C-beting in NLHE 6-max- Part 1

1. Introduction
This is the first part of an article series about flop c-betting in NLHE 6-max. In the previous series “Optimal Postflop Play in NLHE 6-max” we looked at postflop play in the scenario where one player has raised preflop and gotten called by another player in position. We discussed how the player in position can defend optimally against c-bets on the flop, and against 2- and 3-barrels on the turn and river. Then we discussed how the preflop raiser can play the turn and river optimally after c-betting the flop and getting called, to prevent his opponent from exploiting him by floating.

For both the preflop raiser out of position and the flatter in position we built postflop strategies that prevents their opponent from exploiting them by betting or floating with any two cards on any street. The flatter in position has to defend enough against c-bets to prevent the preflop raiser from c-bet bluffing any two cards on the flop. And those times the preflop raiser has c-bet the flop and gotten called, she has to play the turn in such a way that she prevents the flatter from floating on the flop with any two cards (planning to steal the pot on the turn).

In our discussion of turn and river play for this scenario, we simply assumed that the preflop raiser had started postflop play by c-betting her entire range on the flop. When we looked at turn and river barreling we limited our study to dry flop textures, so this assumption was reasonable.

In this article we’ll look more closely at c-betting with “air” on the flop, heads-up as the preflop raiser. We’ll use a model where one player (Alice) openraises out of position and gets flatted by another player (Bob) in position. The flop comes, and Alice has a c-bet decision to make. We want to train our ability to recognize flop textures where Bob’s preflop flatting range has connected poorly, so that Alice can c-bet any two cards profitably on the flop.

We are then assuming that Bob is not willing to defend optimally. Because if he does, we can’t profit from c-betting any two cards per definition of optimal play. So we are assuming that Bob will fold more than the optimal amount on flop textures that are bad for his preflop flatting range (for example, a dry flop like J 6 2). In “Optimal Postflop Play in NLHE 6-max” we built optimal postflop strategies for Bob to use in this scenario, but now we’ll assume he behaves more like the players we meet in practice. And they will typically fold too much on flop textures that mostly misses their range.

In Part 1 of this series we’ll study how well different flop textures hit a typical preflop flatting range (we’ll use our standard 10% “IP flat list” range). Based on this, we can estimate the EV of a c-bet bluff with a worthless hand on different textures. In Part 2 we’ll vary the preflop flatting range and see how the EV of the c-bet changes when we’re up against a tight (~5%) and a loose (~15%) flatting range. This analysis will train our ability to identify profitable c-bet bluffing spots based on the flop texture and our knowledge about the preflop flatter’s range.

The modeling we do in these articles is inspired by the video Alans Common C-betting Spots by Bluefirepoker coach Alan Jackson.

Our approach in this article series about c-betting is exploitive. We make assumptions about various opponent mistakes, and then we move away from optimal play in order to exploit these mistakes. Our previous work on optimal play gives us a starting point, and tells us in which direction we should move our strategy. The main mistake we focus on in this article series is the mistake of folding too much to a c-bet. We want to find spots where our opponent is making this mistake, thus giving us an opening for c-bet bluffing any two cards profitably.

2. Our model
Here are the assumptions we’ll use in this article:

2.1 Assumptions about preflop ranges

 

  • Alice (100 bb) openraises in CO
  • Bob (100 bb) is on the button and follows the previously defined optimal strategies for 3/4/5-betting. Other than that he flats his standard range in position (“IP flat list”).
  • Alice knows Bob’s flatting range based on observations and HUD stats

Alice uses our standard 25% opening range from CO:

22+
A2s+ A9o+
K9s+ KQo
Q9s+ QTo+
J8s+ JTo
T8s+
97s+
87s
76s
65s

326 combos
25%

We assume Bob uses the optimal 3/4/5bet strategy against a 25% opening range, given in the table of optimal strategy pairs built in “Optimal 3/4/5-betting in NLHE 6-max – Part 2”:

Download link (right-click and choose “Save as”): IP_3-bet_summary.doc

So Bob will use the following preflop strategy against Alice’s 25% CO raise:

  • 3-bet {QQ+,AK, 12 air} for value, planning to 5-bet all-in against a 4-bet
  • 3-bet bluff 70% of “IP 3-bet air list”, planning to fold against a 4-bet
  • Flats the entire “IP flat list”: {JJ-22,AQs-ATs,AQo-AJo,KQs-KTs,KQo,QJs-QTs,JTs,T9s,98s} =140 combos when {QQ+,AK} is 3-bet for value

Bob’s standard preflop flatting range then has 140 combos, which is 140/1326 =10.6% of all hands. This range is representative for what many players will flat on the button in this scenario, and it’s a reasonable assumption to use against unknowns.

When the flop comes, Alice tries to determine whether or not she has a profitable c-bet for 0.75 x pot with any two cards. She bases her analysis on her knowledge about Bob’s preflop flatting range, the flop texture, and assumptions about which hands Bob is willing to defend with.

Since Alice c-bets 0.75 x pot, she is giving herself pot odds 1 : 0.75 on a bluff with any two cards. A c-bet bluff will be automatically profitable if Bob folds more than 0.75/(1 + 0.75) =57%. If Alice’s analysis concludes that Bob in practice will fold more than 57%, she can c-bet her entire range profitably on the flop. If not, she has to check and give up with some of her weakest hands. How much hand strength we need to c-bet proftiably in this case will be discussed in future articles.

The purpose of the work we do in Part 1 is to train our ability to come up with a qualitative yes/no answer to the question about whether or not we can c-bet any two cards profitably. We look at the flop, we think about our opponents preflop flatting range, and we analyze how the flop and the range interact. We then introduce some assumptions about which hands opponent will defend in practice against our c-bet, and we have our answer.

2.2 Assumptions about Bob’s flop strategy
We’ll look at two example flop textures in this article:

– Very coordinated
– Very dry

For both textures we’ll first build Bob’s optimal defense against Alice’s c-bet. The optimal defense strategy is designed to prevent her from c-betting any two cards profitably. If Bob uses this strategy, there is nothing Alice can do to exploit him by bluffing a lot on the flop.

Then we’ll make some assumptions about the strategy Bob will use in practice. We’ll assume that Bob will fold some weak hands (for example overcards and weak pairs) that he should not fold on flops where his range is weak and difficult to defend correctly. Then we’ll analyze whether or not Bob’s deviation from optimal play will make it possible for Alice to exploit him by c-bet bluffing any two cards.

Exactly how Bob deviates from optimal play will be a function of the flop texture. Here are three general assumptions we’ll use for the non-optimal version of Bob:

  • 1. He is not willing to bluffraise against Alice’s c-bet
  • 2. He is not willing to call the c-bet with pairs lower than two of the cards on the board (for example, he will fold 77 and all lover pairs on a A 8 2 flop)
  • 3. He is not willing to call the c-bet with naked overcards and gutshots, with no additional draws

In addition we can make specific assumptions about how Bob will play on specific flop textures. If we do make extra assumptions, we’ll use good poker sense and let Bob play the way a typical opponent in our games will play.

In general, we’ll assume that the non-optimal Bob plays like a typical decent-but-not-great low limit player. He plays mostly straightforward, he bluffs little when others have the initiative, and he has limited knowledge about the interaction between flop texture and hand ranges. Also, he does a poor job changing his postflop strategies and ranges based on the pot odds he’s getting.

The non-optimal version of Bob mostly sees each hand as an isolated case, and he does not think about the hand as a part of an overall range. This is typical for how the majority of poker players think. They think things like “I have top pair, which is a good hand” or “I have bottom pair, which is a very weak hand“, and they don’t think about all the other possible hands they could hold in this particular scenario.

3. C-betting on a coordinated flop
In “Optimal Postflop Strategies in NLHE 6-max” we concluded that our standard positional flatting range “IP flat list” is easy for Bob to defend on coordinated flops like J 9 3, since these flops hit his preflop range hard.

Now we’ll show through analysis why c-bet bluffing any two cards on these flops is a bad idea heads-up and out of position against a preflop flatter, even if our opponent is tight and straightforward. This is something most players intuitively understand, but not we’ll “prove” it using theory, and we’ll get a much clearer picture of exactly why this is so. Then we’ll repeat the process on a dry flop, and we’ll see that dry textures give us opportunities for profitable any-two-cards c-bet bluffing if our opponent is somewhat tight.

3.1 Optimal defense against c-betting on a coordinated flop
Alice (100 bb) raises her standard 25% range from CO, and Bob flats his standard 10.6% flatting range “IP flat list” ={JJ-22,AQs-ATs,AQo-AJo,KQs-KTs,KQo,QJs-QTs,JTs,T9s,98s} =140 combos.

Our coordinated flop is:

When Alice c-bets, she bets 0.75 x pot, and Bob needs to defend at least 1/(1 + 0.75) =57% to prevent her from c-betting any two cards with automatic profit.

Bob has 120 remaining combos in his range after adjusting for card removal effects, as shown below:

Bob’s optimal defends is then to defend 0.57 x 120 =68 combos. We remember from “Optimal Postflop Play in NLHE 6-max” that Bob’s defense on coordinated flops has three components:

– Raise the best hands for value
– Flat the next best hands
– Bluff raise some weak hands using a 1 : 1 value/bluff ratio

Below is a suggestion for a near-optimal flop strategy for Bob. At this point in the analysis our only concern is to defend with 68 combos (or thereabouts) overall. If this leads us to folding or bluffing with hands that could have been played more profitably by calling, this is not a problem for us.

  • Value raise:
    {TT,55,QTs,AQ,AJ,KJ} =23 combos
  • Flat:
    {KQ,QJs,JJ,ATs} =24 combos
  • Bluffraise:
    {KTs,JTs,T9s,KJ,KJ,KJ,98,AJ,AJ,AJ,AJ,AJ,AJ,98,98,98} =22 combos
  • Total: 69 combos (optimal: 68)

As we have seen in previous articles, the optimal flop defense ranges are strong on very coordinated flops after we have flatted our default “IP flat list” preflop. We have so many strong hands to use that we can get away with only flatting top pair + best underpair (JJ) + 2nd pair/top kicker (ATs). All lower pairs can be folded or used as bluff raises.

3.2 Non-optimal defense against c-betting on coordinated flop
Now we’ll limit the strategies Bob is willing to use when he defends against Alice’s c-bet:

  • 1. He is not willing to bluffraise against Alice’s c-bet
  • 2. He is not willing to call the c-bet with pairs lower than two of the cards on the board (for example, he will fold 77 and all lover pairs on a A 8 2 flop)
  • 3. He is not willing to call the c-bet with naked overcards and gutshots, with no additional draws

We remember that Bob has to defend less than 57% to give Alice a profitable any-two-cards bluffing opportunity when she c-bets 0.75 x pot. So the question we want to answer is this:

Will the restrictions above make it impossible for Bob to defend at least 57% on the flop?

If this is the case, Alice can c-bet her entire range profitably. We now try to build a defense strategy for Bob where he defends 57% (68 combos) given the limitations above:

  • Value raise:
    {TT,55,QTs,AQ,AJ,KJ} =23 combos
  • Flat:
    {KQ,QJs,JJ,ATs,KTs,JTs,T9s,98,KJs,AJ,AJ,AJ,AJ,AJ,AJ} =43 combos
  • Bluff raise:
    None
  • Total: 66 combos (optimal: 68)

We can easily get to around the optimal defense, even if we’re not willing to bluffraise, call with 3rd pair or lower, or float with naked overcards and gutshots. The weakest draw Bob has to call with is AdJx/AxJd (overcard + gutshot + backdoor flush draw).

3.3 Conclusion for defense against c-betting on coordinated flop
Both the optimal and the non-optimal versions of Bob could easily defend the optimal 57% on this flop texture. These flops hit Bob’s preflop flatting range so hard that the can get away with folding lots of marginal hands, and still defend enough.

A range analysis with Pokerazor illustrates this with numbers:

On this flop we have 2nd pair or better 45% of the time (see the list “Cumulative frequency” to the right). So we can cover most of the optimal 57% defense with good one pair hands. And the rest is easily covered by our draws. Even if we never bluff raise, flat pairs below 2nd pair, or flat naked overcards/gutshots, we can get to 57% defense.

We therefore conclude:

Alice can’t c-bet any two cards profitably on our very coordinated flop texture, even if Bob plays tightly and isn’t necessarily willing to defend an optimal amount. He can easily build defense strategies that defend the optimal amount, even with strong limitations on the hands he is willing to defend.

In future articles we’ll talk more about how much hand strength we need to have a profitable c-bet on these flops. We obviously have to be willing to semibluff a bit, and c-bet some weak draws. But we should check-fold our pure air, like 76, 22 and A4 on this flop. Bob simply doesn’t fold often enough to make it profitable, even if he plays somewhat tight postflop.

4. C-betting on a dry flop
Next we’ll show why c-bet bluffing with any two cards on very dry flops generally is a good idea Even players who defend loosely on the flop will find it difficult to defend the optimal amount, since this requires them to float with lots of air.

4.1 Optimal defense against c-betting on dry flops
Alice (100 bb) raises her standard 25% range from CO, and Bob (100 bb) flats his standard 10.6% flatting range “IP flat list” ={JJ-22,AQs-ATs,AQo-AJo,KQs-KTs,KQo,QJs-QTs,JTs,T9s,98s} =140 combos.

Our dry flop is:

This is the classic super-dry flop with one Broadway card, two medium/low cards, and no flush or open-ended straight draws possible. Again, Alice c-bets 0.75 x pot, and Bob needs to defend 57% to prevent her from bluffing with any two cards, as in the previous case.

After adjusting for card removal effects, Bob has 126 remaining combos in his range:

Bob’s optimal defense requires him to defend 0.57 x 126 =72 combos. We remember from “Optimal Postflop Play in NLHE 6-max” that Bob defends only by flatting on very dry flops. So he slowplays all his monsters (only sets are monsters on this flop), together with hos good hands, and some weak hands. He is often forced to flat with all his one pair hands, and perhaps also float some naked overcards and gutshots in order to defend optimally.

Below is a suggestion for an optimal flop defense strategy for Bob:

  • Value raise:
    None
  • Flat:
    {99,22,KQ,KJs,KTs,JJ-TT,T9s,98s,88-44} =72 combos
  • Bluff raise:
    None
  • Total: 72 combos (optimal: 72)

Bob has to flat all his pocket pairs, except 33. As an alternative, he can fold some low pocket pairs and float his best overcards instead (AQ):

  • Value raise:
    None
  • Flat:
    {99,22,KQ,KJs,KTs,JJ-TT,T9s,98s,88-66,AQ} =76 combos
  • Bluff raise:
    None
  • Total: 76 combos (optimal: 72)

But regardless of how he chooses to do it, Bob has to flat lots of weak hands on this flop texture in order to defend the optimal 57%.

4.2 Non-optimal defense against c-betting on a dry flop:
Again, we introduce limitations for Bob:

  • 1. He is not willing to bluffraise against Alice’s c-bet
  • 2. He is not willing to call the c-bet with pairs lower than two of the cards on the board (for example, he will fold 77 and all lover pairs on a A 8 2 flop)
  • 3. He is not willing to call the c-bet with naked overcards and gutshots, with no additional draws

Then we see how far he can go:

  • Value raise:
    None
  • Flat:
    {99,22,KQ,KJs,KTs,JJ-TT,T9s,98s} =42 combos
  • Bluff raise:
    None
  • Total: 42 combos (optimal: 72)

It turns our that if Bob is unwilling to flat with naked gutshots, naked overcards, and pairs lower than two of the cards on the board, it is impossible for him to defend the optimal amount. He gets to 42/126 =33% defense, and folds 100 – 33 =67%.

Let’s say Alice c-bets with a worthless hand that will never win the pot when Bob doesn’t fold on the flop. Her EV for the bet is:

EV (c-bet)
=0.67 (P) + 0.33 (-0.75P)
=+0.42P

Where P is the pot size on the flop. If the preflop raise was 3.5 bb, the pot is P =2(3.5) + 0.5 + 1 =8.5 bb on the flop. Alice’s c-bet bluff is then worth 0.42 x 8.5 bb =3.6 bb. This is a very nice profit for an any-two-cards bluff with a hand that can only win when Bob folds.

4.3 Conclusion for defense against c-betting on dry flops
Bob could defend our dry flop texture optimally without floating with extremely weak hands, but he had to drop down to the “cellar” and use his lowest one pair hands. Alternatively, he could fold some low pairs and float with some of his best overcard hands instead.

When Bob’s strategies were limited, it was impossible for him to defend enough. If he is unwilling to call with his lowest one pair hand, good ace high hands, or gutshots, he can’t defend our dry example flop optimally. This opens him up for getting exploited by Alice’s any-two-cards c-bet bluffs.

A range analysis with Pokerazor illustrates this with numbers:

On the coordinated example flop we had 2nd pair or better 45% of the time, in addition to many draws. On the dry example flop we have 2nd pair or better only 33% of the time, and we have no strong draws, only naked overcards and gutshots.

Most NLHE players know (or intuitively see) that our dry example flop is an excellent flop to bluff at. So you can expect the preflop raiser to c-bet a lot when you are the preflop flatter on such a flop. Therefore, if you believe the preflop raiser will try to exploit you by c-bet bluffing with any two cards, don’t be afraid to float!.

Remember that you will also call with some good hands like sets, top pair, and good 2nd pair/underpair hands. So if he 2-barrels a lot with air, he will get punished by your strong flatting hands. Think about what his range looks like on this type of flop. If he has raised from CO, his range is full of garbage like A8o, 76s, etc. Force him to play turns with these hands if he is aggressive enough to c-bet any two cards on the flop.

If he keeps betting on the turn, you have to fold low pairs like 55 and floats like AQ, but you will still plenty of hands to continue with (remember, you have slowplayed sets and top pair hands in your range). So your turn range will be decently strong, even if you floated the flop with a weak range.

5. Summary
In this article we have begun studying c-betting on the flop in heads-up pots as the preflop raiser.

We saw that coordinated flops are easy to defend optimally for the preflop flatter, even if he isn’t necessarily willing to defend optimally. When we did the same model study on a dry flop, we saw that it was impossible for the flatter to defend optimally if he was unwilling to float his weakest one pair hands, and/or some floats (overcards/gutshots type hands. When you have identified such players at the table (and they are common at the low limits), you can c-bet dry flops with your entire range against them, and “print money”.

The gist of it is that all flops can be defended optimally, in principle (it’s only a matter of including more and more weak hands, as the flop texture gets drier), but many players are unwilling to do so if it requires them to defend with very weak hands. These players can be exploited by c-bet bluffing a lot on dry flop textures. On the driest of flops, you can c-bet your entire range profitably,.

In Part 2 we’ll continue our modeling. Now we’ll let Bob use two other preflop flatting ranges (tight =5% and loose =15%) in addition to his standard 10% “IP flat list”. This gives us an opportunity to learn about how various preflop flatting ranges hit various types of flop textures, and the consequences this has for our c-betting strategy.

Being able to classify flop textures as coordinated or dry gives us possibilities to c-bet profitable with any two cards, and this was what we learned in this article. If we also train our ability to distinguish between different opponent ranges, we add one extra dimension to our analysis. This will enable us to find even more profitable c-bet bluffing spots. A particular flop texture can give us a profitable c-bet bluff against one opponent range, but not against another. This is the topic for the next article.

Note that the work done in this article defines a method for training our ability to recognize profitable c-bet bluffing opportunities. You can generate random flops using Flopgenerator.com and perform this type of analysis, using assumptions about your opponent’s flatting range and postflop tendencies. This will tell you whether or not you have a profitable any-two-cards c-betting opportunity on the given flop.

Good luck!
Bugs – See more at: http://en.donkr.com/Articles/c-beting-in-nlhe-6-max–part-1-263#sthash.rntipxOO.dpuf

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