Optimal Postflop Play in NLHE 6-max – Part 3

1. Introduction
This is Part 3 of the article series “Optimal Postflop Play in NLHE 6-max” where we’ll study optimal strategies for heads-up postflop play in NLHE 6-max.

In Part 1 and Part 2 we introduced fundamental theory for heads-up flop play in position after flatting preflop. Alice raises from some position, Bob flats in position, and all other players fold. Alice c-bets most flops, and Bob has to defend enough to prevent Alice from c-betting any two cards profitably.

Bob’s response to Alice’s c-bet is to choose:

– A range for value-raising
– A range for flatting
– A range for bluff-raising

And the he folds the rest of his hands. We found that Bob had to defend minimum 57% against a 0.75 x pot c-bet. We also estimated that Bob should use a 1 : 1 ratio of value hands to bluffs when he raises. Our method for estimating Bob’s flop ranges are:

  • 1. Choose a value range (for example, top pair/top kicker or better, plus monster draws). Then we also know how many bluff combos we need (number of bluffs =number of value hands)
  • 2. When the number of value hands/bluffs is counted, we pick enough flatting hands to give us a total defense of 57%. Our flatting hands are chosen from the best hands not strong enough to raise for value (for example, top pair hands weaker than top pair/top kicker, some lower pairs, and non-monster draws).
  • 3. Lastly, we choose our bluff combos from the best hands not strong enough to raise for value or flat (typically the weakest one pair hands, the best overcard hands, and gutshot draws)

In this article we’ll put these principles to work on two different flops:

– A coordinated flop with many draws
– A dry flop without draws

And we’ll place Bob in two different preflop flat scenarios:

– On the button after a CO openraise from Alice
– In the big blind after an SB openraise from Alice

So Bob will defend against Alice’s c-bet on two different flop types, and with two different preflop flatting ranges. This gives us 4 scenarios:

– Bob on the button with a coordinated flop
– Bob on the button with a dry flop
– Bob in the big blind with a coordinated flop
– Bob in the big blind with a dry flop

We’ll work through these scenarios systematically for practice. After reading this article you should be able to do the same type of analysis on your own, so that you can practice optimal heads-up flop play away from the table, using your own standard preflop flatting ranges.

2. Our two practice flops
We go to FlopgGenerator.Com and generate a coordinated (wet) flop and an uncoordinated (dry) flop:

2.1. Coordinated flop

A coordinated flop with two possible straights, and also high cards that will connect with many hands in Bob’s preflop flatting ranges. So we expect this flop to be an easy one to defend.

2.2 Uncoordinated flop flop

A low, rainbow flop that mostly misses Bob’s preflop flatting ranges. There are some possible straight draws, but few of Bob’flatting hands connects with these draws (none, when he has flatted on the button). So we expect this flop to be a tough one to defend enough.

This is also a flop where we have to consider slowplaying the few monster hands in our flop range (basically, our sets) in order to make it harder for Alice to play the turn and river after we flat the flop (since our flop flatting range will be weak on this type of low, dry flop texture). More about this later.

2. Alice’s and Bob’s preflop ranges
We’ll work with two scenarios:

Scenario 1: Alice in CO and Bob on the button
Alice opens her default 25% CO range:

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

326 combos
25%

Bob flats with his default flatting range outside of the blinds (“IP flat list”) given in the overview below:

Here is a download link for this document (right click and choose “Save as”):
IP_3-bet_summary.doc

With Alice in CO, Bob 3-bets {QQ+,AK} for value, so his flatting range contains 140 combos:

“IP flat list” after a 25% CO openraise:

JJ-22
AQs-ATs AQo-AJo
KQs-KTs KQo
QTs+
JTs
T9s
98s

140 combos

This flatting range is weighted towards high/medium suited and coordinated hands. So it will connect well with high/medium coordinated flop textures and be easy to defend on these flops.

But on low, uncoordinated flop textures it might be difficult for us to defend enough, since we simply don’t have enough strong combos in our range. So we might have to accept that we won’t be able to defend the required minimum 57% on very dry flops. But this is not necessarily a problem for us, since we should be able to defend a bit more than minimum on the coordinated flops. So in the long run, these two factors should even out.

Scenario 2: Alice in the small blind and Bob in the big blind
Alice now opens her 35% button range as default from the small blind:

35% button openrange:

22+
A2s+ A7o+
K2s+ K9o+
Q6s+ Q9o+
J7s+ J9o+
T7s+ T9o+
96s+
86s+
76s
65s

458 combos
35%

We discussed this flatting scenario in detail in Part 7 of the preflop series. Since Bob is the only player left to defend the blinds, he has all of the responsibility of defending the blinds enough to prevent Alice from stealing with any two cards. We found that Bob needs to defend with 37.5% of his hands preflop, and he will use a combination of optimal 3/4/5-bet strategies and flatting.

We assumed Bob would 3-bet {JJ+,AK} for value, together with an optimal amount of 3-bet bluffs, and the rest of the defense was done by flatting. We ended up with the following suggestion for a default flatting range (“Blind vs blind flat list”) for Bob to use in the big blind after an openraise from the small blind:

Blind vs Blind flat list

TT-22
ATs-A6s AJo-A7o
K8s+ K9o+
Q8s+ Q9o+
J7s+ J9o+
T7s+ T8o+
96s+
86s+
75s+
65s

362 combos

This flatting range contains many more low combos that the flatting range we use on the button (“IP flat list”), so it will hit more of the low/dry flops. Since we can hit any flop hard, we have the possibility to credibly represent strength on any flop, and thereby create postflop difficulties for the small blind.

But on the other hand we will now have lots of low hand combos in our range that can’t be used to defend high/medium coordinated flops. Whether or not this will create problems for us on the coordinated flops remains to be seen.

In all scenarios we’ll use the strength principle when designing ranges:

– Raise the best hands for value
– Flat with the next best hands
– Bluff with the best of the weakest hands, and fold the rest

4. Bob’s flop strategies after flatting on the button
We now go through Bob’s flop play systematically. First for the coordinated flop, then for the dry flop:

4.1 Play on the coordinated flop after flatting on the button

“IP flat list” after 25% CO openraise:

JJ-22
AQs-ATs AQo-AJo
KQs-KTs KQo
QTs+
JTs
T9s
98s

140 combos

First we count all remaining combos in Bob’s preflop flatting range, given the cards on the board. ProPokerTool’s count function gives us:

So Bob has 117 combos in his range on the flop. In order to defend a total of 57%, he needs to defend 0.57 x 117 =67 combos in total. We choose his value combos first.

Assume Bob will value-raise all his made hands two pair and better on this coordinated flop (so we let all top pair hand go in the flatting range). Bob with then raise a range made up of two pair (QTs, T9s), sets (TT, 99) and straights (KJs). In addition we let him raise the monster draw combo QJs (top pair + open-ended straight draw). This gives us 17 value combos as shown below:

Bob balances this with 17 bluff-raise combos, but before we choose these we pick his flatting hands. Bob needs 67 – 2 x 17 =33 flatting combos to get to 57% total defense. We pick his flatting hands from the next tier of hands on the equity ladder:

– One pair hands
– Open-ended straight draws

It seems obvious to choose from top pair/top kicker (AQs, AQo), top pair/2nd kicker (KQs, KQo), underpair + open-ender (JJ), middle pair + open-ender (JTs). This gives us the 33 combos we need:

Note how strong the ranges for value-raising and flatting are on this flop. We only raise two pair or better + monster draws for value, and our weakest flatting hand is middle pair + open-ended straight draw.

So we have somewhat of a “luxury problem” on these flops after flatting our tight and solid “IP flat” list on the button. We can pick and choose from some very good hands, and we can easily defend the required 57% by only continuing past the flop with quality hands that have good equity.

The last step of the process is to choose Bob’s 17 bluff combos. We step down to the last rung on the equity ladder and choose hands from the low pairs and weak draws (weak one pair hands, overcard hands, gutshots). Note that some open-ended straight draws are counted as weak draws on this flop, since we have so many better made hand and draws to use.

For example, we can pick KTs (2nd pair + gutshot + overcard), ATs (middle pair + overcard), 98s (3rd pair + gutshot) and AJ (open-ender + overcard). This gives us a few too many bluff combos, so we can drop some of the AJ combos. We end up with the following bluffraising range:

Summary
Bob’s total flop strategy on the coordinated flop Q T 9 after flatting on the button is:

  • Raise for value
    {QTs,T9s,TT,99,KJs,QJs} =17 combos
  • Flat
    {AQs,AQo,KQs,KQo,JJ,JTs} =33 combos
  • Bluffraise
    {KTs,ATs,AJs,A J , A J , A J , A J , A J , A J , A J } =17 combos

Bob then defends 17 + 33 + 17 =67 combos in total, which is exactly 67/117 =57% of his total range on the flop. This is the optimal defense percentage we found in Part 1, and Bob’s flop strategy now makes Alice’s random c-bet bluffs break even. We could have designed Bob’s flop strategy in slightly different ways, but our strategy is very reasonable.

But note that we haven’t bothered to defend more than the optimal 57% here, even if we could have. For example, we let Bob fold some draw combos like A J , and the weak pair + draw combos 987s. We have also used potential flatting hands (the weakest middle pair hands) as bluffs, since we had so many better hands to use for value raising and flatting.

We won’t be able to defend the very dry flops as easily, and we should consider overdefending a bit on the coordinated flops to make up for this. For example, we could have moved ATs up to the flatting range and moved the AJ/98s combos we folded up from the folding range to the bluffing range. We have lots of flexibility on this type of coordinated flop, and if we can easily defend more than 57%, we should consider doing so.

We now move on to Bob’s defense with “IP flat list” on the button when the flop comes low and uncoordinated. We’ll see that this flop texture is much harder to defend sufficiently:

4.2 Play on dry flop after flatting on the button

“IP flat list” after 25% CO openraise:

JJ-22
AQs-ATs AQo-AJo
KQs-KTs KQo
QTs+
JTs
T9s
98s

140 combos

As before we begin by counting the remaining combos in Bob’s preflop flatting range:

The poor match-up between this flop texture and Bob’s preflop flatting range is reflected in the number of remaining combos (130 of the original 140). On the coordinated flop we lost a much bigger chunk of our preflop range (117 of the original 140 remained), since our range connected much harder with that flop.

Our standard procedure is to begin by choosing Bob’s value range, but before we do this we should ask: Should Bob have a value range at all on this extremely dry flop?

There are no draws on this flop, and our only monster hands are 9 set combos (3 of each of 88, 55 and 33). If we decide to raise these for value, together with our best overpairs (e.g. JJ and TT), we’ll have an extremely strong value range, but also an extremely weak and easily readable flop flatting range. The reason is that our flatting range will then be made up of two types of hands: Mediocre one pair hands, and some strong overcards (e.g. AQ).

This makes it easy for Alice to play the turn with her value hands. For example, when she has QQ she can bet confidently for value on basically all turn cards, knowing that the best hand we could have on the flop was a pair lower than her. Remember that we would have raised AA/KK preflop, we would have raised all sets for value on the flop, and there are no two pair hands in our range on this flop.

To avoid this problem we can drop all value/bluff raising on the flop and defend entirely by flatting. Then we put all hands worth playing (sets, one pair, good overcards) into our flatting range. Our flop defense range will still be a bit weak, but now Alice can’t bet safely for value with all of her good one pair hands without risking running into a concealed monster hand. If she does, she will every so often get punished by a slowplayed set.

So let’s design a flop flatting for Bob. We want to defend 57% of our range, so we need to find 0.57 x 130 =74 playable combos. It might be impossible to do so without having to flat some unreasonably weak hands, but we’ll see.

We begin with all sets and one pair hands: {88,55,33,JJ,TT,99,77,66,44,22}. This gives us 51 combos, so sets and pairs do most of the work for us. Then we add the best overcard hands: {AQ,AJ} =32 combos.

This gives us 83 combos, and a bit more than we need. We can now use a bit of good poker sense and drop the 6 22 combos. Note that if we are behind a better pair on the flop, it’s better to have AQ/AJ than 22, since the overcard hands have more outs. So we land on the following defense strategy for Bob on the 8 5 3 flop after flatting on the button preflop:

We defend 3 combos more than we need, but that’s fine.

Summary:
Bob’s total flop strategy on the dry flop 8 5 3 after flatting on the button:

  • Raise for value
    None
  • Flat
    {88,55,33,JJ,TT,99,77,66,44,AQ,AJ} =77 combos
  • Bluffraise
    None

So we managed to defend the minimum 57%, but we had to use overcard hands to get there. Of course we technically don’t have the pot-odds to draw to overcard outs, but keep in mind that our overcards are sometimes ahead of Alice on the flop (she has lots of low card hands in her c-betting range). We should also have a bit of implied odds, since Alice might barrel a lot of turn cards that hit our overcards, assuming they are scare cards for us. So she might choose to bluff the turn if a Q falls to barrel us off our weakest one pair hands. Then she donates implied odds to our top pair with AQ, and sometimes she will bet into our slowplayed sets.

We’ll now go through the two example flops one more time, but now with Bob in the big blind after flatting a preflop steal raise from Alice in the small blind. Bob’s preflop flatting range is now wider, and therefore more difficult to defend.

5. Bob’s flop strategies after flatting in the big blind
We’ll now go through Bob’s flop strategies on the coordinated flop and then on the dry flop after flatting in the big blind after a steal raise from the small blind.

5.1 Play on coordinated flop after flatting in the big blind

Blind vs Blind flat list

TT-22
ATs-A6s AJo-A7o
K8s+ K9o+
Q8s+ Q9o+
J7s+ J9o+
T7s+ T8o+
96s+
86s+
75s+
65s

362 combos

Bob has 294 remaining combos in his range, given this flop:

To defend this preflop flatting range optimally, Bob needs to defend 57% of 294 combos on the flop, which is 0.57 x 294 =168 combos. So compared to playing the button preflop range, we will now have to climb further down on the equity ladder and “promote” some button folding hands to flatting and bluffraising hands in the big blind. Note that this is consistent with the fact that we’re up against a weaker raising range (Alice opens her 35% button range in the small blind, but her 25% CO range in CO). So it makes sense that we can value raise and flat with weaker hands than we could on the button.

We now have much more worthless trash in our range, but on the other hands we also have more two pair combos (wider ranges make more “raggedy” two pair combos postflop), and this helps our defense. Which of these two effects is more significant remains to be seen.

We do as we did on the button and put top pair in the flop flatting range. So we value raise two pair(T9s, T9o, Q9s, Q9o, QTs, QTo), sets (TT,99), and straight straighter (J8s, KJs,KJo). This gives us 53 value combos of strong made hands. Then we can add the best pair + draw combos QJs/QJo (top pair + open-ender), and we end up with a value range of 65 combos:

Now we need 65 bluff combos and and 168 – 2 x 65 =38 flatting combos. We pick the flatting hands first from the next rung on the equity ladder (one pair hands and non-monster draws):

For example:

– The remaining top pair hands: AQs,AQo,KQs,KQo,Q8s
– The best middle pair + gutshot hands: KTs,KTo

This gives us 39 combos as shown below:

So we end up with a situation similar to the one we had on the button. We use a tight value range of only two pair and better plus monster draws, and we have plenty of good hands to use as flatting hands. We also have a wide range of mediocre hands to use as bluffs (weak one pair hands and weak draws).

Again, note that we’re not particularly concerned with how to best play a hand like AT on this flop. We simply use the strength principle together with the requirement of 57% total defense, and then we let the hands fall into reasonable categories. In this example AT ended up in the bluffraising range, but this is not very important for us. What counts the most is that we end up with a solid total defense strategy, and that we have a reasonable system for labeling hands as value hands, flatting hands, bluffraising hands and folding hands.

At any rate, what remains is to choose the 65 bluff combos. We pick hands from the remaining one pair hands and draws. For example.:

– The remaining middle pair hands: ATs,ATo,T8s,T8o,T7s
– Bottom pair + open-ender/gutshot: J9s,J9o,98s
– Underpair + gutshot: 88
– Remaining open-enders: AJ,J7s

This gives us 64 combos (close enough) as shown below:

Summary:
Bob’s total flop strategy on coordinated flop Q T 9 after flatting in the big blind is:

  • Raise for value
    {T9s,T9o,Q9s,Q9o,QTs,QTo,TT,99,J8s,KJs,KJo,QJs,QJo} =65 combos
  • Flat
    {AQs,AQo,KQs,KQo,Q8s,KTs,KTo} =39 combos
  • Bluffraise
    {ATs,ATo,T8s,T8o,T7s,J9s,J9o,98s,88,AJ,J7s} =64 combos

Bob then defends 65 + 39 + 64 =168 combos in total, which is 168/294 =57% of his total flop range. Again we see that it’s easy to design a strategy that defends the minimum requirement 57% when the flop comes medium/high and coordinated. We have more weak hands in our preflop range after flatting in the big blind, but we also flop more value hands (more two pair combos).

Like we did in the button scenario we ended up putting some potential flatting hands in the bluffraising range. We used the strength principle as our starting point, chose a solid value range, and let the rest more or less follow from mathematics.

Our last scenario is the most difficult one, namely defending on a dry flop with a wide and weak preflop flatting range:

5.2 Play on dry flop after flatting in the big blind

Blind vs Blind flat list

TT-22
ATs-A6s AJo-A7o
K8s+ K9o+
Q8s+ Q9o+
J7s+ J9o+
T7s+ T8o+
96s+
86s+
75s+
65s

362 combos

Bob has 337 remaining combos in his range, given this flop:

Again we see that most of Bob’s preflop range is intact on a low and dry flop, since the flop connects poorly with our range. We have a flop range of 337 combos and we have to defend with 57%, which corresponds to 0.57 x 337 =192 combos. We use the same philosophy as before, and choose to defend this low and dry flop with only a flatting range.

As we’ll see in a minute, it’s impossible to get to 57% defense without flatting a very wide range of overcard hands. But we start by counting all our combos of one pair or better, and see what we get:

– Sets: 88,55,33
– One pair: TT,99,77,66,44,22,A8,K8s,Q8s,J8s,T8,98s,87s,86s,75s,65s

We have 93 combos of one pair or better:

So with a theoretical 57% total defense, we have to flat 192 – 93 =99 no pair combos. This means we have to reach far down the overcard hierarchy, and we conclude that:

Defending an extremely low/dry flop optimally with a very wide preflop flatting range might me impossible in practice

So we have to accept lots of folding in this scenario, unless we want to defend with lots of ace high and king high hands. We remember that with a tight/solid “IP flat list” on the button (with only 140 preflop combos) we managed to defend this flop 57% by only flatting sets, one pair, and the best overcard hands AQ/AJ. But with a big blind flatting range we have to play many more overcard hands.

Let’s build an optimal 57% defense range, so that we can see what it looks like. We begin by adding our only decent draw (an open-ender with 76s) and then we add overcard hands. If we flat all ace high/king high combos with minimum a T kicker, we get 193 combos (1 more then the 12 we need):

Here we could also have chosen the gutshot + overcard combos 97s/96s, but this will not make a big difference. The gist of it is that we have to defend a very wide and weak range on the flop, and that more than half our flats are no-pair hands.

Summary
Bob’s total flop strategy on the dry flop 8 5 3 after flatting in the big blind is:

  • Raise for value
    None
  • Flat
    {88,55,33,TT,99,77,66,44,22,A8,K8s,Q8s,J8s,T8,98s,87s,86s,75s,65s,AQ-AT,KQ-KT} =193 combos
  • Bluff raise
    None

6. Summary
We have worked our way through 4 flop scenarios where we tried to defend optimally against a c-bet after flatting preflop. We looked at the following scenarios:

– Coordinated flop with a tight preflop flatting range
– Dry flop with a tight preflop flatting range
– Coordinated flop with a loose preflop flatting range
– Dry flop with a loose preflop flatting range

We saw that defending a coordinated flop is an easy task with both preflop flatting ranges. On dry flops we run into the problem of not having enough one-pair-or-better hand or good draws, so we have to resort to overcard hands to reach 57% total defense. On the driest flops we might have to give up more than optimally, but we might be able to make up for this by defending a bit more than optimally on the coordinated flops.

On the extremely dry flops we chose to defend with only a flatting range to avoid polarizing our flop defense ranges into a very strong raising range and a very weak flatting range. If we choose to defend this way, we slowplay all strong hands by flatting them on the flop, planning to raise for value on later streets.

In the next article in this series we’ll go one step further and discuss play on the turn and river after executing our defense strategies in position on the flop.

Good luck!
Bugs – See more at: http://en.donkr.com/Articles/optimal-postflop-play-in-nlhe-6-max—part-3-808#sthash.m4RmAhOM.dpuf

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