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How often have you seen a poker player get all their money in on TV as an 80% favorite only to lose the hand by the showdown? At such times, you may have wondered what any of it really meant and whether the 80% was just fiction. Is there even skill in poker, or is it all down to luck?
The truth, of course, is that skill is a very big element of poker and that equities and expectations matter very much, but they only matter in the long run.
Understanding the concept of expected value separates great poker players from beginners at the poker tables, who tend to be results-oriented and only worry about particular hands.
This guide will cover what the expected value (or EV) in poker is, how it is calculated, and how you can benefit from this knowledge. By the time you are done reading, you may have a completely different outlook on the game, and your decision-making could change significantly in quite a few common spots in poker.
In the simplest terms, the expected value is the average result you expect to get from a certain poker play if it were to be played countless times. The concept of EV can also be applied to other games, and it is quite commonly used to describe decisions and results of games like roulette or blackjack.
To illustrate EV in the simplest way, we are going to use a very common example. Imagine you are tossing a coin, and there is money on the line to get started.
If you only get to toss the coin once for $100, you know that there is exactly a 50% chance of the coin coming up heads or tails. However, only one side will come up this time, making this math irrelevant; you will have to make a decision based on your "gut."
However, if you were to toss the same coin thousands of times, with $100 on the line each time, it would not matter which way you went. You could say heads thousands of times or tails thousands of times; the final result would most likely be that you would neither win nor lose any money.
The expected value of a coin toss is exactly 0, as the chance of each side coming up is exactly 50%. In poker, 50/50 situations are very rare, and one side usually has at least some advantage.
Thinking in terms of expected value instead of hoping for a favorable outcome based on luck is the only way to approach poker in a way that gives you an advantage over your opponents.
In the game of poker, the expected value is calculated by taking all the known parameters into the equation. This includes the size of the pot already on the table, the cost of a certain decision, and the equity of the hands involved.
Top professionals at the poker tables make their decision, with EV being their only concern. This is why tournament players often go all in with relatively weak hands. They are banking on several factors working together to make their move +EV.
+EV means positive expected value, as opposed to –EV, which stands for negative expected value. Each decision you make at the poker table will be either +EV or –EV, and you want to make sure you are making as many +EV decisions as possible.
An easy example of a +EV decision would be to call your opponent's all-in before the flop with AA. Regardless of your opponent's hand, you know you are a big favorite to win, making the decision very easy to make.
On the other hand, there are many other more complicated decisions. For instance, you may face a situation where you are being asked to call off an all-in holding a combo draw of KsQs on a JsTs6h board where you believe your opponent has a hand like AJ or JT.
In situations like this, where equities run close, you will need to look at the size of the pot and the size of the opponent’s all-in to ensure that the value of the money on the table justifies making a call that may otherwise be break-even.
Expected value can also be used when making aggressive plays. You may find yourself in situations where you have a hand that could either call a bet or make a big raise, and EV calculations can come in very handy.
By factoring in the percentage of hands in their range that your opponents will have to fold, you will be able to decide whether or not a big move is worth the risk.
To give you an excellent example of how you can use EV to make good decisions in poker, let’s consider the following situation:
You are playing in a $1/2 cash game with effective stacks of $200, holding JcTc on the button. An early position player raises to $10. You make the call, and so does the big blind.
With $31 in the pot, the dealer puts out 9c5c2h. The big blind checks, the raiser bets $18, you call, and the big blind calls.
With $67 in the pot, the dealer puts out the 8d, and the player continues for $25. You are now faced with a decision with $172 in your stack.
Holding an open-ended straight flush draw and facing such a small bet, you definitely have an easy call to make.
You can use the following formula to make this calculation:
EV = (%W * $W) – (%L * $L)
Of course, we don’t know our opponent’s exact hand at this point, and there is still money to be won on future streets. Yet, even if this bet was your opponent’s all-in and you only had 30% equity, the call would be profitable:
EV = (30% * $92) – (70% * $25)
EV = $27.6 - $17.5
EV = $10.1
Even if your opponent had no money left behind, you would still be winning $10.1 by making this call, considering there is a lot of money in the pot compared to the size of the bet made.
We also assumed that we have 30% equity in the hand, which is a low expectation. Note that the hand in question has 34% equity against AA, 47% equity against a hand like As9s, etc.
However, let us consider if we took a different line and went all-in instead of calling the bet. In that case, there are two possible outcomes. Our opponent would either fold their hand or make the call.
Whenever the opponent folds, we get to win the $67 already out there + the $25 they bet for a grand total of $92. Let us assume they fold 60% of their hands to our fairly big shove. In that case, the EV is:
EV = 60% * $92 = $55.2
Now we must consider what happens if we get called and win/lose the hand. We will assume we still have 30% equity against the calling range, which may be true if they end up folding some top pair hands.
First, let’s see what happens when we get called and win.
EVw = 30% * $239
EVw = $71.7
Now, let's consider all the times we are going to lose at the showdown:
EVl = 70% * $172
EVl = $120
This means that every time our all-in gets called by the opponent’s strong range, we are losing $48.3 ($120-$71.7). However, our shove also wins us the pot 60% of the time, leading to the following final equation:
EV = 60% * $92 – 40% * $48.3
EV = $55.2 - $19.32
EV = $35.88
From this equation, we can see that a shove all-in would have been an even more profitable play, even under the assumption that the other player would call our all-in 40% of the time.
If we were to be more realistic with that assumption and presume that they will fold a lot more than that, then the shove could be even more profitable and lucrative.
In these kinds of situations, you will have to consider your opponent’s tendencies and their possible range to decide just how often they might fold their hand.
Against opponents who like to fold a lot, you will want to take a lot of aggressive lines like this one, as they will maximize your expected value and give you a chance to win more chips in the long run.
Perhaps the most important factor when deciding if your decision, whether a passive or aggressive one, is +EV will be your hand equity.
If facing a shove, you will need to decide what kind of equity you believe your hand has against your opponent’s range. If considering a bluff, you must decide how your hand will do against your opponent's calling range and how often you will get called.
Since you won’t have a tool handy to input your opponent’s entire range and get the calculations you need while playing, you will have to make some estimations yourself.
The easiest way to consider your equity against an opponent’s range is to think about the combos your hand does the worst against and the ones it does the best against.
Try to figure out the equity your hand has against each and the number of such combos in your opponent’s range.
By thinking in these terms, you should be able to come up with a good estimate of how your hand will do against your opponent’s entire possible range and what equity you will have on average when the cards are turned over.
Don’t be disappointed if your opponent turns over the best hand in their range, as long as you believe that you estimated the range fairly and did your calculations correctly.
The one thing that many poker players can’t seem to wrap their heads around is the concept of the long run and variance. Every time you make any decision, whether it’s +EV or –EV in theory, the outcome of the hand will go one way or the other. You will never win what your equity dictates in one particular hand.
This phenomenon is known as variance, which creates the illusion that poker is a game of chance where anyone can win or lose.
While the outcome of any given hand may seem random, the player who makes more +EV decisions is guaranteed to come out on top after many hands of poker.
The exact number of hands or tournaments played you will need to get to that long run will depend on many factors.
The more +EV your decisions tend to be, the easier it will be for you to get to that long run and even out your variance. If you are playing against exceptionally bad opponents, you should reach the long run relatively quickly.
However, don't be surprised to play poker for many days or even weeks on end without the results going your way. If you can stick with it and keep making positive EV decisions, the variance will break even, and you will end up the big winner, thanks to the merits of your decisions.
The next time you sit at the poker table, think about poker in terms of expected value instead of hand results.
Don’t worry about which all-ins you will win or lose or which hands your opponent will turn over in any given instance. Consider your opponents’ ranges, calculate your equities against them, and try to find good +EV spots to make your calls and your bluffs.
At the end of the day, your +EV decisions are the ones that are going to win you money, and your bad –EV decisions will cost you dearly.
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