Heads-up on the Flop OOP: C/C Flop without Initiative - without Showdownvalue

Introduction

In this article

• at least 4.5 outs if the opponent always bets the turn
• at least 3.73 outs if the opponent never bets the turn
• in reality: Nearly always go to the turn if you have 4 outs or more!

The line C/C with no pair and no showdown value (SD-Value) will seem strange at first, considering that you want to play draws aggressively to make better hands fold.

Take the following hand, in which you defend your big blind against a 40% range from the button:

Hero: 6 4

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

Flop: 8 7 2 Equity: 30%

Here the standard move would be to C/R the Flop. You only have a gutshot plus two potential live cards, but you may be able to push the button off A high, K high, Q high J high or even a small pocket pair.

But what if you don't have any fold equity? Let's assume that your opponent will never fold a better hand. In this case you would be completely dependant on your outs.

How do you decide whether you can continue playing your hand profitably? You shouldn't base this decision on the equity on the flop, as your hand has no showdown value. You should instead base it on the possibility of improving on the turn or river.

At this point we need to determine whether you should continue with your hand on the flop. You're getting pot odds of 5.5 to 1 on a bet from the button. If you ignore the implied odds and play strictly by odds and outs, then for C/C flop you need 1/6.5 * 47 Outs = 7.2 Outs. However, 7.2 is too high, seeing as you ...

• ... definitely have implied odds, especially as you have a gutshot, which would give you the 2nd nuts.
• .. could also get a free card, in which case you could see the river for free.

To get further insight, let's look at the two extreme scenarios:

• The opponent ALWAYS bets the turn.
• The opponent NEVER bets the turn.

If the opponent always bets the turn...

In this case we can use our old formula:

EV > 0, if EQ > loss / (profit + loss)

This time the loss is easy to calculate. The loss amounts to 0.5 BB, as the only decision we make, at this point, is whether to call a bet on the flop.

The profit amounts to at least 3.75 BB here (2.25 BB pot size on the flop + 1 BB turn bet from the opponent). However, if you hit the gutshot and your C/R on the turn gets paid off heavily, then you will win an extra 2 BB, bringing your profit to 5.75 BB. We can now simply calculate the required outs on the flop for different implied odds:

1) profit = 5.75 BB
EV > 0, if EQ > 0.5 / (5.75 + 0.5) = 0.08

Caution: As we have set the losses at 1 SB, this equity only applies for the possibility of hitting an out on the turn. One can convert this value into outs.

1 Out = 1/47 = 0.021
0.08 / 0.021 = 3.8

If you count 2 BB implied odds in addition to the opponent's autobet, then you would only need 3.8 outs on the flop, as long as these outs would definitely give you the best hand.

Here is a simple table for the required outs. Bonus bets from the opponent from the turn onwards constitute the implied odds. As we are assuming that he will always bet, this value is always equal to or greater than 1.

Don't forget that this table only applies to a flop situation in which you are getting pot odds of 5.5 to 1. If you have different odds, then your expected profit changes. Change the profit in the above mentioned formula EV > 0, if EQ > loss / (profit + loss), estimate your implied odds, and you can calculate the required outs yourself.

How high are your implied odds in the above situation with 6 4 against the button raise on the 8 7 2 flop? This value cannot be determined precisely, but as the opponent always bets the turn, you will definately get at least one further BB if you hit your gutshot. Your implied odds here are at least 2 BB, so that you require at least 4.5 discounted outs.

However, one must not overestimate the implied odds, as you will often hit a 6 or a 4 on the turn. You will of course also stay in the hand with these cards, but won't have any implied odds, and may even have reverse implied odds, as you will often lose with a 4 or a 6 despite pairing up.

Remember: If you don't think you can get better hands to fold and expect the opponent to always bet the turn, then you need at least 4.5 clean discounted outs to be able to play C/C flop profitably. If it looks like your implied odds are lower, then you should tend towards 5 outs.

You definitely have at least 4.5 clean discounted outs in the 6 4 hand, with the 4 outs to the straight counting fully, as the only hand that would beat the straight is 96. This isn't in the opponents range, so this situation is similar to drawing to the nuts. Now you only need half an out, which you are certainly getting with the 4s and 6s.

Let's take a look at the range from the button and see against which hands 4s and 6s aren't outs for us: 22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, 87s, 76s, 65s, A2o+, K7o+, Q9o+, J9o+, T9o

The opponent holding AA-66, A8, A7, K8, K7, Q8s, Q7s, J8s, J7s, T8s, 98s, 87s, 76s or 65s means that you don't have 6 outs with the 6s and 4s.

Then again, the opponent holding A9+, K9+, Q9+ or J9+ means that you have all 6 outs on the turn with the 6s and 4s, even though the opponent will then of course have redraws. It's obvious the button will be raising a wide range of hands, so you have 10 outs on the flop (4 for the gutshot + 6 for the holecards). Therefore you easily have the 4.5 required outs and can comfortably continue with your hand.

However, remember that the 4.5 required outs are so-called 'nuts outs' that give you the full implied odds. You must therefore discount the 6 outs for the 6s and 4s accordingly, as these cards can produce reverse implied odds because you will often lose even if you have hit these outs.

Therefore, you have about 5.5 - 6 discounted outs on the flop with 6 4 . Hole cards to which there are 2 overcards on the board are each worth around 1 out in this calculation.

Tip: If the opponent were to raise from the cutoff instead of the button in this hand, with a tighter range of just about 27% (44+, A2s+, K6s+, Q8s+, J8s+, T8s+, 98s, 87s, A7o+, KTo+, QTo+, J9o+), then this would hardly change your equity.

Hero: 6 4
Flop: 8 7 2 equity vs button (40%) -> 30%
equity vs cutoff (27%) -> 30%

In this case, the reason is that the opponent raises fewer hands that contain an 8 or a 7 from the cutoff. You may run into overpairs more often, but not hands like K7o.

The opponent never bets the turn

If your opponent were to never bet the turn, then two parameters would change. On the one hand your implied odds drop. From the turn onwards they amount to less than 1 BB on average, as the opponent would invest much less in the hand and the pot would stay small.

On the other hand, you'll always get a free card, so that you can see the river for free and have an additional chance to hit an out.

This additional probabitily of hitting an out is easy to calculate. Let's examine the standard situation, which is that you are defending your big blind against a button raise. You check the flop, he bets, you have pot odds of 5.5 to 1. The question is: How many discounted outs do you need to call the flop if you know that you'll see the river for free?

The following is the case:

probability of hitting an out on the turn or river =
1 – (probability of not hitting any outs) = 1 - ((47 – outs) * (46 – outs) / 47 * 46)

As soon as odds of hitting an out are higher than the pot odds of 5.5:1, you can call the flop. Pot odds of 5.5:1 correspond to 1 / 6.5 = 15,38%. Therefore, you only need 15.4% on the flop here to call a bet. That amount of equity is reached with 3.73 Outs.

Here's a table to show you these relations:

This table shows you how you can use your outs to determine the pot odds required to call a bet on the flop if you can assume that you'll get a free card after the turn.

We use 'P(no Hit)' and 'P(Hit)' respectively to name the probability of hitting an out that you have on the flop by the river. It doesn't follow that P(Hit) is equal to your equity. In this case, the equity is identical to the outs, as you'll always fold the river unimproved and therefore have hardly any SD-value.

Here you must again take into consideration that the implied odds or reverse implied odds aren't included in the calculation. On the one hand, you can get additional profit if you hit by the river, but on the other hand, you'll often hit a pair and still loose. A more in-depth analysis isn't useful at this point, as the premise that the opponent will never bet the turn is unrealistic anyway. Nevertheless, it's clear that a free is worth more than the one BB additional implied odds that you would be getting in the case of an autobet from the opponent on the turn, as you need 0.8 fewer outs for a call in the case of an autocheck than in the case of an autobet (4.5 outs).

Conclusion

In reality, of course, people bet the turn in heads-up play more often than they check behind. Of course, this doesn't mean that people always bet. As an approximation, one can say that you should always see the turn if you have at least 4 discounted outs. Therefore, it is, for example, clear that with pot odds of 5.5 to 1 in heads-up you must never fold a gutshot.

The calculations also show you that the more often the opponent gives you a free card on the turn, the more loosely you can call. You can make a rough estimate of the frequency of your opponent checking behind on the turn based on the "Continuation Bet Turn" value that Pokerace gives you. On average, this value is around 70% for TAGs. If the opponent has a much lower value (e.g. only ca. 60%), then you can try to play marginal hands profitably with these "free card calls OOP".

As a consequence, the following points are usually prequisites for the C/C OOP line without SD-value:

• You don't think you can make your opponent fold a better hand by check-raising often enough.
• You have at least 4 - 5 clean discounted outs. The more aggressively your opponent plays on the turn, the closer your required amount of outs is to 5. The more passively your opponent plays the turn, the closer your required amount of outs is to 4. The amount of outs you require depends on the implied odds you'll have when you've hit an out. The closer hitting an out brings you to holding the nuts, the higher the implied odds.

Examples

Hero: J 9

Villain's range from the button: (ca 40%) 22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, 87s, 76s, 65s, A2o+, K7o+, Q9o+, J9o+, T9o

Hero: J 9
Button raises, Hero calls

Flop: T 6 2 Equity: 26%

We will divide possible opponents into three categories:

• a) TAG
• b) SD-bound and passive on the big streets
• c) extremely aggro-LAG

As first, you need to determine whether this hand is generally worth playing on with. How many outs do you have here? With two backdoor draws and two potential live cards you should have at least 5.5 to 6 outs.

Therefore, you must definately play on with this hand. If you think the opponent might fold better hands, then you should play C/R flop, bet turn. If you think it unlikely that you can make your opponent fold, then play C/C flop.

Therefore this is how you should play:

• if a), then C/R flop vs TAG
• if b), then C/C flop vs SD-bound calling station
• if c), then C/C flop vs maniac

Hero: T 9

Villains range from the button: (ca 40%) 22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, 87s, 76s, 65s, A2o+, K7o+, Q9o+, J9o+, T9o

Hero: T 9
Button raises, Hero calls

Flop: J 5 3 Equity: 22%

a) The very aggressive LAG player

Playing against this opponent, you must assume that he'll nearly always bet the turn after betting the flop. Also, you have no direct outs to the nuts or a monster, so that your implied odds are 2 BB at the most. Let's take a look at the table for the required outs again:

If you estimate your implied odds from the flop onwards at between 1.5 and 2 BB, then you need 4.5 to 5 outs here.

How many outs do you have on the flop in the described hand? You have two potential live cards with one overcard on the board and a backdoor straight draw. On the one hand, it's a heads-up situation, but on the other hand, there is an overcard on the board and your live cards could be dominated. With just one overcard on the board you should therefore halve the number of outs for your hole cards.

Consequently, you have 3 outs + backdoor straight draw = ca. 4.25 outs.

You can see that this is a close call, but you need at least 4.5 - 5 outs to play on against a very aggressive opponent. Therefore, you should play check/fold against a very aggressive LAG player.

b) the passive postflop player

Here you have the chance to get a free card on the turn. You don't know precisely how often you'll get a free card, but if we assume that the opponent will only bet the turn if he has at least a pair, then the probability of him betting is roughly 50%. This, of course, depends on the board.

The key point here is that the number of outs you require becomes lower in view of a potential free card on the turn. If you assume that the difference between autobet turn and autocheck turn is ca. 0.8 outs, then halving this difference gives you a good approximation.

This means that if you need ca. 4.5 - 5 discounted outs on the flop against an aggressive LAG player, then you need closer to 4.0 - 4.5 discounted outs against a passive player. The more passively the opponent plays the turn, the closer your required outs are to 4.0.

The estimated 4.25 outs are in fact more than enough to call with here, and you can check/call flop against the depicted opponent.

c) the TAG

Playing against a TAG here is difficult. You shouldn't speculate on a free card, as you'll only rarely get one. The standard play here is check/fold flop. You also have little equity for a bluff. Whether you should try bluffing is very much dependant on your opponent. If your opponent has a low WTS value (<36%), then a bluff may be profitable.

Summary of the hand:

Hero: T 9

Villain's range on the button: (ca. 40%) 22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, 87s, 76s, 65s, A2o+, K7o+, Q9o+, J9o+, T9o

flop: J 5 3 equity: 22%

• a) check/fold flop against a very aggressive LAG player
• b) check/call flop against a passive postflop player
• c) check/fold against a TAG player; If you sense weakness, then you should attack the board with a C/R.

The situation drastically changes if you are holding T 9 instead of T 9. Your equity increases from 22% to just about 26% due to the backdoor flush draw. This gives you nearly one whole additional out.

Here's how you should act in this case:

• a) check/call against a very aggressive LAG player
• b) check/call flop against a passive postflop player
• c) check/raise flop against a TAG player

You will probably have noticed that even if you have no SD-value, you still shouldn't play too tightly on the flop in heads-up situations. Both your holecards are live too often and implied odds and the probability of a free card shouldn't be underestimated. Nevertheless, you must calculate your discounted outs with great care.

The correct application of the evaluation methods described here gives you a clear edge over your opponent in marginal situations. However, you can only benefit from your edge in the long run if you maintain strict discipline when evaluating your hands and don't make any sloppy calls on the flop due to laziness.

Furthermore, you must understand the principles of turn play in such situations. You can only really play marginal situations profitably if you have understood the whole strategic concept. Otherwise, your plays will backfire and you will waste your edge.

After Preflop-3bet

Up until now we have discussed how you should continue playing on the flop after defending your blind if you have no showdown value. Now we want explain what happens on the flop after a preflop 3bet. We'll start with an example:

Preflop: Hero is CO with J 9
Hero raises, Button 3-bets, Hero calls

Flop: K 8 4

3-betting-range on the button: 44+, A5s+, KTs+, QJs, JTs, A8o+, KJo+ (in accordance with Preflop-Expert-Theory from the Gold-section: to the article)

The hero's EQ on this flop is 18%. How should you continue playing this hand?

Here we will again start with the mathematical approach that we have used before: Your pot odds on the flop are 8.5 to 1. If you ignore the implied odds and play strictly by the odds and outs, then you need 1/9,5 * 47 Outs = 5 Outs for C/C flop. However, implied odds and a potential free card have a roll to play here too. The potential free card isn't as important, as you can nearly always count on the opponent betting the flop and turn after a preflop 3-bet..

Therefore, we will again assume that the opponent always bets the flop and the turn. How many outs do you have on the flop and how many discounted outs do you need to be able to play C/C profitably?

For this we will again make use of the tried and tested formula:

EV > 0, if EQ > loss / (profit + loss)

Here the loss is again equal to 0,5 BB, as we at first just decide whether we'll call a bet on the flop.

The profit amounts to at least 5.25BB (3.75 BB pot size on the flop + 0.5 BB opponent flop bet + 1 BB opponent turn bet). However, the question is how often you'll actually win if you hit J or 9 on the turn. This question is easily answered:

Preflop: Hero is CO with J 9
Hero raises, Button 3-bets, Hero calls

Flop: K 8 4 equity: 18%

Turn: 9 equity: 52%
Turn: J equity: 55%
Turn: 9 equity: 45%
Turn: 2 equity: 26%

These figures make it clear that even if you hit the J or the 9, you'll still only be a marginal favourite to win the hand. You would have 52% equity on average. Furthermore, if you hit an out, then you can't choose a line that includes C/R turn for extra bets, as you would be playing OOP and really wouldn't want to see a 3-bet on the turn or a raise on the river.

This shows that you have no implied odds on the turn. You get one BB from the opponent if you are ahead and lose one BB if you are behind. Both outcomes are equally probable. What happens on the river if you hit J or 9? Here it again doesn't look great. If you connect on the turn, then you are usually showdown-commited, but will only win the hand every second time. When you lose the hand you'll nearly always pay the full 2.5 BB postflop, as every better hand will bet for value on the river.

However, if you are ahead on the river, then it isn't certain that you will get an extra BB from the opponent. If you check the river, then the opponent will often check behind with worse hands. If you donk the river, then he may call with worse hands, but he will sometimes fold if he doesn't have anything and doesn't want to start a bluff. By donking you are risking a raise, which will nearly always end badly for you. You may have the same costs with bet/folding as with calling down, but you will lose sleep thinking about the tough laydown. You'll lose value in the future through a lack of concentration when playing, caused by lack of sleep!

Conclusion: Both hitting and missing nearly always costs 1BB on the river. Hitting and winning doesn't guarantee getting another BB on the river. Taking into account the fact that you can also win some additional money on the turn, it is clear that you rather have reverse implied odds in this situation.

Back to the question in hand: We want to know whether you have enough outs on the flop. The analysis has shown that you must halve your outs for J and 9, which gives you 3 outs. You can add 1.5 outs for the backdoor flush draw and 0.5 outs for the backdoor straight draw. As all outs are now discounted and you have no additional implied odds, you have exactly 5 outs here. Therefore, you should check/call the flop.

There may be a distinctly larger pot on the flop in the depicted situation than in a blind defence situation, but due to the weakness of your outs you have substantially worse implied odds, so that you need the same amount of outs as in a blind defence situation with a gutshot.

It would definately be -EV to C/C flop if you didn't have a backdoor flush draw. Without the backdoor flush draw it would be definitely -EV to play C/C on the flop. It becomes clear that the quality of your outs has a major effect on your implied odds and the estimate of the expected profit for the application of the formula EV > 0, if EQ > loss / (profit + loss). You can determine the quality of your outs by letting the outs appear on the turn in the Equilator and then calculating the resulting equity.

In general, you can, of course, play fairly loosely on the flop after a preflop 3-bet. Backdoor flush draws with suited hole cards are usually playable, and every gutshot is a no-brainer to see the turn with. Nevertheless, you must be ctitical when evaluating your outs despite the good pot odds, as you mustn't ignore the danger of being dominated and mustn't go into "I will never fold to a 3-bet on the flop" mode.

Even if it's good for your metagame never to seem too weak, you mustn't call people down too easily. If you notice that the opponent don't make any light 3-bets preflop, then you should be able to fold on the flop after a 3-bet. Only if you notice that the opponent is making loose preflop 3-bets should you yourself be loose on the flop, as the danger of being dominated is smaller and your implied odds increase, due to the wider range of your opponent.

LINKS
related articles: Heads-up on the Flop: Introduction Heads-up on Flop OOP: C/C Flop without initiative - With showdown value