Optimal Postflop Play in NLHE 6-max – Part 4

1. Introduction
This is Part 4 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.

I Part 1, Part 2 and Part 3 we introduced fundamental theory for flop play heads-up in position after flatting preflop. We then put the theory to use by working through several examples of flop play. We placed Bob as the preflop flatter heads-up in position against Alice’s openraise, and then we let him defend optimally against Alice’s c-bets.

The result of this work was a method for estimating defense ranges on the flop against the preflop raiser’s c-bet:

  • We found that we need to defend ~57% of the time, using a combination of value raising, bluff raising and flatting on the flop in order to prevent Alice from profitably c-betting any two cards as a bluff
  • Then we estimated Bob’s optimal value/bluff ratio for flop raising to be 1 : 1
  • We start by choosing our value range. Now we also know how many bluffs we need (number of bluffs =number of value hands), and also the total number of raising hands
  • Then we choose our flatting hands from the best hands not good enough to raise for value. We choose enough flatting hands to make the total number of valueraising + bluffraising + flatting hands equal to 57% of our total flop range
  • Then we choose the bluff combos we need from the best hands not good enough to raise for value or flat, and we fold everything else

We studied play on coordinated flops and dry flops separately. We found that coordinated flops (particularly those with medium/high cards) were easy to defend. On these flops we have many value hands and good flatting hands to use, and we defend with a combination of raising and flatting. On the dry flops we have few value hands, and we concluded that there are advantages to flatting everything on the flop (i.e. we slowplay our strongest hands, planning to raise for value on later streets).

By generating random flops (using Flopgenerator.com) and then building flop defense ranges for these flops, we can train our ability to quickly and accurately estimate optimal defense strategies. We don’t have to get it precisely right at the table. What we need is a sound qualitative understanding of how to play different types of hands on different types of flops.

We group our playable hands into 3 categories: Value hands, flatting hands, and bluffraising hands. As a start, using the simple classification scheme below will work well:

– Value hands: Two pair and better + monster draws
– Flatting hands: Good one pair hands and non-monster draws
– Bluffraising hands: Mediocre one pair hands, overcards, gutshots

Part 1, Part 2 and Part 3 gave us the necessary tools for defending in position on the flop against a c-bet after flatting preflop. But we did not talk about turn or river play. When we defend the flop against a c-bet from Alice, we have the following outcomes:

  • 1. We raise the flop, Alice 3-bets
  • 2. We raise the flop, Alice folds
  • 3. We raise the flop, Alice calls
  • 4. We flat the flop, Alice checks the turn
  • 5. We flat the flop, Alice bets the turn

The scenarios 3-5 leads to play on the turn. To complete our postflop strategies after flatting in position preflop we’ll now move on to play on later streets, after we have executed out optimal defense strategies on the flop. We’ll limit our discussion to the scenario where Bob flats preflop, flats the c-bet on the flop, and then Alice has the opportunity to bet again on the turn.

We can study this scenario from both sides. For Bob it’s important to play the turn in such a way that Alice can’t automatically profit from 2-barreling any two cards after getting called on the flop. For Alice it’s important to play the turn in such a way that Bob can not automatically profit from floating (calling with a weak hand, planning to steal the pot on later streets) any two cards on the flop.

If Alice checks and gives up on too many turns, Bob can exploit this by flatting any two cards on the flop, planning to bluff the turn when Alice checks and gives up. Alice prevents this by betting and check-calling/check-raising enough on the turn after c-betting the flop.

In this article we’ll look at Bob’s turn/river strategies and study them by working through two scenarios. We let Alice raise from CO, Bob flats on the button, and we get a heads-up postflop scenario. We use our default preflop ranges as a starting point, and we’ll do the work on the two flop textures we used in Part 3 (a coordinated flop and a dry flop).

2. Preflop ranges, flop textures and postflop model
We begin by defining our preflop ranges, the flop textures we’ll work on, and assumptions about postflop play.

2.1 Preflop ranger
We use our standard ranges. Alice opens her default ~25% range from CO, and Bob flats with the hands in “IP flat list” on the button:

Alice’s ~25% CO openrange

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

326 combos
25%

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

Here is a download link for this table in document form (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 is made up of the following 140 combos:

“IP flat list” after 25% CO openraise:

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

140 combos

2.2 Flop textures
We’ll look at two postflop scenarios, one on a coordinated flop, and one on a dry flop. We use the two flop textures we worked on in Part 3:

Coordinated flop

On this flop Bob defends with a combination of value raising, bluff raising and flatting.

Dry flop

On this flop Bob elected to defend only with a flatting range. He slowplayed all his strong hands, planning to raise for value on later streets.

2.3 Postflop model
In both scenarios we’ll let Bob face a 3-barrel from Alice those times he does not raise. When Bob flats the flop, Alice continues to bet the turn. If Bob flats again on the turn, Alice bets again on the river. So Bob has to make sure he defends enough on turn and river to prevent Alice from having an automatic profit by 3-barreling all 3 streets when Bob only calls (and signals a weak range which Alice might think she’ll be able to exploit by bluffing a lot).

The bet sizing scheme those times Alice bets all 3 streets is:

  • Alice raises 3.5 bb preflop, and the pot is 8.5 bb after Bob’s call
  • Alice c-bets ~3/4 pot on the flop, and the pot is ~21 bb after Bob’s call
  • Alice bets ~3/4 pot on the turn, and the pot is ~53 bb after Bob’s call
  • Finally, Alice bets 32 bb (06 x pot) into the 53 bb pot on the river

For both the coordinated and the dry flop we’ll use theory and assumptions from Matthew Janda’s brilliant Cardrunners video Visualizing your entire range, and we’ll apply the theory to our own default ranges for these scenarios.

3. Postflop play on coordinated flop
We first define Bob’s total flop strategy, and then we move on to turn play after Bob has flatted the flop:

3.1 Bob’s defense strategy against a c-bet on a coordinated flop

We remember from Part 3 that Bob defined the following flop strategy against Alice’s c-bet:

  • 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

We found that the original 140 combos in our preflop flatting range was reduced to 117 combos on this flop. Bob defends (17 + 33 + 17)/117 =57%, which is the optimal defense frequency. He defends 33/117 =28% by flatting and the rest by raising.

So the range we bring with us to the turn after flatting the flop is {AQs,AQo,KQs,KQo,JJ,JTs} =33 combos.

3.2 Bob’s turn strategy after flatting the flop
We generate a random turn card, and the turn board texture becomes: 9 Q T Q

Alice now fires a 2nd barrel for 3/4 of the pot. How should Bob play his {AQs,AQo,KQs,KQo,JJ,JTs} range on the turn?

We start by counting Bob’s turn range:

The flatting range Bob brought with him to the turn is reduced from 33 to 25 combos when this turn card falls. Since Alice bets 3/4 pot, she is getting pot-odds 1 : 0.75 on a any-two-cards bluff. She needs to succeed 0.75/(1 + 0.75) =43% to have an automatic profit bluffing the turn with any two cards, and Bob needs to defend 100 – 43 =57% on the turn to prevent this. Note that this optimal defense percentage is the same as the one we used on the flop, since Alice uses the same 3/4 pot bet sizing on both streets.

Defending 57% is trivial for Bob, given this turn card. 57% of 25 combos is only 14 combos. Bob can meet this requirement by only raising trips for value. The then defends 16 combos as shown below:

A bit more than we need, but that’s of course fine. In theory Bob should balance his value raises with an equal amount of bluffs, but that’s not necessary to get to 57% total defense. The simple turn defense job is a consequence of having a very simple defense job already on the flop. The flop hit our preflop range hard, which gave us a strong flop flatting range. And when the turn card makes our flop flatting range even stronger, we are left with mostly value hands in our range.

Let’s generate another random turn card so that Bob will have some decisions to make: 9 Q T 3

This turn card is a blank that doesn’t touch Bob’s flop flatting range, and he still has all the 33 flop flatting combos in his range on the turn:

In order to defend the required 57% against Alice’s turn bet, he needs to defend 0.57 x 33 =19 combos. Since his range did not improve noticeably between the flop and the turn (apart from picking up two flush draws with A Q and K Q), it’s obvious that the hands we classified as flatting hands on the flop are still (at most) flatting hands on the turn. So we go to the river with only a flatting range.

We then choose the 19 best combos, which ends up being a turn flatting range of only top pair hands. We then use all our AQs/AQo combos (12) plus 7 of the KQ combos. We obviously choose K Q , and then we add 6 more. For example K Q , K Q , K Q , K Q , K Q , K Q .

Bobs’ turn defense against Alice’s 2-barrel then consists of flatting the range {AQs,AQo,K Q , K Q , K Q , K Q , K Q , K Q , K Q } =19 combos.

Note that we have now begun the job of getting away from top pair hands in order to avoid paying off Alice better hands too much. We continue with all our top pair/top kicker hands, but we fold some of the weaker top pair hands. This intuitively makes sense, since always calling down with all top pair hands won’t be profitable against a competent opponent.

3.3 River strategy after flatting flop and turn
We continue with the second random turn card and assume that the board was 9 Q T 3 on the turn.

Bob flatted the turn with the range {AQs,AQo,K Q , K Q , K Q , K Q , K Q , K Q , K Q } =19 combos

We generate a random river card and get: 9 Q T 3 6

The river is a blank that doesn’t touch our turn flatting range, and we still have the 19 combos we flatted on the turn:

So by flatting the flop and the turn, given this board, we have gone to the river with a range of flatting hands that weren’t strong enough to raise for value at any point. Therefore, they are not strong enough to value raise on a blank river either. In other words, we have a range of bluffcatchers on the river.

Alice now bets 0.6 x pot (32 bb into a 53 bb pot), and she gets pot-odds 53 : 32 on a 3-barrel bluff. She needs to succeed more than 32/(52 + 32) =38% to automatically profit from bluffing any two cards on the river. Bob’s task on the river is therefore to defend at least 100 – 38 =62% to prevent this.

Since Bob has no value hands in his range on the river, he doesn’t have to think about balancing a raising range. He simply flats with enough of his bluffcatchers to prevent Alice from bluffing any two cards profitably, and then he folds the rest of his hands.

He needs to flat 0.62 x 19 =12 of the 19 top pair hands he brought with him from the flop to the turn to the river. We obviously choose the 12 AQs/AQo combos and fold all our KQ combos.

Again, we continue the process we began on the turn of getting away from our weaker one pair hands in order to avoid paying off too much to Alice’s better hands (she can have lots of straights, sets and two pair hands). But we call down with sufficiently many hands to prevent her from bluffing any two cards profitably anywhere along the way from flop to turn to river.

3.4 Summary of play on coordinated flop
Bob had an easy job on the flop 9 Q T when turn and river were blanks. On a flop texture that hits his preflop flatting range hard, he ends up with a strong flop flatting range with many good one pair hands. So when the turn and river brick off, Bob simply has to “peel off” his weaker one pair hands along the way, and the he calls the final river bet with his best bluffcatchers. In this example, this turned out to be his top pair/top kicker hands, which makes good sense (they quickly turn into bluffcatchers when our opponent keeps betting into us on a coordinated board).

4. Postflop play on dry flop
First we define Bob’s total flop strategy, then we move on to turn play after Bob has flatted the flop:

4.1 Bob’s defense strategy against c-betting on a dry flop

We remember from Part 3 that Bob defined the following flop strategy against Alice’s c-bet:

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

The original 140 combos in the preflop flatting range were reduced to 130 combos in this flop, so Bob defends 77/130 =59% (a bit more then the minimum 57%, which is fine). All defense is done by flatting for reasons discussed in Part 3.

So the range we bring with us to the turn after flatting this dry flop is: {88,55,33,JJ,TT,99,77,66,44,AQ,AJ} =77 combos

4.2 Turn strategy after flatting the flop

We generate a random turn card, and the turn texture becomes: 3 8 5 Q

Alice now fires a 2-barrel for 3/ of pot. What is Bob’s strategy on the turn with the range {88,55,33,JJ,TT,99,77,66,44,AQ,AJ}?

We begin by counting Bob’s turn range. The turn card hits a part of his flop flatting range, and we have 73 combos in our range on the turn:

To defend the required 57% against Alice’s 3/4 pot turn bet, Bob has to defend 0.57 x 73 =42 combos. We have some value hands in this range after slowplaying the flop, so we can raise the turn with a mix of value hands and bluffs.

We let our value hands be the 9 set combos {88,55,33} =9 combos Next we balance this range with some bluffs. We’ll make it simple and use the same 1 : 1 ratio we used on the flop. Note that this isn’t necessarily 100% correct, since the exact ratio we need depends on the equities of the hands involved, but we’ll assume that a 1 : 1 value/bluff ratio works well on both the flop and the turn. So we need 9 bluff combos, and end up with a total turn raising range of 9 + 9 =18 combos.

This means we have to defend 42 – 18 =24 combos by flatting to get to 57% total defense. We have many one pair hands to use, and it’s obvious to begin with the 12 AQ combos that made top pair on the turn. Then we add our best underpairs JJ/TT =6 + 6 =12 combos, and we are done. Our flatting range is then {AQ,JJ,TT} =24 combos.

Lastly, we pick 9 bluff raising combos for balance. We can choose from the remaining one pair hands (underpairs lower than TT) and our overcard hands. For example, we can choose the 4 AJs combos plus 5 of the 6 99 combos (for example 9 9 , 9 9 , 9 9 , 9 9 , 9 9 ). In other words, all AJs and all 99 with a spade or heart.

Our total turn defense is then:

– Value raise: {88,55,33} =9 combos
– Bluff raise: {AJs,9 9 ,9 9 ,9 9 ,9 9 ,9 9 } =9 combos
– Flat: {AQ,JJ,TT} =24 combos

When we raise for value, the rest of the hand plays itself. If Alice 3-bets, we get all-in on the turn with good equity. If she calls, we bet the rest of our stack on the river. After a bluff raise we fold to a 3-bet and have no decisions to make in that case. If Alice calls our bluff raise and checks the river, we choose between bluffing again or giving up and checking down. Note that the last decision is not a forced and tricky one, even if it can be hard to choose the best alternative.

Note that when Alice has checked the river after calling our turn bluff, this simply means we get one more chance to steal the pot (instead of having to fold to a turn 3-bet) without having risked any more money to get this opportunity. If we’re not sure about what to do, we can simply check down and not risk more chips, and when we see a good bluffing opportunity, we an take it. At any rate, we are under no pressure to make a difficult choice after raising the turn and getting checked to on the river. Additional bluffing opportunities on the river are simply gravy.

So now we look at what happens on the river after our turn flat with the range {AQ,JJ,TT} =24 combos.

4.3 River strategy after flatting the flop and turn
The board was 3 8 5 Q on the turn.

We assume Bob flatted Alice’s turn barrel with the range {AQ,JJ,TT} =24 combos. We then generate a random river card and let Alice fire a 3-barrel.

The river board texture becomes: 8 5 Q 2

A complete blank that doesn’t touch our turn flatting range, and we still have 24 combos in our range on the river:

Since none of the flatting hands improved between the turn and the river, and since none of them were value hands on the turn, we obviously have a range of bluffcatchers that we call or fold. In other words, the exact same river scenario we had on the second random river card for the coordinated flop previously.

When Alice bets 32 bb into thee 53 bb pot, we found previously that Bob needs to defend 62% to prevent a profitable any-two-cards river bluff. So Bob defends 0.62 x 24 =15 of the 24 bluffcatchers he brought to the river.

We call with the 12 AQ hands plus 3 of the best underpairs (3 JJ combos). We choose the 3 JJ combos with a spade: J J , J JJ J .

Bob’s river strategy is then to call with {AQ,J J , J JJ J } and fold his remaining JJ and TT hands.

As on the coordinated flop we ended up calling down with a range of medium strong bluffcatchers that failed to improved to value hands. But we folded many of them along the way, and only called all the way down with enough hands to prevent Alice from bluffing with any two cards anywhere long the way.

For practice, lets generate a river card that improves us enough to raise some hands. Assume that the river board texture now is 3 8 5 Q J .

This river card gives us a set, and the number of combos in our range is reduced from 24 to 21:

62% river defense means we defend 0.62 x 21 =13 combos. We now use the 3 JJ combos as value raising hands. We have about 74 bb left in our stack after calling 3/4 pot bets on the flop and turn. So when Alice bets 32 bb on the river, we shove to 74 bb, and Alice has to call 74 – 32 =42 bb to win a 53 (initial river pot) + 32 (Alice’s bet) + 74 (our shove) =159 bb pot. She gets pot-odds 159 : 42 =3.8 : 1 on this call.

We now want to balance our value raises (3 combos) with enough bluff combos to make Alice indifferent to calling of folding with the hands that can only beat us if we’re bluffing (her good-but-not-great hands like top pair and overpairs). When Alice is getting pot-odds 3.8 : 1, we need 1 bluff combo for every 3.8 value combos to make her calls with her bluffcatchers break even (she’s getting 3.8 : 1, and the odds against us bluffing are 3.8 : 1). So we need 3 x (1/3.8) =0.8 bluff combos, which we simply round to 1.

We choose one of the TT combos to use as a bluff: T T

Then we need 13 – 3 – 1 =9 flatting combos to get to 13 defense combos in total, and we then obviously choose 9 combos of AQ. For example A Q , A Q , A Q , A Q , A Q , A Q , A Q , A Q , A Q .

Bob’s river strategy when improving on the texture 3 8 5 Q J is then:

– Raise {JJ} =3 combos for value
– Raise {T T } =1 combo as a bluff
– Flat {A Q , A Q , A Q , A Q , A Q , A Q , A Q , A Q , A Q} =9 combos

We happily raise our 3 set combos for value, balance it out with one bluff combo so that Alice can’t save money by folding all her bluffcatchers, and then we do the rest of the defense by flatting with most (but not all) of our top pair/top kicker hands.

5. Summary
We have gone one step further in our study of optimal postflop play heads-up after flatting preflop. Previously, we have looked at defense strategies against a c-bet on the flop. In this article we have moved on to turn and river play after flatting the flop.

We worked on two flop textures (coordinated and dry) and looked at how the player in position has to play the turn after flatting the flop, and then play the river after flatting the turn. This gave us insight into how we defend against a preflop raiser that 3-barrels (bets all 3 streets) postflop when the player in position keeps calling.

We saw that our defense ranges grew stronger and stronger from flop –> turn –> river. This makes good sense, intuitively. In the cases where our flatting range on the turn and river only contained bluffcatchers (good one pair hands), we saw that we started the process of getting away from these (possibly losing) hands on the turn. Then we continued this process on the river those times we did not improve. We ended up calling down with just enough bluffcatchers to prevent the raiser from barreling any two cards as a bluff on any street.

This is an important mindset that will help you get away from situations where you are calling down way too much with so-so one pair hands in the hope that your opponent is bluffing. It can work well when you have a read on a very aggressive player, but if you call down mindlessly with all decent one pair hands against a good, thinking opponent who keeps betting into you, you will lose a lot. Against a player who keeps betting into you, even your good top pair hands quickly turn into bluffcatchers. But you should of course call down with enough of your bluffcatchers to prevent profitable bluff-barreling with any two cards.

And in the cases where we do improve along the way, we also defend by raising for value, and balancing this with some bluffs. The rest of the defense is done with our bluffcatchers, as before.

The strategies we have discussed here are of the type you need to train between sessions in order to use them in practice. You will not have the time to do all this thinking at the table, so train away from the table and aim for a good qualitative understanding of the principles involved. You don’t need to build perfect strategies at the table, and any reasonable approximate strategy will work fine.

The next topic in this article series is postflop play as the preflop raiser heads-up and out of position after getting flatted preflop. Now we’ll study how Alice should play postflop in order to prevent Bob from exploiting her by floating any two cards on the flop or turn, planning to steal the pot later.

Good luck!
Bugs – See more at: http://en.donkr.com/Articles/optimal-postflop-play-in-nlhe-6-max—part-4-810#sthash.9WZ7jsWH.dpuf

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s