Online Poker » Poker Strategy » Texas Hold Em » Poker Equity. The term equity simply refers to the value of an item, place or thing minus any liens owed or interest by other shareholder's. The most common example would be the equity one might have in their car or home. Equity in poker is the share of the pot that is yours based on the odds that you will win the pot at that point in play. Equity changes after each street – pre-flop, flop, turn and river. Home equity is the value of your ownership stake in your home, calculated by subtracting your outstanding mortgage from the property's market value. May 12, 2017 Equity Definition – this is the% of the pot that belongs to you Example: If you have 50% equity, then you can expect to win half the pot You can also think of equity as how often you can expect to win the hand right now.

Understanding how equity works in poker can be a difficult task for even seasoned players. When you start talking about hand equity versus ranges and how to use that information to play better poker, confusion can creep in and it’s difficult to sort out why the heck any of this math stuff really matters. The real problem is that while learning the definition of equity is easy, the hard part is figuring out how to implement that information into your poker game in a practical way.

Today, while most players now understand what equity is, being able to translate that information into quality decisions remains a mystery. The goal of this article is to broaden your understanding of how post-flop equity works and help clarify how to form better post-flop lines against your opponents.

What is Equity in Poker?

One of the keys to winning at poker is learning how to play a variety of different types of hands after the flop. The first step is recognizing whether your hand has enough value to warrant contributing more chips to the pot. This is where the rubber meets the road and an understanding of math becomes important since the way we measure the value of a hand is through equity.

Equity is defined as the share of the pot that each player involved in a hand owns based on the mathematical likelihood of their current holding winning by the river. As streets progress from pre-flop to flop, flop to turn, and turn to the river, equity changes until the final equity is achieved on the river. Equity can change a maximum of three times during a Texas Hold’em hand.

Equity = Percentage Chance of Winning By The River

Example Equity Calculation Between Top Pair and a Flush Draw

Using Equity to Make Decisions

While we do not know the exact hand that our opponents hold, we can make reasonable assumptions about our equity versus their range. This information contributes to our making quality decisions at the poker table. However, just knowing the equity of your hand versus a range doesn’t really help you optimize your lines since there are different types of hands in our range that lead to similar equities. In other words, sometimes holding a draw or a pair will give us a similar equity to our opponent’s range.

In order to clarify the decision-making process, I find it helpful to further subdivide equity down based on how different holdings play out versus the ranges of our opponents. The logical way to do this is to separate the equities of our range into two categories: made hands and drawing hands. The reason it is useful to divide our range this way is because, versus opponent ranges, made hands play very different than draws as streets progress. In fact, how those equities change as a hand plays out is the main theoretical difference between made hands and draws.

What is a Made Hand?

A “made hand” is associated with having a pair or better and does not need to improve further to have a chance of being the best hand by the showdown. There are generally very few cards that can further improve a made hand. For example, if you have one pair, there are potentially only 5 cards left in the deck that would either give you two pair or three of a kind.

Made hands come in varying strengths and can be categorized three different ways:

• Monster Hands
  Monster hands are hands that are better than one pair. Examples include two-pair, trips, straights, flushes, and full houses.
• Strong Hands
  This includes overpairs and most top pair hands.
• Marginal Hands
  Marginal made hands include middle pair, bottom pair, and under pairs to the board. Any hand less than top pair is usually marginal since they are vulnerable to any number of other made hands.

What is a Drawing Hand?

A drawing hand or “draw” is when you have a hand that is not likely the current best hand but has several “outs” to improve to the best hand by the turn or river. The most common draws that come to mind for people are flush draws and straight draws. Here are a few examples of draws along with how many potential outs each might have.

• Two Overcards: 6 Outs
• Open-Ended Straight Draw: 8 Outs
• Two-Card Flush Draw: 9 Outs
• Two Overcards and a Gutshot Straight Draw: 10 Outs
• Flush Draw and One Overcard: 12 Outs
• Open-Ended Straight Draw and Two-Card Flush Draw: 15 Outs

Understanding how basic equity and pot odds work with draws are basic fundamentals of poker. In this article, we will focus on taking another angle and explore an advanced way of using equity to help us make better players after the flop.

The Equity of Made Hands Versus Draws

Both strong made hands and strong draws tend to have a lot of equity on the flop. The difference between the equity of a made hand versus a draw is that the former tends to have fairly constant equity versus an opponent’s range on the flop, turn, and river but does not fair well if our opponent improves. In other words, if you have a made hand like top pair and are ahead of your opponent’s range, then it is very likely that you will have a similar equity on the turn and the river. The equity will not go down or up much and will remain relatively stable. But, if your opponent does improve, you will likely be far behind their equity. A draw works very differently as your equity will vary wildly from street to street. However, a draw will maintain it’s equity fairly well no matter how strong an opponent’s range is. This is called the concept of stable and variable equity.

Stable Versus Variable Equity

Before we can discuss how to use the differences between the equity of made hands versus draws, first we must change how we think of them. This requires that we revise their definitions. By categorizing our holdings based on the dynamics of equity, we can redefine made hands and draws as follows:

• Made Hand
  A hand with stable equity with the progression of streets and variable equity across ranges.
• Draw
  A hand with variable equity with the progression of streets and stable equity across ranges.

What this basically means is that a made hand tends to maintain its equity over multiple streets but has a much weaker equity as our opponent’s range gets stronger. Conversely, a draw will tend to lose equity as streets progress but has strong equity against a wider range of hands.

Understanding Equity

Try to picture in your head how your equity looks with a made hand versus a medium to weak range. On the flop, you are way ahead, and on the turn, you are almost always even further ahead. Therefore your equity is “stable” over progressing streets. On the other hand, imagine that you have a draw against a weak made hand and miss your draw on the turn. Your equity will now be a lot less than it was on the flop, meaning your equity is “variable” over progressing streets.

Now think about how a made hand looks against a range of hands that includes a few really strong hands in it. Since you are way ahead against a lot of hands and also way behind against some of the hands, you have variable equity across the various hands, or ranges, your opponent could have. Conversely, if you have a draw, your equity is pretty much the same against nearly the entirety of your opponents’ made hands. In other words, you have stable equity across the range of hands.

To illustrate, let’s do some Pokerstove calculations to see how this works. First, we’ll take a look at the equity of made hands.

The Equity of Made Hands

A made hand is said to have stable equity as streets progress. In the first example, let’s give our opponent a range that might continue on a particular flop.

Hero’s Hand: AK

Flop: K♠ 7♦ 2♣

Hero Range: 73.737% { AK }
Villain Range: 26.263% {22, 77+, AK, KT+ }
——————————————————————————–
Turn: K♠ 7♦ 2♣ 9♥

Hero Range: 72.252% { AK }
Villain Range: 27.748% {22, 77+, AK, KT+ }
——————————————————————————–
River: K♠ 7♦ 2♣ 9♥ 4♠

Hero Range: 76.119% { AK }
Villain Range: 23.881% {22, 77+, AK, KT+ }

Notice how the hero’s equity remains stable street by street, starting at 74% on the flop, changing to 72% on the turn, and finishing at 76% on the river. Now let’s look at how the equity of a made hand changes as a range narrows only leaving the strongest hands in our opponent’s range.

Flop: K♠ 7♦ 2♣

Hero Range: 74.293% { AK}
Villain Range: 25.707% {22, 77+, AK, KT+ }
——————————————————————————–
Flop: K♠ 7♦ 2♣

Hero Range: 45.833% { AK }
Villain Range: 55.644% { KK+, 22, 77, AK, KQ }

When the range narrows to a much tighter range, the hero’s equity drops a full 30%. This is how made hands have variable equity over different ranges. Now let’s look at similar examples where we have a draw in place of a made hand.

The Equity of Draws

A draw is said to have variable equity as streets progress. Let’s look at another example to illustrate this concept.

Hero’s Hand: A♠Q♠

Flop: K♠ 7♠ 2♣

Hero Range: 44.348% { A♠Q♠ }
Villain Range: 55.652% {22, 77+, AK, KT+ }
——————————————————————————–
Turn: K♠ 7♠ 2♣ 9♥

Hero Range: 25.612% { A♠Q♠ }
Villain Range: 74.388% {22, 77+, AK, KT+ }

We have lost almost 20% in equity in one street. If our hand doesn’t hit on the river, our equity will be 0%. Therefore, our draw in this example has variable equity from street to street.

Now, let’s narrow our opponent’s range again and see how that affects the equity of a draw.

Turn: K♠ 7♠ 2♣

Hero Range: 44.348% { A♠Q♠ }
Villain Range: 55.652% {22, 77+, AK, KT+ }
——————————————————————————–
Flop: K♠ 7♠ 2♣

Hero Range: 36.478% { A♠Q♠ }
Villain Range: 63.522% { KK+, 22, 77, AK, KQ }

We took away all but the nut hands and we still only lost 8% equity. This shows how draws have stable equity over ranges.

You may be thinking, “this is great, but how do I use this information?.” The answer lies in the particular lines or actions you take with various holdings.

Using The Concept of Stable & Variable Equity

Here are a few inferences that we can take away from what we have learned so far:

1. Stable equity over multiple streets hands (made hands) play better against weaker ranges and benefit from multiple rounds of betting.
2. Hands with variable equity over multiple streets (draws) play better against stronger ranges and benefit more from aggressive play on early streets.
3. The fewer hand combinations we beat, the better it is to have stable equity over ranges (draws).
4. The more hand combinations we beat, the better it is to have variable equity over ranges (made hands).
5. Against straightforward opponents, you will tend to have more equity when you semi-bluff shove and get called than if you shove with a made hand.
6. Made hands benefit from getting to later streets; draws benefit from ending the hand early.

Poker Fold Equity Definition

Now we use these assumptions to our advantage and figure out the best way to play each hand based on the type of equity it has. As you read further, keep in mind that the suggestions I make are very general and based on looking at the player pool as a whole. Against strong or tricky opponents who are good at hand-reading, you must adapt your lines accordingly when trying to form profitable lines and optimize your c-bet frequencies.

How To Play Made Hands

Since we know that made hands have stable equity as streets progress, we generally want to play straightforward and build pots when our opponent’s range is weak. The standard play should be to go for as many streets of value as possible. With mid-strength made hands, bet-folding is our friend against most opponents. By bet-folding, I mean you bet for value and then fold if raised. This works best against most weak opponents and ABC type opponents.

However, when our opponent’s range for continuing is narrow, we want to avoid building giant pots unless SPR dictates otherwise. When an opponent’s range is strong, we tend to want to pot control more often and try to get to showdown without building huge pots. Taking more passive lines such as checking back the flop is often warranted when it’s hard to get value from worse hands. Instead, we benefit from keeping in the weaker parts of an opponents range which we can bluff catch against on later streets.

How To Play Draws

With variable equity as streets progress, we know our equity will take a nosedive if we don’t get there on the next street. There is no benefit to stringing our opponents out over multiple streets. Therefore, when we have high equity draws, we generally want to exert maximum pressure against the weak to medium strength hands in our opponent’s range. The idea is to elicit folds with a profitable frequency based on fold equity.

The standard play should be to try to leverage your stack on the flop or turn whether against strong or weak ranges. A typical line is to go for flop check-raises or turn check-shoves out of position against aggressive opponents. In position, making slightly larger bets, in general, is also a good tactic when playing a draw. Whatever line you think will exert maximum pressure against the weaker made hands in your opponent’s range is key. Just represent whatever your opponent will believe to be legitimately strong, whatever that happens to look like in a particular dynamic based on his perceived level of thinking.

The exception is when you hold a lower equity draw. In that case, it is often better to take whatever line will allow you to realize equity with a higher frequency. The balance between collecting on fold equity and equity realization is a constant struggle for good players and something you will need to actively work on.

Equity Denial

Equity denial is a concept I have been talking about for several years that has finally come to the forefront of poker thinking. Basically, it means when your opponent is forced to fold a reasonable amount of equity against your hand or range. In my opinion, the concept is basically the same as protection and mostly applies to when you have a weak made hand and are looking to “protect” the hand versus the parts of your opponent’s range that are too weak to continue to aggression but have a fair amount of equity against you. In other words, equity denial is an argument against pot controlling marginal made hands, especially on a dynamic board where there’s more potential for an opposing range to catch up.

However, this does not mean that we should just go hog wild with all of our made hands and just bet bet bet our opponents into oblivion. In fact, a large portion of made hands in our range might benefit from more passive play. For example, let’s say we hold a weak top pair or a mid pair type hand and the board is QT7. This is a fairly dynamic board and our opponent will certainly have parts of his range that can give him the best hand on the next street. Even so, he also likely has numerous hands that might give him a second best hand against us as well. This fact alone often cancels out the benefit of equity denial by itself.

Additionally, if we factor in the times that aggressive opponents might bluff on the turn and/or river, pot controlling actually becomes a lot more attractive with some mid-strength and even weaker strength made hands. The better we get at reading hands and opponents, the better we can pick and choose particular runouts to bluff catch or even raise our opponent off better hands on later streets.

Which Hands Should We Protect or Deny Equity?

In my opinion, the only hands we should really ever be protecting just for the sake of denial are weak made hands that will very often be caught up with by the river anyway. Underpairs and bottom pairs are the best candidates. Every other part of our made hand range benefits from more nuanced play with specific adjustments against each opponent we face. Basically, what I am saying here is that we should be careful in using “equity denial” as a reasoning for betting except in very specific instances. Most of the time there are other factors that we should be considering, namely our equity type versus our specific opponent’s range, in making betting line decisions.

Equity in Multi-Way Pots

When we look at how variable and stable equity works, we can make a couple of assumptions about how being multi-way might affect the value of a made hand versus a draw. First off, we know that against stronger ranges it’s better to have a draw. Secondly, we know that made hands like top pair go down in value the more ranges that are involved in the hand. It only makes sense that the more ranges you add to the mix, the stronger your hand will need to be in order to profitably stack off.

Therefore, when holding a mid-strength made hand, we should be more inclined to play a pot control type line when involved in a multi-way pot. Conversely, we should theoretically play draws (to the nuts) much more aggressively the more ranges we are up against. This is partially due to the increased amount of dead money in the pot but also because something magical happens when we end up in a multi-way situation against two strong ranges on the flop. Take a look at the following Pokerstove examples:

Draw Versus Two Made Hand Range

In the first example, we have an Ace-High flush draw versus a range of made hands on a K72 board. We have a respectable equity of 40%. In spots where we have only a small amount of fold equity, we can profitably stack off most of the time. In the second example, look what happens when our flush draw is up against two made hand ranges. We are actually quite a bit ahead of both of them! In this spot, we would gladly get the money in multi-way every single time. Even though we would only be winning 36% of the time, we would be raking in the long-term EV dollars. And, if you factor in that sometimes our opponent(s) might get the money in with an inferior flush draw, this situation becomes a fist pump. Which leads us to a conclusion.

Nut draws play extremely well in multi-way pots and often do not require fold equity to profitably commit to the pot.

Interestingly, even if you only included the absolute top of our opponents’ ranges, we still would have a reasonably high amount of equity for a multi-way spot, as shown below.

This example proves the concept of stable equity over ranges, exhibited by draws.

Balancing Our Play

One of the main concerns of many stronger players is in balancing out their ranges. It’s true that you have to be careful not to play one type of holding the same way every time and never take similar lines across the spectrum of your entire range. Therein lies the beauty of focusing on equity when making your post-flop decisions.

When you base your decisions on the perceived range of an opponent, you are already baking into the equation what he or she is thinking about your range. The use of stable and variable equity allows us to counter what our opponents are doing before they even have the chance to adjust to us. Only the very strongest opponents you will face will be balanced enough for us to be overly concerned about how balanced our own play is. The vast majority of your mental resources should be dedicated to an exploitative style of poker, not trying to play game theory optimal.

My advice is to build a core strategy that is inherently balanced and then make targeted adjustments based on the opponents you face. Those adjustments include equity considerations, tweaked based on stable and variable equities. It’s not as complicated as it sounds, once you understand how it works in a practical way. Hopefully, this article has shed some light on the subject for you.

Summary

Overall, understanding equity in poker all comes down to the relationship between how made hands or draws play out versus opponent ranges. Among the concepts you must master to win at poker is to develop our sense of how to approach post-flop play using equity and ranges as a tool to optimize your lines based on the information at hand. By adjusting your lines according to the makeup of those ranges, you can maximize your profit while also simplifying the decision-making process.

Fold equity is somewhat of an advanced poker concept, and while the logic is straightforward, the math can be tricky. The concept of fold equity is base on the truism that if nobody calls your bet, you will win 100% of the time. Stated in another way, you have 100% equity in all pots in which you bet and nobody calls. Of course you cannot know in advance if your opponents will all fold to you. When you make a bet, sometimes your opponents will all fold and sometimes they will not. When calculating fold equity, you must make an educated guess about the probability that each will occur. For this reason, a fold equity calculation is a type of implied odds calculation, and can be either positive or negative.
Here is how you construct a fold equity calculation mathematically. For simplicity’s sake, we will consider your bet as an all in gambit, although in real life this will not always be the case.
Consider Pf as the probability that all opponents will fold if you bet, Es as your showdown equity, Pw as the probability you will win at showdown, and Pl as the probability you will lose at showdown, such that Fold Equity = (Pf * Pot amount before your wager) + Es. And Es = [(Pw *Pot amount after your wager) +( Pl * Pot amount after your wager)] (1-Pf)
What this means is that the percentage of time that all opponents fold multiplied by the amount of the pot prior to your bet can be considered as your equity, but you also have to include in the equation what occurs when you are called. When you are called, some percentage of the time you will win, and some percentage of the time you will lose. When you win, you will win the amount in the pot after betting and being called. Likewise, when you lose, you will lose the same amount. Multiply each by the probability of each occurring. Then add these two products together. This sum can be a negative or positive amount, depending upon whether or not you have the best starting hand. Even if you have the worst hand, and Es is negative, and it often will be, fold equity can still be positive, because you still have to add the equity you receive when you steal the pot successfully.
Fold equity is an important concept to master for effective bluffing in both live and tournament play. It is most frequently applied to the stealing of blinds in the later stages of tournaments, where it is absolutely crucial for success. In tournament play, a missed opportunity to steal the blinds can be fatal. Understanding when you have fold equity is absolutely critical. A key aspect to this is making a good prediction about the value of Pf, the probability that all opponents will fold. Remember, you are estimating this, and you will have to consider many things if you are to come up with an accurate estimate. Things to consider when predicting how often your opponents call include, how loose or tight they are, your table image, the size of your bet, the size of your stack and your opponents’ relative to each other as well as to the size of the blinds, and many other factors.
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