C-beting in NLHE 6-max- Part 2

1. Introduction
This is Part 2 of the series “C-Betting in NLHE 6-max” where we take a closer look at flop c-betting in NLHE 6max. In Part 1 we looked at c-betting heads-up and out of position as the preflop raiser. We studied c-betting with “air” (worthless hands) on two example flops:

Coordinated flop

Dry flop

We assumed that the raiser had opened our standard 25% CO range:

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

326 combos
25%

While the flatter used our standard ~10% “IP flat list”, defined in the article series “Optimal 3/4/5-betting in NLHE 6-max”, and given in the summary document below:

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

We wanted to find out whether or not c-betting any two cards was profitable on these two flop textures, against this preflop flatting range. First we let the flatter defend optimally against the c-bet on both flop textures. When he does, the preflop raiser can (per definition) not profit from c-betting any two cards as a bluff. The flatter defends just enough to prevent it (1/(1 + 0.75) =57% defense if the c-bet is 0.75 x pot).

Next, we let the flatter deviate from optimal flop play. We let him play closer to the way a typical weak-tight opponent plays, namely folding too much on certain flop textures and not defending aggressively enough. More specifically, we gave him the following restrictions on the flop:

  • 1. He is unwilling to bluff raise
  • 2. He is unwilling to call c-bets with pairs lower than two of the board cards (e.g. he will fold 77 and lower pairs on a A 8 2 flop).
  • 3. He is unwilling to float naked overcards or naked gutshots without additional draws

In other words, we assumed that the flatter would play straightforward against c-bets, and that he would see each hand as an isolated case. He does not think about defending his total range sufficiently against c-bets, but thinks only about whether or not the hand he has right now can be played profitably on the flop in a vacuum.

Folding a lot on the flop can be better for him than calling c-bets with lots of weak hands, if he does a poor job of stealing on later streets (you need to be willing to sometimes steal on the turn and river if you are floating a lot of weak hands on the flop). But note that if you’re not willing to defend correctly on the flop, you might lose money by flatting preflop. For example, if you’re not willing to sometimes raise J9 as a bluff on a T72 flop, or float and bluff turns when checked to, you might not have a profitable flat preflop with this hand.

Based on the assumptions above we reached the following conclusions:

  • It was unprofitable for the raiser to c-bet any two cards on the coordinated example flop, even with restrictions on the flatter’s flop defense strategy
  • It was clearly profitable for the raiser to c-bet any two cards on the dry flop texture, when we imposed restrictions on the flatters flop defense strategy

We concluded that the preflop raiser should check and give up with his total “air” hands (like 22, 22, A3, and 76) on the very coordinated example flop. Also when the flatter defends in a weak-tight manner on the flop. Simply put, such very coordinated flops are very easy to defend correctly, and there is nothing the preflop raiser can do about it.

However, on the very dry flops we can c-bet all our “air” hands against an opponent who plays weak-tight on the flop. If he is not willing to defend with all his pairs and some naked overcards and weak draws on dry flops, we can fire away. The reason is that very dry flops mostly miss a typical preflop flatting range. So in order to defend optimally on these flops, it becomes necessary to defend with some very weak hands. Most players are uncomfortable doing that.

In Part 2 we’ll build on the modeling we did in Part 1. There we let the preflop flatter use our standard ~10% “IP flat list” that we introduced in “Optimal 3/4/5-betting in NLHE 6-max – Part 2”. This is a flatting range we defined as our standard range in position outside of the blinds, regardless of the raiser’s position.

Now we’ll give the flatter the option to vary his flatting range. We’ll give him two more choices:

– A tight ~5% flatting range
– A loose ~15% flatting range

We’ll repeat the modeling process from Part 1 using these two ranges, and we’ll see if our conclusions change. We’ll find answers to the following questions:

  • Which range is easier to defend on a coordinated flop?
  • Which range is easier to defend on a dry flop?
  • Will the weak-tight restrictions we impose on the flatter’s flop defense strategies be more limiting for him with a tight range or with a loose range?

When this work is done on the very dry and very coordinated example flops. we’ll look at some more intermediate flop textures in Part 3. This will give us more insight into how various preflop flatting ranges interact with various flop textures, and the consequences this has for the profitability of c-bet bluffing with any two cards.

2. Assumptions about ranges
Assume the following model:

  • Alice (100 bb) raises to 3.5 bb preflop with her standard 25% CO open range. She gets flatted by Bob (100 bb) in position
  • Alice c-bets 0.75 x pot on the flop, and we want to know if this is automatically profitable for her with any two cards

We let Bob use 3 different preflop flatting ranges:

– A tight 5% range
– A medium 10% range (our standard “IP flat list”)
– A loose 15% range

Bob’s 10% “IP flat list” range was given earlier in the article. His other two options are defined as:

Tight 5% flatting range

JJ-55
AQs-AJs AQo
KQs

66 combos
5.0%

Bob here chooses to 3-bet or fold his lowest pocket pairs 44-22, and then he flats his remaining pairs and the best high card hands that he doesn’t 3-bet for value ({QQ+,AK} are value hands for Bob against Alice’s 25% CO range). This is a very tight flatting range, and Bob is giving up some profit by folding hands like 44-22, ATs and QJs. On the other hand, this range should be easy to defend on many flops, since it’s so strong.

Loose 15% flatting range

JJ-22
AQs-A6s AQo-ATo
K9s+ KQo
Q9s+
J9s+
T8s+
97s+
76s
65s

200 combos
15.1%

Bob now flats all pairs plus a wide range of high/medium unpaired hands. The unpaired hands are weighted towards suited and coordinated hands that will often flop draws (while hands like ATo depends more on flopping a decent pair).

We expect this flatting range to be harder to defend correctly postflop, since it often flops medium/weak hands and draws. When we start out with a wide and weak range, we will often have to defend with weak hands against a flop c-bet. If we’re not willing to do that, we risk folding so much that the preflop raiser can exploit us by c-betting any two cards profitably.

It follows that in order to flat preflop with a wide and weak range, we have to be comfortable bluffing and floating with weak hands postflop. If we’re not, many of the hands we flat preflop might be unprofitable for us. This is something we want to look at in our model study.

3. C-betting on coordinated flop

We’ll now build Bob’s defense strategies on the coordinated example flop from Part 1 with the 3 preflop flatting ranges he has at his disposal (and the work for the 10% range was done in Part 1). For each range we first estimate his optimal flop strategy. On coordinated flops, Bob’s defense consists of:

– Raising his best hands
– Flatting his next best hands
– Bluff raise with some weak hands in a 1 : 1 value/bluff ratio

Then we build a strategy that the non-optimal version of Bob can use under the following weak-tight restrictions:

  • 1. He is unwilling to bluff raise
  • 2. He is unwilling to call c-bets with pairs lower than two of the board cards (e.g. he will fold 77 and lower pairs on a A 8 2 flop).
  • 3. He is unwilling to float naked overcards or naked gutshots without additional draws

When Bob defends optimally on the flop, Alice can’t c-bet any two cards profitably per definition. When Bob deviates from optimal play, she might be able to. She c-bets 0.75 x pot, so she can c-bet any two cards with a profit if Bob folds more than 1/(1 + 0.75) =57%.

If we conclude from our analysis that the non-optimal version of Bob will defend less than 57%, Alice has an automatically profitable c-bet bluff, regardless of her cards. We can then estimate the EV of her bluff with an EV calculation.

3.1 Defense against c-bets with a tight 5% flatting range
On this flop, 55 combos remain in Bob’s 5% flatting range, as shown below:

Optimal defense against a 0.75 x pot c-bet means Bob has to defend 57% of his total range, which is 0.57 x 55 =31 combos. Here is one way to do it:

  • Value raise:
    {TT,55} =6 combos
  • Flat:
    {AQ,KQs,AJ,JJ} =22 combos
  • Bluff raise:
    {AJ,AJ,AJ,99,99,99} =6 combos
  • Total: 34 combos (optimal: 31)

Bob can easily get to the optimal defense and then some. Note that a queen high flop texture “smashes” his flatting range, since almost all of his unpaired hands contain a Q. A king high flop would have given him fewer pairs to use, but on the other hand a K high and coordinated flop would have given him various draws he could use.

Now we restrict Bob’s flop defense strategy and see what we get. A possible strategy for Bob to use under these conditions is:

  • Value raise:
    {TT,55} =6 combos
  • Flat:
    {AQ,KQs,AJs,JJ} =25 combos
  • Bluff raise:
    None
  • Total: 31 combos (optimal: 31)

Bob has to stretch a bit by floating AJ,AJ, and AJ that only give him overcard + gutshot combos. He is unwilling to float naked overcards or naked gutshots, but he can float hands that give him a combination of such weak draws. AJs makes the cut.

We see that the non-optimal version of Bob manages to (barely) get to optimal defense with his tight 5% flatting range on our coordinated example flop. Alice can not c-bet any two cards profitably in this scenario. But note that she might have been able to, if the flop had been king high instead of queen high (we can always to a separate analysis if we want to look further into this).

3.2 Defense against c-bets with a medium 10% flatting range
This scenario was discussed in Part 1, and we only include the results here:

The remaining number of combos in Bob’s range is 120:

Optimal 57% defense with 0.57 x 120 =68 combos:

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

Non-optimal defense under weak-tight restrictions:

  • 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)

Bob can easily get to optimal defense with his 10% flatting range on our coordinated example flop. Alice can’t c-bet any two cards profitably in this scenario either.

3.3 Defense against c-bets with a loose 15% flatting range
The number of remaining combos in Bob’s 15% flatting range is 174:

Optimal 57% defense means Bob has to defend 0.57 x 120 =99 combos. Here is one way to do it:

  • Value raise:
    {TT,55,QTs,AQ,AJ,KJ,J9} =24 combos
  • Flat:
    {KQ,QJs,Q9s,JJ,AT,KTs,A9,A8,A7,A6,98,97,87,76,65} =48 combos
  • Bluff raise:
    {JTs,T9s,KJ,KJ,KJ,J9,J9,J9,AJ (not AJ)} =27 combos
  • Total: 99 combos (optimal: 99)

It’s still easy for Bob to defend optimally on the coordinated flop, even with a loose preflop flatting range. His range is dominated by suited and coordinated high card hands, and it hits this type of flop very hard. He has more than enough strong/medium hands and draws to use.

When Bob is given weak-tight restrictions, defending enough will be harder. Mainly because he now loses the option to bluff raise, which is an important component of the defense on coordinated flops. Now he has to call more, but it might be difficult for him to come up with enough flatting hands, since he can’t use naked overcard/gutshot draws or his lowest pairs.

Here is one way to defend under weak-tight restrictions:

  • Value raise:
    {TT,55,QTs,AQ,AJ,KJ,J9} =24 combos
  • Flat:
    {KQ,QJs,Q9s,JJ,AT,KTs,JTs,T9s,T8s,A9,A8,A7,A6,98,97,87,76,65,KJ,KJ,KJ,JS9,J9,J9,AJ (not AJ)} =72 combos
  • Bluff raise:
    None
  • Total: 96 combos (optimal: 99)

Bob can get to optimal defense is he is willing to call the c-bet with all pairs 2nd pair or better, as well as AJ for a overcard + gutshot draw. Alice still can’t c-bet any two cards profitably on our coordinated example flop.

4. C-betting on dry flop

Now we build Bob’s defense strategies on the dry example flop from Part 1. For each range we first build his optimal strategy. On dry flops, Bob’s defense consists of

– Flatting with all his defense hands

The reason for using a flatting-only strategy on dry flop textures has been thoroughly discussed in the article series “Optimal Postflop Play in NLHE 6-max”. When the optimal strategies have been found, we impose the weak tight restrictions:

  • 1. He is unwilling to bluff raise
  • 2. He is unwilling to call c-bets with pairs lower than two of the board cards (e.g. he will fold 77 and lower pairs on a A 8 2 flop).
  • 3. He is unwilling to float naked overcards or naked gutshots without additional draws

Raising is not an option on dry flops regardless, so the restrictions only concern the hands Bob is willing to flat with on the flop.

4.1 Defense against c-bets with a tight 5% flatting range
Bob has 62 remaining combos in his 5% flatting range after accounting for card removal effects_

Optimal defense means defending 57% of these, which is 0.57 x 62 =35 combos. Here is one way to do it:

  • Value raise:
    None
  • Flat:
    {99,KQs,JJ-TT,88-66} =36 combos
  • Bluff raise:
    None
  • Total: 36 combos (optimal: 35)

Bob can easily get to optimal defense with his tight 5% range, without having to float with naked overcards. Then we impose the weak-tight restrictions and see how that changes things. Now Bob can’t flat naked overcards, naked gutshots or pairs lower than the 9 on the board. This makes it impossible for Bob to defend enough. If he goes as far as he possibly can, he ends up with:

  • Value raise:
    None
  • Flat:
    {99,KQs,JJ-TT} =18 combos
  • Bluff raise:
    None
  • Total: 18 combos (optimal: 35)

Bob’s problem in this scenario is that he is not willing to flat his lowest pairs and best overcards (AQ). When he folds these hands, he can only get to about 1/2 of the necessary defense. He defends only 18/62 =29% of his range (as opposed to the optimal 57%), and folds 100 – 29 =71%. Alice can now exploit him by c-betting any two cards.

Alice’s EV for a pure c-bet bluff that can never win unless Bob folds on the flop is:

EV (c-bet)
=0.71 (P) + 0.29 (-0.75P)
=+0.49P

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. The EV of Alice’s c-bet bluff is then 0.49 x 8.5 bb =4.2 bb.

Note that when Bob’s preflop flatting range is tight, our conclusions are very dependent on the exact cards that come on the flop, as well as the exact hands Bob’s range is made up of. For example, if Bob had elected to flat the 12 KQo combos instead of the 12 66/55 combos, he would have been able to defend about optimally on this king high flop texture, also with the restricted strategy.

When Bob’s range is very tight, we can gain a lot from paying close attention. Some players flat all pairs, others fold or 3-bet-bluff the lowest pairs and flat more Broadway hands instead. Observe hands that go to showdown, and take notes. If your PokerTracker/HEM database has many hands on a player, you can use it to extract information and take notes between sessions (this is a smart thing to do for opponents you meet regularly).

4.2 Defense against c-betting with a medium 10% flatting range
This work was done in Part 1, and below is a summary of the results:

The number of combos after card removal is 126:

Bob defends 0.57 x 126 =72 combos when playing optimally. Here is one way to do it:

  • 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)

And here is one way Bob can defend under the weak-tight restrictions:

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

Bob now defends only 42/126 =33% of his range and folds 100 – 33 =67%. Alice can exploit this by c-bet bluffing any two cards. Her EV for a c-bet bluff with a worthless hand is:

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

Where P is the pot size on the flop. With a pot of 8.5 bb, the EV is 0.42 x 8.5 bb =3.6 bb.

4.3 Defense against c-betting with a loose 15% flatting range
We’ll see that this is a difficult job for Bob when we impose weak-tight restrictions. The number of combos that remain in his range after accounting for card removal effects is 180:

Optimal 57% defense means Bob has to use 0.57 x 180 =103 combos. Here is one way to do it:

  • Value raise:
    None
  • Flat:
    {99,22,K9s,KQ,KJs-KTs,JJ,TT,A9s,Q9s,J9s,T9s,98s-97s,88-55,AQ,QJs,JTs} =104 combos
  • Bluff raise:
    None
  • Total: 104 combos (optimal: 103)

Bob has to flat almost all of his pairs, plus some overcard hands (AQ) and gutshots (QJs, JTs). It’s hard enough to defend optimally when Bob can use all hands, and when we impose weak-tight restrictions, it becomes impossible. Here is what Bob comes up with when he goes as far as he can:

  • Value raise:
    None
  • Flat:
    {99,22,K9s,KQ,KJs-KTs,JJ,TT,A9s,Q9s,J9s,T9s,98s-97s} =56 combos
  • Bluff-raise:
    None
  • Total: 56 combos (optimal: 103)

The defense is more or less identical to the optimal defense, except that we have dropped all pairs lower than 9, all naked overcard hands (AQ) and all naked gutshots (QJs, JTs). Bob now defends about 1/2 of the optimal amount: 56/180 =31% of his range. So he folds 100 – 31 =69% on the flop, and the EV for Alice’s’ c-bet bluffs becomes:

EV (c-bet)
=0.69 (P) + 0.31 (-0.75P)
=+0.46P

Where P is the pot size on the flop. With P =8.5 bb, the EV becomes 0.46 x 8.5 bb =3.9 bb.

So a c-bet bluff will be automatically profitable on the flop, but note something else as well: Bob is forced to defend on the flop with many low pairs and weak draws, also under weak-tight restrictions. So Alice should have many opportunities to 2-barrel profitably on the turn. Bob can protect himself somewhat against 2-barrel bluffs by slowplaying his strongest hands on the flop, but life will still be tough for him on the turn if Alice decides to bluff a lot.

So a good player with knowledge about Bob’s preflop flatting range and his postflop tendencies should be able to make even more money from c-bet bluffing by sometimes continuing to bluff on the turn and the river. But note that we don’t have to continue out bluffs in order to have a nicely profitable c-bet bluff in isolation on the flop.

5. Summary
We used the two example flop textures (very coordinated and very dry) from Part 1 and continued our modeling of c-bet bluffing. This time we let Bob use 3 preflop flatting ranges:

– A tight 5% range
– A medium 10% range (our standard “IP flat list”)
– A loose 15% range

Based on our modeling, we conclude the following:

  • We can’t c-bet bluff profitably with any two cards on a very coordinated flop against any reasonable flatting range, even if our opponent defends weak-tight
  • On very dry flops we can c-bet bluff profitably with any two cards, if our opponent defends weak-tight

We noted that the profitability of a c-bet bluff against the tight 5% range on a dry flop was very sensitive to the exact flop texture and the exact composition of the flatting range. At the other end of the spectrum, this became relatively unimportant against the loose 15% range.

A wide and weak preflop flatting range is impossible to defend correctly against c-bets on a very dry flop, unless the player is willing to flat just about any pair plus lots of overcard and gutshot combos. Exactly what the flop is, and exactly which hands we flat is now less important, since we have to defend lots of weak hands/draws regardless.

We summarize:

On very coordinated flops we can’t get away with any two cards c-bet bluffing regardless of our opponents preflop flatting range. If he defends weak-tight, this does not help you a lot, since very coordinated flop textures are so easy to defend.

On very dry flops you can probably get away with any two cards c-bet bluffing regardless of your opponent’s flatting range, as long as he isn’t willing to always defend optimally. A wide flatting range gives you the best opportunities, since wide ranges are very hard to defend optimally on very dry flops. Of course, against an opponent that always defends optimally, we can’t buff any two cards profitably, per definition. But most players are unable or unwilling to defend enough on dry flops. So our starting assumption can be that any-two-cards c-bet bluffing is profitable on very dry flops. If we are wrong against a particular opponent, we can adjust later, and start checking more hands.

In Part 3 we’ll look at some other flop textures in the region between very coordinated and very dry flops. We’ll also introduce a software tool (“Flopzilla“) that lets us quickly analyze the profitability of a c-bet bluff, without having to write out complete strategies like we have done up to this point.

Good luck!
Bugs – See more at: http://en.donkr.com/Articles/c-beting-in-nlhe-6-max–part-2-274#sthash.IbkJIeKk.dpuf

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