Equity Boot Camp

Introduction

In this article

           
• How ranges affect your equity
• How ranges and board textures influence each other
  
• Mnemonics to help you with equity calculations
• Comprehensive practice section in further parts
  

In Fixed Limit, you will very often find yourself in a situation where you passively defended your big blind with Ax or a pocket pair and then miss the flop or see three over-cards.

You cannot always play A-high c/f when you didn't hit a pair or only hit a draw (find more about this in the Platinum article "Heads-up on the Flop OOP: C/C Flop without Initiative - With Showdown Value"). Due to the many possible flops and the different ranges depending on opponent, position as well as your own hand, it is pretty much impossible to illustrate every conceivable situation.

This article will therefore focus only on the most difficult situations - playing pocket pairs and A-high with showdown value. Remember the following prerequisites for a flop call with showdown intention:

• 37% equity against a normal opening range
• 38-39% against smart turn betters
• 28%-29% after a 3-bet preflop

The influence of different ranges on your equity

Depending on his position, Villain will raise with different ranges. The following rule usually applies here: The later the position, the looser the range. If you want to defend 55 for example, your equity varies depending on the range you are up against. This article will solely deal with ranges of TAGs, since they make up the biggest part of your regular opponents. Also, the ranges of LAGs can vary significantly depending on each individual player.

MP2: 66+, A8s+, KTs+, QTs+, JTs, ATo+, KJo+ (13.12%):
Equity = 42.10%

MP3: 55+, A5s+, K9s+, Q9s+, J9s+, T9s, A9o+, QJo (15.69%):
Equity = 43.46%

CO: 44+, A2s+, K8s+, Q8s+, J8s+, T9s, 98s, A7o+, KJo+, QTo+, JTo (23.68%):
Equity = 47.72%

BU: 33+, A2s+, K2s+, Q6s+, J7s+, T8s+, 98s, 87s, 76s, A2o+, K7o+, Q9o+, J9o+ (37.71%):
Equity = 51.90%

SB: 22+, A2s+, K2s+, Q2s+, J2s+, T3s+, 94s+, 85s+, 76s, A2o+, K3o+, Q4o+, J5o+, T6o+, 97o+, 87o (62.29%):
Equity = 54.44%

Since the game is not over preflop, the next step when defending your blinds is to compare the typical ranges with the flop and to re-evaluate your hand. The ace makes up the biggest percentage of high cards in each range, the king the second biggest, the queen the third biggest, etc.

The MP2 range 66+, A8s+, KTs+, QTs+, JTs, ATo+, KJo+ comprises a total of 174 hand combinations, 72 (A8s+, ATo+ = 41.37%) of these contain an ace, 52 (AKs, KTs+, AKo, KJo+ = 29.88%) have a king (not including pocket pairs). Consequently, Villain will have top pair or better more frequently on an A-high flop than he would on a K-high flop.

Passively defending pocket pairs

Preflop: Hero is BB with
XX raises, XX folds, Hero calls.

Playing pocket pairs out of position is often difficult. Especially when you have a small pocket pair, there will often be two or three over-cards on the board, and when you are behind, you will only have two outs to a set; however, you can't just always play pocket pairs for set value.

First of all, we want to analyse the best possible board, which has one broadway card, in order to find out whether one high card can already decrease the equity so much that check/call on the flop would no longer be mathematically correct.

The best possible board is X22 rainbow, since the 2 represents the smallest percentage in all ranges and therefore rarely improves a range to a pair or better.

Passive defense with 33:

Passive defense with 55:

Passive defense with 88:

You can deduce from this that against an MP2 range of a TAG (66+, A8s+, KTs+, QTs+, JTs, ATo+, KJo+), an ace on the flop already means that you have insufficient equity, even with 88. On a flop between Q22 up to T22 on the other hand, every pocket pair gives you enough equity to continue profitably, even against tight ranges.

In the following examples, we will analyse the equity of different hands on the worst boards.

Passive defense with 33:

Passive defense with 55:

Passive defense with 88:

The conclusion is that you cannot continue with pocket pairs on boards that have three broadway cards, not even if you are up against very loose ranges. If you have 55 on a JT9 flop, you will not even get close to the required 37% equity even if Villain has a loose SB range (22+, A2s+, K2s+, Q2s+, J2s+, T3s+, 94s+, 85s+,7 6s, A2o+, K3o+, Q4o+, J5o+, T6o+, 97o+, 87o). To get a better idea of the equities, let's analyse some more selected flops:

Passive defense with 33:

Passive defense with 55:

Passive defense with 88:

The suits also influence the equity. This becomes obvious when you analyse the equity of 55 on three different flops. In the following table, you neither have a backdoor flush draw (double-suited) nor a flush draw (single-suited).

While the decrease in equity from the rainbow board to the double-suited board is relatively low with an average of ~2%, the single-suited board lowers the equity by another ~6-7% as compared to the double-suited board.

In the next table, you have a backdoor flush draw or a flush draw.

The backdoor flush draw only has a very small influence on the equity, namely ~1-1.5%. The flush draw however has a significant effect on the equity. For example, it raises the equity on a JT2 board from 27.69% (double-suited) to 40.29%. This means that 55 moves into a playable zone on a single-suited board.

To sum up, we can establish the following rules of thumb for the passive defense of pocket pairs:

• The higher the pocket pair, the better the equity.
• The mere presence of a high card ace is already deadly to your own equity when up against tight ranges.
• Three broadway cards make pocket pairs unplayable, even against very loose ranges.
• If you have a small pocket pair and there are two broadway cards on the flop, you can only continue against very loose ranges.
• If the board is paired, you can often continue playing if the third card is not an ace and the pair is not in the playable zone (A-9).
• If there is no broadway card on the board, you can profitably continue with your pocket pair in almost all cases.
• On low card boards, the equity against loose ranges is only slighty better (but always playable) as if you were confronted with tight ranges.
• Single-suited boards have a considerable influence on the equity, depending on whether or not you have a flush draw.

Passively defending Ax

Continuing with A-high is characterised by a different problem compared to playing pocket pairs. With Ax, the kicker is a decisive factor to determine whether the equity is high enough for a call or not. The better the kicker, the more often you will dominate a weaker A-high, the worse the kicker, the more often your A-high is dominated.

With A-high, you will have three outs left against a major part of Villain's opening range. The better the kicker and the looser Villain's range, the more clean outs you will have on average due to the kicker. To illustrate this further, let's look at the equities of different A-highs (offsuit) on against the TAG ranges established previously.

The problem of domination becomes particularly evident when you look at the considerable equity jumps between A9 and AK against the MP2 range.

First, we again want to analyse the best possible board for Ax with a given high card. Again, X22 rainbow is the best possible board for the equities.

As the table clearly shows, a K on the flop is lethal for A-high, Q and J are similarly bad. T is slightly better, but you can still only continue to play when up against relatively loose ranges or if you have a good kicker. If the highest card on the flop is < T and the other two somewhere between 2 and 7, you have to fold A-high only against very tight ranges.

Next, we want to take a look at high card heavy boards to see whether or not you can continue with A-high against loose ranges on such boards. The following table only considers BU and SB ranges. An ace high that forms a pair or a draw with more than four outs will not be included.

If there is more than one broadway card on the board, it becomes very evident how big of a factor domination is against loose ranges. While you have to fold A3o against a BU range on any of the boards, you already have a profitable check/call on almost every board with A9o. AT-AK always finds a profitable call on the flop on boards with two broadway cards, alone due to the gut shot on a rainbow board.

The suits of the flop also have a negative or positive influence on the equity of A-high. In contrast to a pocket pair, it is important here which of the two cards forms a backdoor flush draw or a flush draw, respectively.

and

Villain's range: 66+, A8s+, KTs+, QTs+, JTs, ATo+, KJo+

Flop:

Equity of = 36.39% => Fold
Equity of = 38.11% => Call

This example shows how important t he strength of the backdoor flush draw is when you have to make a marginal decision. An A-high backdoor flush draw brings an extra ~4% in equity, while a small back door flush draw is only good for another 2% in equity.

The next table shows the negative change in the equity on a single-suited board or a double-suited board, respectively, as compared to that on a rainbow board provided that Hero does not have a backdoor flush draw or a flush draw.

Similar to pocket pairs, the change in equity from a rainbow board to a double-suited board is relatively low with ~2.5% here; therefore, it really only becomes relevant when you are forced to make a marginal decision. The equities from the single-suited board drop by ~8-9% when the board is double-suited. A simple call against an MP2 range therefore turns into a simple fold.

For A-high, we can establish the following rules of thumb:

• K-high flops are deadly. Q, J and T-high are only slightly better.
• The looser Villain's range, the more important your own kicker becomes.
• Between A2 and A7 or A8, respectively, the changes in equity are only marginal.
• If you have A-high with a low kicker, you can usually only continue on low card boards.

Pocket pairs after a 3-bet

You will sometimes find yourself confronted with a 3-bet OOP preflop. Of course, you can't just always play check/fold here.

When you are up against a 3-bet, you should pay attention to the following things:

• 3-bets are much stronger than a normal open-raise.
• The required equity drops from 37% to 28%-29% due to the bigger pot.
• 3-betting ranges are made up differently than opening ranges.

We want to illustrate the last statement with an example. The opening range of a TAG from the CO contains the following hands:

44+, A2s+, K8s+, Q8s+, J8s+, T9s, 98s, A7o+, KTo+, QTo+, JTo (24.59%)

A 3-betting range vs a button open raise consists of: 22+, A2s+, K9s+, QTs+, A3o+, KTo+ (23.98%). The difference is only made up of 8 hand combinations or 0.62%.

If you compare the equity of 66 on a  board, you will notice that you fare much worse against the 3-betting range than against an opening range that's similar in terms of hand combinations.

Equity with 66 on vs. 44+, A2s+, K8s+, Q8s+, J8s+, T9s, 98s, A7o+, KTo+, QTo+, JTo (24.59%) = 41.59%

Equity with 66 on vs. 22+, A2s+, K9s+, QTs+, A3o+, KTo+ (23.98%) = 29.64%

This very considerable difference of ~12% is due to the fact that a 3-betting range contains a lot more A-highs and pocket pairs and is generally more high card heavy than a regular opening range. Therefore, your own equity decreases if an A or another broadway card appear on the flop.

In the following tables, you see your equity with 77 on different boards vs typical 3-betting ranges. Again, the 3-betting ranges from the "Approx Chart" serve as the basis for the ranges. The ranges look as follows:

• 3-bet vs MP2 open: 77+, ATs+, KQs, AJo+ (7.84%)
• 3-bet vs MP3 open: 66+, A9s+, KQs, ATo+, KQo (10.41%)
• 3-bet vs CO open: 44+, A5s+, KTs+, QJs, A8o+, KJo+ (16.14%)
• 3-bet vs BU open: 22+, A2s+, K9s+, QTs+, A3o+, KTo+ (23.98%)

Again, we first have to look at the best possible boards with a high-card:

You clearly see the huge difference between A22 and K22. Against a 3-betting range, the ace is the ultimate death card for a pocket pair, even much worse than with a normal opening range.

As you can see, the equity of a pocket pair on a board that does not contain any aces is good enough for a call against a 44+, A5s+, KTs+, QJs, A8o+, KJo+ range, even if it has three broadway cards.

A-high after a 3-bet

As previously mentioned, 3-betting ranges are very A-high heavy. That's why your own kicker is even more important when against 3-betting ranges than it would be against opening ranges. This is already obvious if you look at the equity of ace highs with different kickers against 3-betting ranges.

The following tables will show you why this is. They illustrate how many A-highs you dominate with your hand and how many dominate you.

For clarification: A 3-betting range against MP2 contains a total of 52 combinations that have an ace (ATs+, AJo+). If Hero has an ace himself, there will only be three aces left in the deck for Villain. This makes a total of 52/4*3 = 39 hand combinations for Villain. A2o dominates 0 combinations of Villain's 3-betting range, but is dominated by all of them.

Since the major part of a usual 3-betting range is made up of pocket pairs and Ax, we will now look at different flops and see how they affect Hero's equity. Again we will exclude flops on which Hero has a pair or a draw with more than four outs.

When analysing the different equities on the various boards, we can establish the following rules of thumb for A-high in a 3-bet pot:

• The smaller the kicker, the lower the equity (domination).
• If you have a small kicker, you should usually fold even on good boards, unless you are up against loose 3-betting ranges.
• High cards that don't give Hero a pair are still very bad for the equity.
• A-high with a very good kicker(AJ+) only has to check/fold on extremely bad boards.

Summary

This is a very complex topic and theory knowledge alone will not suffice. That's why a practical section in the form of the four quizzes below will help you train your skill to determine your equity in a game. When you start out, you have to make sure that you stick to the outlined rules of thumb. If you are not sure or not happy with the results, simply go through the particular sections again, memorise the rules and have another go.

Good luck!

The equity of your pocket pair and therefore the decision whether or not you should play depends on many different factors. How big is your pair, are there broadway cards on the board, how loose or tight is your opponents range, is the board single-suited or double-suited and many more. Think about these rules once more and put your knowledge to the test in the following quiz. Find out if you can turn the lessons of this section into practice!

Equity Boot Camp Quiz (1): Passively Defending Pocket Pairs

A 3-bet is of course a lot stronger than a normal open raise. Still, you can't just give up every flop. Ask yourself what your opponent's 3-betting range is composed of, how much equity you need and decide whether or not the spot is profitable for you. In the second quiz on this article you can take a practically oriented test to see how well you manage such situations.

Equity Boot Camp Quiz (2): Playing Pocket Pairs After a 3-Bet Out of Position

If you are on the flop with A high and ask yourself if you can play or should fold, remember the factors that influence your equity: You usually cannot play K-high boards, the looser you expect Villain's range to be, the more important your kicker; with a low kicker you will usually only be able to continue playing on low card boards. In the following quiz you get to use your acquired theory knowledge and check if you have really understood the theory.

Equity Boot Camp Quiz (3): Passively Defending Ax

If you are on the flop with A-high and are up against a 3-bet pot, your kicker is decisive. Depending on the size of your kicker, the board texture and your opponent's range, you will often have to give up in such spots. However, there may also be situations that are profitable for you. In the following quiz you can test whether you are able to identify such spots.

Equity Boot Camp Quiz (4): Playing Ax After a 3-Bet OOP

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