Turnplay OOP without initiative with showdown value

Introduction

In this article

Your opponent will bet in 2 of 3 cases
You can call with 27%+ equity
You can call with 22%+ equity after a 3-bet before the flop

In the 'Heads up on the Flop OOP: C/C Flop Without Initiative - With Showdown Value' article, you learned when and why to play check/call on the flop with a marginal hands when you don't have initiative.

One of the central points in this article is: You can generally continue playing with the intention of seeing the showdown with app. 37% equity on the flop after defending your blind with A high. You then play C/C on the flop.

Of course, this doesn't mean you should just switch to a rigid calldown mode when you have 37% equity on the flop. You have to pay attention to the development of the board. Depending on the turn card, a hand that looked like a profitable calldown on the flop may not be playable on the turn any more.

We will now take a detailed look at the rules you should follow when playing your hand under these conditions and how to correctly use the additional information gained on the turn.

DOWNLOADS

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

Excel Chart to calculate the needed equity for a calldown

How much equity do you need for a turn call?

Let's start with the mathematical approach. How much equity do you need to theoretically call a bet on the turn with the intent of going to the showdown profitably?

Initial situation:

Hero is BB

Pre-flop: Button raises, Hero calls

Flop: Hero checks, Villain bets, Hero calls

Turn: Hero checks, Villain bets, Hero???

Now we use our familiar formula:

EV > 0,when EQ > losses / (winnings + losses)

First, we have to be clear on what the winnings and losses would be in this situation. Let's start with the worst case scenario again: your opponent plays the river perfectly. This means your losses will amount to 2 BB, while your winnings only consist of the size of the pot after your opponent's turn bet.

Winnings = 4.25 BB
Losses = 2 BB

EV > 0, when EQ > 2 / (4.25 + 2) = 0.32

If you give your own hand an equity of 32% or higher in the described situation, you can profitably call the turn with the intention of seeing the showdown.

As explained in a number of other articles, it would be quite pessimistic to always assume you are in a worst case scenario. That's why we will now analyze the exact costs for a showdown after a turn bet from the opponent.

Our basic task is answering the following questions:

1: How often will you be confronted with a river bet after the turn bet?
2a: How much equity do you have after a bet from your opponent on the river?
2b: How does this influence your possible winnings and losses?
2c: How much equity do you need to calldown after a turn bet?
3: How much equity do you have against a turn bet which, contrary to the flop bet, can't be considered as fixed betting sequence (FBS)* any more??

* Fixed Betting Sequence: a fixed betting sequence (FBS) is a sequence of bets that solely depends on the pre-flop action and which is always played in the same manner, regardless of one's own hand or the board. The most simple example for a FBS is a continuation bet on the flop against one opponent when you have initiative.

Point 1: How often will the opponent bet the river?

It would be worth a try to ask your opponent nicely for a written account of his betting standards. Unfortunately, most players are very uncooperative when it comes to this request, so you have to use other methods to get your answers.

In this concrete case, we used an empirical approach. The procedure is simple: We asked all PokerStrategy members for their hand histories, reaching from the micro limits up to 100/200. All hands were made anonymous and we only used the hands in which the hero (= TAG) got cards. All in all, this amounted to a total of about 3.2 million hands. All of these hands were then loaded into a database.

To answer the question on how often the opponent bets on the river, we made the following database query:

Hero is in the BB and defends his BB against a raise from MP2, MP3, CO or BU.
Hero is heads up on the flop.
Flop: Hero checks, Villain bets, Hero calls
Turn: Hero checks, Villain bets, Hero calls
River: Hero checks, how often does Villain bet?

All in all, we were left with a total of 2837 hands that met these conditions. Out of these, opponents bet in 1927 cases, or 68% of the time.

In another query, we only used hands from the limits 0.5/1 - 30/60. This query delivered a result of 1616 bets on the river, a bet frequency of 66%. Of course, the sample size for these spots wasn't huge, but it was sufficient to get a good idea of an approximation for the actual betting frequency. Deviations of 2-3% are definitely possible, but at least we now have an approximate value that we can use for further calculations.

From now on, we assume a bet frequency of 2/3 = 0.667.

As the micro limits don't necessarily reflect the kind of opponents you will encounter on the small and mid stakes, hands from the 0.5/1 - 30/60 limits could be the better foundation. As mentioned previously, small deviations are possible, but in the following results, they would hardly have an impact.

Points 2a, 2b, 2c: How high is your equity and how much equity do you need to call?

Let's answer a few more our questions:

2a how much equity do you have against a bet on the river?
2b how does this influence your possible winnings and losses?
2c how much equity do you need to calldown after a turn bet?

We've just established that the probability of a bet on the river can be set at 0.667; now we can calculate the amount of equity we needed to call on the turn. Let's look at the formula again.

EV > 0, if EQ > winnings / (winnings + losses)

Now we have to redefine the variables.

LOSSES

With a bet frequency of 2/3, the costs for a showdown are 1.667 BB on average (1 BB for the call on the turn + 0.667 BB on the river). Again, it would be too pessimistic to assume that the opponent will play the river perfectly every time. You might as well fold every time when you don't think you can bet a bet.

It's more realistic to expect your opponent to play his hand optimally than perfectly. In this case, optimal means playing with a non-exploitable bluff frequency on the river. Such a frequency is attained when 1 / (Pot +2) of his river bets are bluffs.

Example: There are 5.25 BBs in the pot on the river. If 1 / 7.25 (corresponds to 1 / (pot + 2)) of his bets are bluffs, he would have a non-exploitable bluff frequency. On average, you would lose 1 BB in 6.25 out of 7.25 cases, and win 6.25 BBs in 1 out of 7.25 cases, which equates to an EV of 0.

Your equity on the river is defined as 1 / (size of pot after turn bet), which corresponds to roughly 14% in our example with a 5.25 BB pot.

The losses can now be computed as follows: you pay 1 BB on the turn and 0.667 BB on the river. This sums up to a total of 1.667 BBs. Since, however, you still have 13.8% equity on the river on average, your costs on the river sink to 0.667 * (1 - 0.138) = 0.575 BBs

Your losses are therefore 1.575 BBs

WINNINGS

The minimal amount you can win = the size of the pot after your opponent's turn bet, or 4.25 BBs. You could win even more if your opponent bluffs on the river. This so-called 'bluff catch value' is made up of the probability of facing a bet and the probability of facing a bluff on the river.

Winnings = 4.25 BBs + 0.667 * 0.138 = 4.34 BBs

4.25 BBs are already in the pot. Now you add the probability of facing a bet (2/3, or 66.7%) / the probability of that being a bluff (13.8%). You can add 0.09 BB in expected winnings, giving you a total of 4.34 BBs in winnings.

We have now defined our variables fairly precisely, which gives us this complete formula:

EV > 0, when EQ > losses / (winnings + losses)
losses= 1.575 BB
winnings = 4.34 BB

EV > 0, when EQ > 1.575 / (4.34 + 1.575) = 0.266

This means that exactly 26.6% equity would be sufficient for a call. You should round this up to give yourself a small buffer.

You can call a turn bet on a 4.25 BB pot with the intent of going to the showdown with showdown value after having defended your blind when you have 27%+ equity.

Please keep in mind that this value (27%) changes based on blind structure and pot size.

CHANGING VARIABLES

Of course, when it comes to the actual bet and bluff frequencies of your opponents, it' to each his own. This influences the amount of equity needed to call.

Example:

River betting frequency of 100% required EQ = 30%
River betting frequency of 0% required EQ = 19%
River betting frequency of 70% required EQ = 27%
River betting frequency of 65% required EQ = 26%
Bluff frequency of 0% required EQ = 28%

Finally, it's always a good idea to play around with the parameters yourself. You can see a screenshot of an excel sheet that computes the value automatically when you change the parameters below.

You can download it here: excel sheet for the computation of the required equity

You can use this to adjust the parameters when you have a read on an opponent.

Computation of the required equity with the help of an Excel sheet

Point 3: when the turn bet is not part of a fixed betting sequence

Let's get to the last question:

3. How much equity do you have against a turn bet which, contrary to the
flop bet, can't be considered as part of a fixed betting sequence (FBS)
any more?

After computing the required equity for a showdown-bound call, we have to find out what's the best way to determine your equity against a turn bet from the opponent.

Determining the opponent's range is much harder on the turn than on the flop, however. Whereas every player can make a contibet on the flop with his entire pre-flop range, a bet on the turn isn't necessarily an automatic continuation bet, meaning you can't automatically keep your opponent on the same range he had before the flop.

At the same time, this doesn't necessarily mean the opponent's range is stronger after a turn bet. If an opponent is capable of a check behind on the turn, he usually does this for bluff catching and pot control purposes with a hand that has showdown value and dominates a hand like A high. Your opponent will also try to get you off the better hand with hands that you have beat on the turn.

Let's take a look at an example from the article on flop play:

Hero: A

Opponent's open-raising range: (ca. 40%) 22+, A2s+, K2s+, Q6s+,
J8s+, T8s+, 98s, 87s, 76s, 65s, A2o+, K7o+, Q9o+, J9o+, T9o

Flop: J 6 3 Equity: 38% C/C
Turn: 9 Equity: 29% C/C

You have 29% equity against the entire 40% range and can thus profitably play C/C turn with the intent of going to the showdown.

If you assume or know that the opponent is capable of check behind on the turn however, you have to ask yourself with which hands he does this. Even though you can never look inside your opponent's head, a check behind on the turn usually has 2 intentions:

The opponent has SD value, but thinks his hand is too weak for a value bet and wants to avoid a check-raise. He's in position and wants to see the showdown for a maximum of one bet. The opponent's standard play will be to call another BB on the river.
The opponent has a draw but attributes himself too little fold equity from better hands to bet. In this case, he wants to take advantage of the free card and will usually give up his hand to a bet on the river (if he didn't make his draw).

Experience tells us that the first point is the most common reason why TAGs and even LAGs decide to play check behind on the turn.

The possible intentions behind a check behind also depend on the board, of course. On the board in this example, a check behind with a draw is rather unlikely and you can assume that it probably comes from a hand with SD value trying to avoid a check-raise.

Let's suppose the opponent would check behind any A high on the turn, but bet all pairs and all trash hands (K high and worse), with which he hopes to generate some fold equity.

If we remove A high from his range on the turn, we get the following picture:

22+, AJs, A9s, A6s, A3s, K2s+, Q6s+, J8s+, T8s+, 98s, 87s, 76s, 65s, AJo, A9o, A6o, A3o, K7o+, Q9o+, J9o+, T9o

You now have 31% equity with A 2 against his range, as opposed to the 29% you had against his entire pre-flop range.

As you can see, your equity against an opponent that ops for a check behind on the turn with A high in order to see a cheap showdown increases, as he misses out on a value bet and the percentage of bluffs and semi-bluffs in his range increases.

But what if your opponent is capable of checking behind with a draw? Let's assume he would check behind with a good draw like KT and QT. Adding these hands to his A high checks results in the following range:

22+, AJs, A8s, A6s, A3s, K2s+, QJs, Q9s-Q6s, J8s+, T9s, 98s, 87s, 76s, 65s, AJo, A8o, A6o, A3o, K7o+, QJo, Q9o, J9o+

You have 27% equity.

If you assume the opponent will always bet A high for a free SD and only play check behind with draws like KT, QT or T8s, we obtain the following range:

22+, AJs, A8s, A6s, A3s, KJs+, K9s-K2s, QJs, Q9s-Q6s, J8s+, T9s, 98s,
87s, 76s, 65s, AJo, A8o, A6o, A3o, KJo+, K9o-K7o, QJo, Q9o, J9o+

You have 26% equity.

All in all, we have the following picture:

Hero A

against 40% range from BU

Flop: J 6 3 equity: 38% C/C
Turn: 9 equity: 29% against autobet C/C
Turn: 9 equity: 31% against cb Turn with A high C/C
Turn: 9 equity: 27% against cb Turn with A high, KT and QT C/C
Turn: 9 equity: 26% against cb Turn with KT and QT C/F

Even though your required equity is about 27% in all cases, your actual equity can fluctuate depending on the opponent's playing style. Your opponent's range isn't necessarily stronger against your hand after a bet, even if he is capable of playing check behind.

In practice, TAGs usually check behind with hands like A high rather than with draws, as they still hope to make better hands fold to their draws with a bet. You are rarely worse off after a bet from a potential "behind checker" than you were before the flop.

If you have no information about the checking standards of the opponent, you should just assume to be up against his entire pre-flop range. Whenever you do have a read, however, you should definitely take it into account in order to estimate your equity more exactly.

This approach is a good way to calculate whether you have enough equity for a call on the turn or not. As these calculations are usually very hard to make on the fly while playing, we will now take a look at some examples that can help you to develop a feeling for this kind of situation and for estimating your equity. We will, among others things, use the same examples as in the article on flop play.

We will assume all bets on the turn are autobets, as this will allow us to compare individual hands more closely. Once again: Always use the reads and information you have when making a decision!

EXAMPLE 1

You defend your BB against a 40% range from BU:

22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, 87s, 76s, 65s, A2o+, K7o+, Q9o+, J9o+, T9o

Hero A

Flop: T

equity: 40%

C/C
Turn: 6

equity: 43%

C/C
Turn: J

equity: 29%

C/C
Turn: Q

equity: 29%

C/C
Turn: K

equity: 23%

C/F

Hero A 7
Turn: K equity: 27.0% C/C or C/F equivalent

Hero A 8
Turn: K equity: 29% C/C

With a bit of consideration, it should soon be obvious to you that you have enough equity on a T 6 3 flop to continue playing with your A5o. Furthermore, you can also call most turn cards profitably if you're still up against the opponent's complete pre-flop range. K is the only card that will inhibit a profitable calldown with A 5. Even though A 7 doesn't seem so different, you have a whole 4% more equity which makes this a borderline case for a call. This case is so close that it doesn't really matter what you decide to do. With A 8 you have a clear call however.

Please note that we don't need to make any concrete adjustments to the opponent's turn betting range in this example. If he is a thinking opponent, he will see the K or a Q as an 'A high killer' and bet any hand again. A tighter betting range is better from the equity point of view for you anyway. The situation could only worsen if he decided to play Q9 and QJ with a selective check behind after the K on the turn.

Hero A

Flop: T 6 3
Turn: K equity: 25% C/F if your opponent would check behind with Q9 and QJ on the turn.

EXAMPLE 2

You defend your BB against a 25%-range from CO:

44+, A2s+, K7s+, Q9s+, J9s+, T9s, 98s, 87s, A7o+, K9o+, QTo+, JTo

Hero A

Flop: T 6 3 equity: 35% C/F

This board is too weak to continue playing your A high against this much tighter range.

Flop: 9

equity: 39%

C/C

Turn the T into a 9 and you can fight for the pot. Take a look at your equity on a few different possible turn cards.

Turn: 6

equity: 42%

C/C
Turn: 8

equity: 37%

C/C
Turn: T

equity: 22%

C/F
Turn: J

equity: 23%

C/F
Turn: Q

equity: 23%

C/F
Turn: K

equity: 22%

C/F

You see that high cards influence your equity (negatively) much more strongly against a typical CO range than against a range from the BU. Every high card on the turn gives you a whopping 15-16% less equity than a low card like the 8.

Hero A

against a 25% range from CO
Flop: 9

Turn: T

equity: 30%

C/C, the gutshot could save the day
Turn: J

, Q

equity: <27%

C/F

Hero A 8 against a 25% range from CO
Flop: 9 6 3

Turn: T equity: 34% C/C
Turn: J equity: 29% C/C
Turn: Q equity: 29% C/C
Turn: K equity: 28% C/C

Compared to a 25% range from CO

Hero A

Turn: J

equity: 29%

C/C

Hero A 2
Turn: J equity: 23% C/F

Against a 40% range from BU

Hero A

Flop: 9

Turn: J

equity: 36%

C/C

Hero A 2
Turn: J equity: 28% C/C

This clearly shows that your kicker strongly influences your equity. Against the BU raise, your A 8 has a whole 8% more EQ on the 9 6 3 J board than A 2. One of the main reasons is that the opponent will usually raise any ace, meaning you have him dominated more often with a higher kicker.

You are also more likely to have 3 additional outs against a small pocket pair or a low pair.

We could take a look at an infinite number of examples of such situations. You should make this kind of analysis regularly in order to develop a feeling for your equity in these situations.

EXAMPLE 3

Hero BB with 2

vs. 40% range from BU

Flop: A 6 3 equity: 42% C/C
Turn: K equity 27% borderline C/C
Turn: No K equity > 27% C/C

From a mathematical point of view, the turn card is completely irrelevant when you play a baby pair on an A high board and assume your opponent is still on his entire pre-flop range when he bets on the turn. The only real question is: With which hands will the opponent bet again on the turn after you C/C the flop on this board? A lot of opponents will give up their hand.

An example of what is meant: In such a situation, you could make a bluff call on the flop in order to check behind on the turn and complete your bluff on the river. But this is another matter and goes beyond the scope of this article.

EXAMPLE 4

Hero BB with K

vs. 40% range from BU

Flop: 4 2 2 equity: 37% C/C
Turn: < 9 equity > 29% C/C
Turn: 9, T, J equity 27% borderline C/C
Turn: A equity 34%! C/C

With K high, there are not many flops that you can continue playing profitably. However, K 7 can fare better than you would expect when you do hit a decent flop. Low cards give you more than enough equity to keep playing; you would even have a borderline call against 9-J.

The ace is obviously the only high card that allows you to keep playing comfortably, since it is then less likely that your opponent has an A, as well. Consequently, an A is usually a good card when your hand doesn't have A high beat.

Once again, reducing your opponents range is nearly impossible. He will usually continue to bet with his entire pre-flop range in this situation, since he knows you are likely to have overcards (or better).

Taking the rake and blind structure into consideration

Just as on the flop, you also need to take the rake and blind structure into consideration when calculating your needed Equity on the turn. You can how these factors influence your equity with the following excel sheet.
(the sheet is explained in more detail in the article: Heads-up on Flop OOP: C/C Flop without initiative - With showdown value).

Download the Excel Sheet

EXAMPLE

$3/$6, 5-handed, Hero SB

CO raises, Hero 3-bets, CO caps

Flop: Hero checks, CO bets, Hero calls

Turn: Hero checks, CO bets, Hero???

Base EQ on the Turn = 21%
Influence of Rake 4-5 handed $3/$6 = +2%
Influence of 1/3 Blind structure = +0.5%
-> Needed EQ for a profitable C/C on the Turn = 21% + 2% + 0,5% = 23.5%

After a 3-bet before the flop

Aside from after having defended your blind, you will often find yourself oop and without initiative after open-raising and getting a 3-bet from the CO or the BU. How to evaluate this kind of situation correctly can be seen in the 'Heads up on the Flop OOP: C/C Flop Without Initiative - With Showdown Value' article.

We will now deal with play on the turn after you've decided to play C/C on the flop. The necessary mathematics have already been established in the first part of the article. We showed that you can continue to fight for the pot after a continuation bet on the turn when you have 27-28%+ equity and when there are 8.5+ BBs in the pot.

A few parameters change in 3-bet situations:

A different pot size (influences the possible winnings)
A different hand range for your opponent (influences your equity)
A different betting frequency on the river (?) (would influence possible losses and will be explained later)

We resume with a situation that has already been analyzed in the article on flop play:

Pre-flop: Hero is CO with A 8

2 folds, Hero raises, Button 3-bets, Blinds fold, Hero calls

Flop: (7,5 SB) T 5 3 (2players)
Hero checks, Button bets, Hero calls (31% EQ)

Turn: (4,75 BB) 6 (2players)
Hero checks, Button bets, Hero???

To compute the necessary equity for a call on the turn, we take a look at our formula again:

EV > 0, if EQ > losses / (winnings + losses)

As we did in the first part, we have to define the variables for the possible winnings and losses again. We encounter the same question we previously did: how often does the opponent bet on average on the river after a bet on the turn?

As we saw previously, we used an empirical approach to be able to make a fair estimate about how often you will be confronted with a river bet. We filtered the 3.2 million hands, played by TAGs, according to the following rules:

Pre-flop: Hero is in front of the BU and raises, Villain is not SB or BB and 3-bets
Flop: Hero checks, Villain bets, Hero calls
Turn: Hero checks, Villain bets, Hero calls
River: Hero checks, Villain bets in what % of all cases?

The results are as follows: after a pre-flop 3-bet, the villain will bet the river in position in ~68% of all cases
(1023 out of 1499 spots).

In comparison: we had an average value of 66.67% in blind-defense scenarios.

Even though you could assume a stronger hand range after a 3-bet and thus would expect a value bet on the river more frequently, the analysis shows that there is only a minor difference between this and a "BU vs BB" situation. The betting frequency on the turn, however, shows a clear difference: while the opponent bets about 70% of the time in a "BU vs BB" situation, he tends to bet 79% on the time in 3-bet situations.

Thanks to this information, we can now define the variables for the possible winnings and losses, allowing us to find out the required equity for a call on the turn with the intent of going to the showdown.

EV > 0, if EQ > losses / (winnings + losses)

We saw in the first part how to compute these variables in detail. This time, we will leave the work to Excel and just fill in the changed parameters, namely:

Pot after a turn bet (in BB) = 5.75
P(river bet) = 0.68
Pot after river bet = 7.75

Computation of the required equity with the Excel sheet

In the described situation, you need 21.4% equity in order to continue playing. Again, round this number up to give yourself a small buffer.

After a pre-flop 3-bet, you can call a turn bet out of position and with showdown value with the intent of going to the showdown when there are 5.75 BBs in the pot and you have at least 22% equity.

Once again, different blind structures and pot sizes influence the amount of equity you need to stay in the hand.

Let's take a look at a few more examples to help give you a feeling for these situations. Once again, we will assume that any bet on the turn is an autobet. This assumption is also more justifiable, since our data base shows us that a bet is made nearly 80% of the time after a 3-bet before the flop, compared to 70% of the time in a blind-defense scenario.

However, this doesn't mean every opponent will make an autobet on the turn.

EXAMPLE 1

Let's first look at the example from the beginning of this section once again.

Hero CO with A