Heads-up on the Flop OOP: C/C Flop without Initiative - with Showdown Value

The video to the  article

Introduction

In this article

• As of 37% equity Ace high becomes profitable

• As of 38-39% against smart turn bettors

• As of 35% against tight turn bettors

• As of 28-29% after pre-flop 3bet

It happens very often that you defended your big blind with Ax and missed the flop. This is the typical situation in which you realize the bad playability of A high with a small kicker.

Your Options after the Flop

Actually you have no idea where you stand after the flop and, forlorn, you have to play out of position against the pre-flop aggressor. Fact is though, that it is too weak to always simply play C/F if you didn't hit a pair or a strong draw - since A high is often the best hand against steal raises even if it remains unimproved.

Yet this hand is usually also too weak for C/R and as you have showdown value yourself, it's also difficult to get better hands to fold. Thus in this situation check/call flop is often the only option to usefully continue playing your equity after the flop.

But how are you supposed to know if your hand is good enough to still be played or not? The following article will give you the needed information. It will show you how to evaluate your hand after the flop without a pair or a strong draw, and how to decide if you can continue playing your hand or not. For this we generally assume that the opponent will ALWAYS make a continuation bet on the flop. In real life, this is the case >95% of the time.

DOWNLOADS

Excel Chart to calculate the needed equity for C/C Flop

Excel Chart to calculate the needed equity for a calldown

First thoughts about the necessary equity

Let's assume you have A 2 in the BB. The button open raised, you called. Your expected value for the further progress of your hand is:

EV for your hand = Chance to win x Profit – Chance to lose x Loss

From a mathematical point of view it looks like this:

EV = EQ x P – (1-EQ) x L
EQ = Hero's equity on the flop = chance to win
1 – EQ = Chance to lose
P = Profit = Pot on the flop + bonus winnings
L = Loss = Post-flop losses if you continue playing your hand and lose

This formula is valid for almost every EV calculation in poker. The complexity lies in the calculation resp. definition of the variables profit (P) and loss (L). Therefore it is first determined under which premise the EV > 0, which is done by simply revising the previously shown equation:

EV > 0, if applies:
EQ x P > (1 – EQ) x L
EQ x P > L – EQ x L
EQ x P + EQ x L > L
EQ x (P + L) > L
EQ x (P + L) – L > 0

If we want to calculate the necessary equity to continue playing, we resolve the equation for EQ:

EV > 0, if EQ > L / (P + L)

In words:

EV > 0, if EQ > Loss / (Profit + Loss)

With this simple formula you are able to quickly calculate the minimum equity you need when profit and loss have been determined.

Now we have to create the basic conditions to calculate profit and loss. For that we have to ask ourselves:

• How often will the opponent bet the turn again after a C/C flop?

• How high are our implied odds when we improve?

• How much can we save if we make smart folds?

Let's begin with the worst case: You are facing an opponent who always plays perfectly against you after the continuation bet on the flop, while you strictly play C/C on every street. In this case you always get to the showdown and lose 2,5 BB, but only win 2,75 BB (2,25 BB at the flop + 0,5 BB continuation bet) if you are ahead, as the opponent won't give you more money on the big streets.

So here applies:

EV > 0, if EQ > 2,5 / (2,75 + 2,5)  EQ > 2,5 / 5,25 = 0,48 = 48%

Thus you need 48% EQ at the flop to continue playing profitably. This is the very lowest margin as we explain the worst case here. Above this equity, any fold would be a fatal mistake.

Let's assume the opponent is a robot who stubbornly bets through every street. In this case L = 2,5 and P = 4,75 (2,25 BB at the flop + 3 x opponent bet post-flop).

Now applies:

EV > 0, if EQ > 2,5 / (4,75 + 2,5)  EQ > 2,5 / 7,25 = 34%

In this case you're able to profitably play call down, if your equity on the flop is at least 34%.

In real life, the truth is always somewhere in between. Let's now assume that the opponent always bets the flop and turn, but plays the river perfectly. Thus our costs are still at 2,5 BB, the profits at 3,75BB (2,25 BB at the flop + 1,5 BB post-flop for bet flop and bet turn).

This results in:

EV > 0, if EQ > 2,5 / (3,75 + 2,5)  EQ > 2,5 / 6,25 = 40%

In this case you need 40% EQ to continue playing after the flop.

Further refinements

The deliberations so far, which lead to 40% equity as the lowest margin for a profitable continuation after the flop, ignored 3 points:

1. You don't stubbornly play call down with every hand, no matter how the board develops, but you also make intelligent folds.
2. The opponent could skip value bets on the river, and thus not always play perfectly.
3. You have implied odds if you hit an out, preferably the ace.

Points 1 and 2 decrease your losses, point 3 increases your profits.

But back to the beginning. Let's assume you have A 2 in the BB. Button open raises, you call. We pick the opponent who always bets the flop and turn. Theoretically, you could always simply play call down after the flop with an equity of more than 40% and automatically make profits.

But as you will make smart folds in certain situations or raise, you will need even less equity in theory:

EQ > 1 / (2,50 + 0,12 * 0,7 BB) = 1 / 2,58 = 39%

Explanation of the formula: 2,5/6,25 = 1/2,5 = 40% EQ, in accordance with the previously shown reference point. In the numerator we'll now add 0,12 * 0,7 BB. 0,12 is the probability to hit an ace, which gives you an assumed 0,7 BB of implied odds.

But it goes on even further: The opponent will not always also bet the river when we are unimproved, he will also miss value bets. Furthermore you are able to make a good fold on turn or river on certain boards.

On average you can assume though, that you will be able to continue playing your hand with showdown intention, with A high after a blind defense, when you have about 37% equity on the flop.

Examples with the Equilator

Hero: A 2

Opponent's open raise range at the button: (about 40%) 22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, 87s, 76s, 65s, A2o+, K7o+, Q9o+, J9o+, T9o

If Hero sees the flop with A high, it could look like this:

Flop: K T 6 Equity: 25% -> C/F Flop: T 9 3 Equity: 31% -> C/F Flop: T 8 3 Equity: 35% -> C/F Flop: K 6 3 Equity: 33% -> C/F Flop: Q 6 3 Equity: 37% -> C/C Flop: J 6 3 Equity: 38% -> C/C Flop: K 3 3 Equity: 40% -> C/C

Hero: K 7

With K high it already becomes decidedly more difficult to reach 37% EQ.

Against the previously mentioned 40% range of a button raiser, the situation looks like this:

Flop: Q T 6 Equity: 23% -> C/F Flop: T 8 3 Equity: 26% -> C/F Flop: 9 6 3 Equity: 30% -> C/F Flop: 5 4 2 Equity: 35% -> C/F Flop: 4 2 2 Equity: 37% -> C/C Flop: 2 2 2 Equity: 40% -> C/C

Hero: Q 7

With Q high the fun really comes to a grinding halt against a button raise. Against the previously mentioned 40% range of a button raiser:

Flop: 2 2 2 Equity 32% -> C/F

Hero: 2 2

If Hero has a pair, the situation clearly improves. Let's pick the worst pair on unpleasant flops. Against the previously mentioned 40% range of a button raiser:

Flop: A 6 3 Equity: 42% -> C/C Flop: Q J 3 Equity: 40% -> C/C Flop: K Q 3 Equity: 36% -> C/F Flop: K Q 3 Equity: 29% -> C/F Flop: A K 3 Equity: 28% -> C/F

You see that you can continue playing almost any pair. Only the absolutely worst flops have to be folded.

Hero: 3 2

If you had the smallest low pair instead of a pocket pair, your equity improves considerably as you now have more outs for a two pair. Against the previously mentioned 40% range of a button raiser:

Flop: K Q 3 Equity: 43% -> C/C (36% Equity with 2 2)

The low pair gives you a substantial 7% more EQ than the underpair with 2 2, which only had 36% equity on the same flop .

Hero: A 2

Next we will track the influence of a bigger raise range. We give the button a looser steal range this time.

Open raise range of the button: (52%) 22+, A2s+, K2s+, Q2s+, J6s+, T7s+, 97s+, 87s, 76s, 65s, 54s, 43s, A2o+, K2o+, Q7o+, J7o+, T8o+, 98o+

Flop: K T 6 Equity: 32% -> C/F (25% equity against 40% range) Flop: T 9 3 Equity: 38% -> C/C (31% equity against 40% range) Flop: K 6 3 Equity: 39% -> C/C (33% equity against 40% range) Flop: K 6 3 Equity: 37% -> C/C

Against a very loose open raise range of the button you can continue playing A high hands on many boards, even if they don't look nice. Against the 52% range, you would have a pre-flop equity edge with A 2, and could theoretically even 3bet. But as you play OOP a call is often better if you, as a good player, are able to correctly evaluate your hand at the flop.

Any number of examples is possible here. On the table you don't have the opportunity to calculate the EQ during the hand, but with enough examples over time you will get a feeling for the patterns which will intuitively guide you to the correct decision.

Examples of such patterns are:

• Against a button raise, almost any pair is playable in the BB.

• On paired ragged boards even K high is playable.

• With two cards in the playing zone, A high is usually at < 35% EQ.

• … create further patterns

Keep in mind that the decisions so far were not about you peeling to the turn, but to figure out if you have a hand which has the potential to reach a profitable showdown. How you simply play by odds and outs to see the turn or not will be explained in the article Check/Call Flop without Initiative and without Showdown Value.

Influence of rake on the needed Equity

As shown you need at least 37% equity in order to profitably play C/C on the flop with ace high in a blind defence situation given ½ SB blind structure. Yet you have to in every situation also take the rake into consideration. You therefore need to subtract this amount from your expected winnings, which in turn will influence the minimum equity needed.

You are in a familiar situation: Hero BB: Button raises, Hero calls.

You already know the formula for calculating your needed EQ.  Now we take rake into the calculation.

EV > 0, when EQ > Losses / ((Winnings – Rake) + Losses)

The expected winnings are 3,75 BB. Should you win the hand, the rake will lower the expected winnings by an average of 0,25 BB. As a result:

EV > 0, when EQ > 2,5/ ((3,75-0,25) + 2,5) = 41,7%

When you subtract 3% from the 41,7% - just as in the example 40%-3% = 37% - you end up with 38,7% Equity.

That means when taking the additional cost factor of rake into consideration you need about ~39% Equity, in order to profitably play C/C on the flop.

With an approximate added EQ of up to 2%, the rake represents a significant factor when calculating your minimum equity needed on the flop. .

Only after moving up to the limits of 15/30 and higher can you start ignoring it in your calculations.

Influence of the blind structure on the needed EQ

If you defend your big blind, the pot size may slightly vary depending on the blind structure. Thus the pot in a 1/3 structure is at the flop 1/6 SB smaller, but in a 2/3 structure 1/6 SB bigger. The blind war won't be treated here, as you play in position in this spot, which will be discussed in a special article.

If we include the changed pot size into the already known formula: EV > 0, if EQ > Loss / (Profit + Loss), it ensues that the blind structure makes a difference of up to 0,5% for the necessary equity at the flop.

This results into the necessary equities for a potential call down at the flop:

1/3 SB structure: 37,5%
2/5 SB structure: 37,3%
1/2 SB structure: 37%
2/3 SB structure: 36,5%

Chart for the calculation of the needed EQ to play C/C Flop

By using the following downloadable Excel-chart you can easily calculate the needed equity for playing C/C on the flop in different situations.  

Download the Excel Chart

For making the calculation you need to take the following steps:

• Calculate your base EQ by evaluating the pre-flop action.
• Take the influence of the rake into account.
• Take the influence of the blind structure into account.
• Calculate your needed EQ.

PartyPoker 5$/10$

3-handed: Button folds, Hero SB raises, BB 3 bets, Hero calls

• Base EQ on the Flop = 33%
• Influence of the Rake 2-3-handed 5$/10$ = +0.5%
• Influence of /5 Blindstruktur = +0,3%
• -> Needed EQ for a profitable C/C Flop = 33% + 0.5% + 0,3% = 33.8%

As you can see, the rake and blind structure have a significant influence on the needed EQ, so you should account for them on the flop.

Attention: Since the rake and blind structure can vary, all further calculations will only take the base EQ into consideration.  Consider that you have to adjust them according to your own limits and the blind strucuture of the site you are playing on.

Adaptation against smart turn bettors

In the previously shown analyses we assumed that your opponent bluntly plays bet flop and bet turn. If he doesn't do that in real life, it of course changes the situation when you always play call down. In this case it decreases your profits.

If we assume that the opponent always “smartly” conti-bets the turn in only 80% of the cases and we don't make any profit on a check behind, our average profit only amounts to 3,55 BB (2,25 in the pot + 0,5 BB conti-bet flop + 1BB * 0,8 conti-bet turn).

The ensuing result:

EV > 0, if EQ > 2,5 / (3,55 + 2,5) = 41,3%

Essentially you would only need 41,3% EQ in this situation to be able to continue playing. One example here would be an opponent who increasingly plays check behind on the turn even with A high. In this case you are dominated and barely gain any profit from the free card. On the other hand you are also able to increasingly put in good folds on the turn in reaction to his bet (which in this case means more strength).

You see that at this point many parameters affect the situation, which makes things randomly complicated. But keep in mind that an opponent who smartly uses his conti-bets at the turn and avoids partially “useless” bets, slightly worsens the situation for a call down.

By how much is barely quantifiable in exact numbers, as generally, a very high bet frequency on the turn without a pair is the optimal playing style against the C/C line with SD value. But if you have a good opponent who is difficult to outplay, you should increase your minimally required equity to about 38% to a maximum of 39% on the flop.

Practically this means: If the decision becomes very marginal, it's preferable to use the fold button, especially against smart aggressive opponents. With more than 39% EQ, a fold is almost always a mistake though if you have understood the principles of the C/C line and also know how to play your hand on the turn.

Adaption against weak turn bettors

If your opponent often plays check behind on the turn, you could assume at first that your expected profit decreases and thus your necessary equity on the flop increases. But this isn't the case, as a) the opponent often gives away free cards with too many check behinds from which you could profit, and b) bluffs, against which you would fold on the turn, give up too early so that you sometimes win the hand after a check behind turn and a check/check river.

Thus your costs for a call down decrease significantly. From this it follows that you can call even looser against such opponents. By how much exactly is once again hardly quantifiable, but with a 35% equity you can definitely continue playing your hands with SD value on the flop.

Furthermore, you will find many good folds against turn bettors who are too tight, which decreases our total costs. From this it of course follows that you yourself have to play tighter on the turn accordingly, as a bet from such an opponent has to be treated with more respect than from a “blind” turn bettor.

A rough influence on determining the opponent's bet frequency on the turn is the “continuation bet turn” value, which PokerAce is able to show you. An average TAG has a value of about 70%. If he moves towards 80%, he blindly bets the turn too often, but if he gets to 60% or below, it seems that the opponent rarely bets the turn. You have to keep in mind that you need at least about 1000 hands to have a sufficiently big enough sample size to evaluate your opponent in this respect.

You see that you are often able to continue playing profitably on the turn with A high even without a pair or without a strong draw on the flop, as you have a showdown value with this hand and are able to win it even unimproved. At first, the passive line looks very fishy, but it also avoids your vulnerability for bluff/semi-bluff raises on the turn if you want to play aggressively. Furthermore you are able to induce bluff bets from your opponents.

Important: The introduction of the C/C line with the previously mentioned hands requires a special balancing. Otherwise a good opponent is able to anticipate that you only have a marginal hand after C/C, as you usually only play C/R with a good draw and pairs. Therefore it is important that you have also internalized the chapter Turn play OOP without initiative before you apply the here described strategy.

After pre-flop 3bet

We immediately start this subchapter with an example:

Preflop: Hero is CO with A 8
2 folds, Hero raises, Button 3-Bets, Blinds fold, Hero calls

Flop: (7,5 SB) Q, 7, 4 (4players)
Hero checks, Button bets, Hero?

In this situation two defining parameters have changed. For one thing, your pot odds at the flop following the button's 3bet and the folded blinds are now 8,5:1 instead of 5,5:1 as in the previous blind defenses. For another thing, you have to consider your opponent's range even more, as it is not a steal raise from the button, but a 3bet against your steal raise.

But now you face this unpleasant flop. What do you do in such a situation? How can you evaluate if you are able to continue playing your hand or not?

You already learned the basic answers to this question in the previous chapter. The basic prerequisite is an opponent who always bets flop and turn, just as it usually happens in real life. After the pre-flop 3bet, he often has a good hand, and as the flop will be rarely folded due to the bigger pot, his continuation bet will next to always follow on the turn. This bet could then be from a made hand or A high. Sometimes the opponent might not have anything at all, but he will still bet to bluff you. No matter what, the bet on the turn will come even more frequently than in the previously elaborated blind defense cases.

We use the same formula here:

EV(Call down) > 0, if EQ > Loss / (Profit + Loss)

This is same formula as with a blind defense, but now the parameters have changed.

Profit: The profit with very smart river play of the opponent now amounts to 5.25 BB (3.75 BB on the flop + 1.5 BB for bet flop bet turn)

Loss: The usual 2,5BB for the call down

The result:

EV(Calldown) > 0, if EQ > 2.5 / (5.25 + 2.5) = 0.323 = 32.3%

If you bluntly play call down from the flop on, you would need at least 30.3% equity for 8,5:1 on the flop HU. Here potentially mitigating circumstances also have to be taken into consideration as you won't blindly call down no matter what. The opponent will leave out value bets as well (nobody is able to play the river perfectly) and you also have implied odds if you hit. As already seen above, these circumstances amount to about 3%-4% EQ diminution.

Now let's figure out your equity in the previously mentioned hand. We assume that the opponent follows PokerStrategy's 3betting standards.

Preflop: Hero is CO with A 8

3betting range of the button (according to the Pre-flop Expert Theory Gold section (link)): 44+, A5s+, KTs+, QJs, JTs, A8o+, KJo+

Flop: Q 7 4 Equity: 26%

This flop isn't really friendly and you aren't close to the necessary 27-28% EQ to be able to call. You have to play C/F flop here.

To get a feeling for which flops are playable and which aren't, let's change this one a bit and observe the effects on your EQ.

Flop: K Q 7 Equity: 19% -> C/F K+Q are deadly Flop: K 5 3 Equity: 22% -> C/F Even the lone king leaves a sour aftertaste on the flop Flop: J 6 4 Equity: 24% -> C/F Also without the Q it's not enough Flop: K 5 3 Equity: 25% -> C/F Despite back door flush draw not enough Flop: J 5 3 Equity: 26% -> C/F Not worth it Flop: T 5 3 Equity: 31% -> C/C Without a face card it's suddenly playable Flop: Q 5 3 Equity: 27% -> C/F Absolutely borderline, better C/F Flop: Q 4 3 Equity: 28% -> C/C Absolutely borderline, lowest C/C margin Flop: Q 7 4 Equity: 28% -> C/C The back door flush draw allows a call Flop: J 5 3 Equity: 29% -> C/C The back door flush draw allows a call Flop: T 7 7 Equity: 36% -> C/C Paired board looks good Flop: K K 3 Equity: 23% -> C/F The king remains a bad card

These analyses show that very subtle changes on the board are enough to push your equity from the playable to the unplayable zone.

Nonetheless we want to try and find some patterns which give you some rough clues about the playability of your hand:

• A king on the board is generally bad

• Back door flush draws make many hands playable (if there is no king on the board)

• Without face cards most boards are playable

• Paired boards without a king are generally playable

• … create further patterns

Here as well the reminder that this is the answer to the question whether to play C/C flop with showdown intention or not. This is an essential approach, as a substantial part of the equity of A high hands is achieved through the showdown value. After all, you might hold the best hand even if it remains unimproved.

Determination of the opponent's range

A major problem when determining your equity is of course the range of the opponent. Some make very tight pre-flop 3bets, others very loose 3bets. Let's show you how the 3bet range is able to influence your equity on the flop. For this we'll use the first example again.

Preflop: Hero is CO with A 8
2 folds, Hero raises, Button 3-Bets, Blinds fold, Hero calls

Flop: (7,5 SB) Q, 7, 4 (2 players)

We take different 3betting ranges from the button:

A) 44+, A5s+, KTs+, QJs, JTs, A8o+, KJo+ -> Equity: 26%
B) 55+, A6s+, KJs+, QJs, A8o+, KQo -> Equity: 19%
C) 22+, A2s+, KTs+, QTs+, J9s+, T9s, 98s, 87s, A6o+, KTo+, QJo -> Equity: 32%

Range A) matches the 3betting chart according to the Pre-flop Expert Theory Gold. Against this range we already analyzed that you have a marginal C/F on the flop with your 26% equity.

If we now take a very tight player with range B), it's hardly surprising that your equity decreases dramatically. Against this range, you only have 19% EQ on the flop.

A player with range B could be someone with stats like e.g. 23/14/1,7/40 (VP$IP / PFR / AF / WTS). It doesn't happen very often anymore on higher limits, but you might still come across the odd rock every now and then. But if you play against e.g. 38/27/2,0/42, you eventually have to assume that the opponent plays looser than our 3betting chart.

Against an increased range with case C, you only have 32% equity on the flop and have to play C/C flop at first. The change from a tight to a loose 3betting range in the described situation makes an equity difference of 13% for you. For this kind of equation they are worlds apart.

The problem is of course that you won't always have meaningful stats for every player at your disposal. Furthermore, the mere PA stats only reveal a limited view of your opponent's 3betting range. For more precise informations it is thus crucial that you watch your opponents.

Nonetheless we can try to create a pattern to determine the opponent range. It will never be very precise, but we'll try to get as close as possible.

PokerStrategy's 3betting chart should always be used as your default for the 3betting range of the opponent. Take a tighter range if the stats imply so (e.g. tighter than 25/18/2,0 with 1/2 SB Structure) or a looser range if the opponent has >25 PFR. The most important factor hereby is your power of observation. Stats alone only give you first hints about the range, but you should be curious enough to collect empirical data.

In plain language: Even if you don't actively play a hand, do NOT watch TV, chat, surf or stare at the wall, but watch your opponents. If there have been 3bets pre-flop, take notes in case of a showdown if the opponent 3bets too loosely pre-flop (a simple notice could be something like this: 3bet from Bu with 65s vs CO Raise).

For too tight 3betting it's of course not possible to collect empirical data directly. Here your PT/PSE stats have to suffice along with the your monitoring eventually, if your opponent is generally very passive pre-flop. Keep in mind though that you need a sufficient sample size for such observations, as even the biggest LAG could be card dead for quite a while.

The determination of your opponent's range is difficult and will never claim to be absolutely precise. But if you observe your opponents closely and include their PT/PSE stats, you will reduce the average discrepancy of your assumed range to the actual range to a minimum. With enough effort you will thus get close to the optimal playing style and make the most out of your marginal hands.

Conclusion

In this article you've learned the concepts of how to play on the flop OOP without initiative and with showdown value. You see how extremely important it is to correctly evaluate your equity on the flop. As your opponent also misses in 2 out of 3 flops, an A high or sometimes even a K high hand turns into a playable hand which definitely has the potential to get to the showdown even unimproved.

This article showed you, which parameters you have to consider to evaluate your hand on the flop OOP and without initiative, to come up with the best possible decision about the further progress of your hand.

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Related articles: Heads-up on Flop: Introduction Heads-up on Flop OOP: C/C Flop without Initiative - without Showdown value Forum discussions: Feedback thread for this article