make +EV plays. Because EV is mathematical there is a formula, but it’s not that scary. This is one of the simpler EV equations we will use in poker:
EV = (%W * $W) – (%L * $L)
Let’s break it down simply. We have %W which is how often we will win a given hand. We have $W which is how much we will win the times we do in fact win. We have %L which is how often we will lose this hand. And lastly, we have $L which is how much money we lose when we lose this hand. Not too bad right? But how can we actually use this? I’m so glad you asked!
A Simple EV Game
You and I are going to play a game. It’s a fun game where we take out a fair coin, with one side heads and one side tails, and we flip it. In this game, if the coin lands on heads I will pay you $3 and if the coin lands on tails you will pay me $1.
If we pull out our EV formula again we can start filling in the variables and solve it. We know that when you win you get $3, so $W = $3, and we know that when I win you lose $1, so $L = $1. We also know that because this is a fair coin that there is a 50% chance of it coming up heads and a 50% chance that it comes up tails. So both W% and L% are 50%. Just a quick trick that you can remember is that %W + %L always equals 100%, so if you know one you always know the other.
So if we do the math quickly we see $1.5 – $.5 = +$1. This means that in the long run you are expected to win $1 each time we flip the coin. Now if we only flip the coin two times your only outcomes are +$6, +$2, or -$2…so you can see how in the short term the results can seem quite different than the +$1 expected value we calculated a second ago. But if we flip the coin millions of times you will average a $1 profit each time I flip.
In poker we focus on the long run, not the short term. We recognize that the results can vary wildly in small samples, but we know that in the long run the math will bring everything back to its expected value. This means two very important things:
We want to constantly find little games like this that are +EV
We want to avoid playing games where the EV is negative
With that said, let’s see how this all applies to poker.
A Simple Poker EV Example
In this hand, it folds around to the small blind who goes all-in. We hold AQ and are debating what we want to do. Now that we are armed with the knowledge of EV we can actually prove this situation mathematically. We just pull out our fancy formula and start plugging in numbers.
So in this situation, we can easily figure out $W and $L. If we call and win we will win the SB’s stack and also our $1 big blind. Once money has been put into the pot, even just a forced bet like the big blind, it no longer belongs to us. That means the $W in this spot is $1 + $12 for $13 total.
The $L is simply how much we would lose if we called this and lost the pot. Well since the $1 big blind doesn’t belong to us we can only lose $11 by calling this. So $L equals $11.
The last thing we need is the %W and %L. In the coin flip example, we knew that a coin had a 50/50 chance of coming up heads or tails. But what about in a poker hand? To figure out our %W and %L we can use an equity calculator like Equilab and figure out our equity (or estimated chance of winning) against our opponent’s range of hands.
For simplicity’s sake, let’s just assume that the SB would shove 77+/AJ+/KQ here. I would normally assign a much wider range, but to make life simpler, let’s just use that range for the time being. We can plug that into an equity calculator like Equilab and we see that our AQ has 47% equity. So we expect when we call here with AQ we will win 47% of the time and lose the other 53%.
Now we just plug everything in, solve it, and ensure that a call here is +EV.
EV = (.47 * $13) – (.53 * $11) = 6.11 – 5.83 = +$0.28
If we look at our two options here, between calling and folding, a fold would be 0EV because we don’t make or lose anything…and a call would be +EV to the tune of $0.28. This means that a call is not only +EV, it is also optimal here.
An EV Poker Hand Example
Want another example? Let’s look at a very simple river example where we can plug in variables and solve for the EV. Take this spot where we decide to bluff the river with a missed draw:
We have enough information to start filling in parts the EV formula. We know if we ever get action we will lose, so $L is $125. We know that if the button folds to our bet then we win the pot, so $W is $187. So the formula is now:
EV = (%W * $187) – (%L * $125)
%W in this spot is how often the button would fold against our bet. An important trick to remember is that %W + %L = 100%. So if you only know %W you can always figure out %L (and vice versa). In spots like this you make an assumption of how often the button would fold when you bluff. You can go really in-depth and do a full combination and frequency analysis of his hand range, but let’s just simplify it here and assume he’d fold 45% of the time. Now we can solve everything:
(0.45 * $187) – (0.55 * $125) = +$15.4
So this bet is +EV given that assumption, and of course, if he folds even more than 45% of the time this play just gets more and more profitable! These kinds of situations are very common in poker and by using EV we can prove the validity of our plays.
Practice With EV & Other Math
Want to practice putting your new knowledge and other poker math skills to work? Take my free 20-question quiz and do your best to score 80%+.
Don’t worry if you find it challenging. If you can’t figure out an answer within 30 seconds, just take your best guess and move on as there is a complete answer key available at the end.
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