Optimal 3-bet/4-bet/5-bet strategies in NLHE 6-max – Part 7

1. Introduction

This is Part 7 in the series Optimal 3-bet/4-bet/5-bet-strategies i NLHE 6-max, and the last theoretical part of the article series (a practical part might come later, and we’ll talk about this at the end of this article). In Part 6 we began testing the strategies laid out in Part 1 to Part 5, and we’ll continue this work in Part 7.

As in Part 6 we’ll use modeling with Pokerazor to estimate EV for our heads-up 3/4/5-bet strategies (including flatting) to confirm that they are fundamentally sound. The work done in Part 6 showed that both the raiser’s and the 3-bettor’s strategies were solid, and that they defended well against an opponent trying to bluff with any two cards. This was what the strategies were designed to do, and we can now be sure that they work the way we want them to.

Part 7 will be about:

  • Flatting in position and comparing the EV for flatting vs 3-betting for value with hands in between the regions of clear value hands and clear flatting hands
  • Adjusting the heads-up 3/4/5-bet theory to blind vs blind scenarios


1.1 Introduction to Pokerazor simulations of flatting in position

In Part 7 we’ll discuss the part of the 3-bettors strategy that comes in addition to 3-betting. When Alice has openraised and Bob has position, he will 3-bet a range of hands according to his part of an optimal strategy pair, and in addition he will flat some range of hands he thinks can be played profitably. In Part 2 we defined the following default flatting range for Bob in position:

IP flat list

ATs+ AJo+
KTs+ KQo

Without {KK+}: 162 combos
Without {QQ+}: 156 combos
Without {QQ+,AK}: 140 combos
Without {JJ+,AK}: 134 combos

And we remember that the number of combos in the flatting range depends on how wide of a range Bob 3-bets for value. Against a ~15% openraise from Alice, Bob’s value range is only {KK+} (plus 7 combos of Axs that he 3-bets as a bluff, planning to 5-bet bluff if Alice 4-bets). So QQ/AK are put in the flatting range, and Bob now has 162 combos that he flats. Against Alice’s ~25% CO raising range, Bob 3-bets {QQ+,AK} for value (plus 12 combos of Axs 5-bet bluffs), so he has 140 flatting combos in this scenario.

All of this is summarized in the overview over optimal strategy pairs that we made in Part 2:

Below is a link for downloading this document (right click and choose “save as”):

In a similar way, when Alice has position after she has openraised and Bob has 3-bet her from the blinds, she will respond to the 3-bet with a mix of optimal 4-betting and flatting. In Part 3 we defined the following standard defense range for Alice after she has opened her default 35% openrange and Bob has 3-bet from the blinds:

– 4-bet: {QQ+,AK} for value + {ATo,A9s-A7s} as a bluff
– Flat JJ-88,AQ-AJ,ATs,KQ-KJ,KTs,QJ,QTs,JTs[/pre]

Bob’s total defense strategy from the blinds heads-up against Alice’s button openraise is summarized here:

Download link (right click and choose “save as”):blind_defense_vs_button_summary.doc

In this article we’ll focus mostly on Bob’s flatting in position after an openraise by Alice. We’ll use the standard positional flatting range as our starting point, and then study how the best flatting candidates (for example QQ and AK) move between the value range and the flatting range when Alice’s openrange varies. To illustrate this we’ll use Pokerazor to estimate the EV of using QQ as a value 3-betting hand and as a flatting hand. This will give us insight into the best way of playing QQ preflop, as a function of Alice’s openrange.

We shall see that some hands can be played profitably both ways. For example, QQ is +EV against Alice’s ~15% EP openrange both when we 3-bet it for value and when we flat. So when we decide to flat QQ as our default play in this scenario, it’s because we assume that flatting is more profitable than value 3-betting. we’ll use modeling and Pokerazor simulations to show this.

We’ll also discuss adjusting our 3-betting/flatting ranges when we play against weak players that flat lots of medium strong hands out of position after a 3-bet. Bob’s optimal 3-betting strategy in position is based on the assumption that Alice either 4-bets or folds out of position, so he polarizes his 3-betting range into premium hands (for example, {QQ+,AK} and bluffs (for example K9s), and then he flats some hands in the region between his value 3-betting hands and his 3-bet bluffs (for example, AQ). But when the raiser flats a lot of 3-bets out of position, it might be better for Bob to move his best flatting hands up to the value range. For example, Bob might elect to 3-bet all pairs AA-JJ for value, together with AK-AQ. The reason for this adjustment is that JJ and AQ should do well as value hands against a player that flats JJ-99, AQ-AT, KQ-KT, QJ and similar hands out of position (so we’re raising for value mainly against the range that calls us and not necessarily against the range that 4-bets us).

The last scenario we’ll model is flatting versus value 4betting with JJ after Alice has openraised JJ on the button and gotten 3-bet by Bob in the blinds. This choice was discussed in Part 3, and we talked about the consequences of putting JJ in the value range versus flatting the 3-bet with it. Pokerazor will give us an estimate of the best way to play JJ against a 3-bet in this scenario.

1.2 Introduction to the scenario “blind vs blind”

The last topic of Part 7 is a look at the heads-up scenario blind vs blind. Small blind openraises and big blind defends by 3-betting or flatting. We then get two possible scenarios:

– A heads-up 3/4/5-war preflop
– Postflop play in a raised pot with the big blind in position

First we’ll look at how mathematics (the pot-odds small blind is getting on a steal raise) dictates how often big blind needs to defend preflop. Then we’ll use the theory for heads-up 3/4/5-betting from previous articles as a starting point, and then adjust it to the blind vs blind scenario. We know this theory well by now, and this work will be straightforward application of familiar concepts.

2. Pokerazor simulations of flatting in position

We’ll estimate EV for 3-scenarios using Pokerazor and simple modeling:

  • Flatting versus 3-betting with QQ heads-up with position on a ~15% UTG raiser who defends against 3-bets by 4-betting or folding
  • Flatting versus 3-betting with QQ heads-up with position on a ~15% UTG-raiser who defends against 3-bets by 4-betting, calling or folding
  • Flatting of 3-bet vs 4-betting with JJ heads-up on the button against a 3-bet from the blinds (where the 3-bettor is using our default blind defense strategy outlined in Part 3)

In the first two model studies we’ll justify our choice of flatting QQ (and similarly, AK) in position against a tight ~15% openrange (a typical tight-aggressive UTG range in 6-max play) where the raiser defends against 3-bets by 4-betting or folding. In previous articles we noted that QQ is not strong enough to be a favorite against the ~15% raiser’s optimal value range {QQ+,AK}, so we’d rather flat QQ and play it postflop with position on his total openraising range.

But if the raiser defends against 3-bets by also flatting some medium strong hands (e.g. JJ-99, AQ, AJ, KQ) out of position, we’ll see that the EV for value 3-betting QQ increases. The reason is obviously that we can extract more value from all of these medium strong flatting hands by playing against them postflop instead of winning the pot against them preflop (since the raiser will mostly fold them to our 3-bet if he follows our optimal strategy out of position).

The last model study we’ll do is comparing the EV for flatting vs value 4-betting when we have openraised JJ on the button and have gotten 3-bet from the blinds. In Part 3 we designed a default defense strategy for this scenario, and we used JJ as a flatting hand. But we commented that JJ would also work as a value 4-betting hand, and we defined an alternative defense strategy with JJ in our 4-bet value range. Here we’ll use modeling to determine what works best (and we’re guessing right now that it’s a close decision).

2.1 A simple model for estimating preflop + postflop EV

When we flat hands preflop we are setting ourselves up for seeing a flop and then playing postflop. Postflop strategies are impossible to write out in full detail, since we have to take into consideration all possible combinations of flops, turn cards and river cards. We’ll simplify things by using the following simple model:

  • Both players start with 100 bb stacks
  • The raise and the 3-bet are pot-sized
  • A 4-bet is to 27 bb (a little less than pot-sized)
  • A 5-bet is all-in
  • We specify preflop ranges and preflop strategies exactly, based on our default openranges and optimal 3/4/5-bet strategy pairs from previous articles
  • We assume that all other players fold preflop
  • Those times we have to play postflop, we assume both players check to showdown

This is a very simplified model that won’t give us precise estimates for specific EV-values. But what we want is to compare EVs for various scenarios. If we can assume that the model gives about the same error for all scenarios, we can assume that EV differences can give us useful information. For example, of the model tells us that flatting has higher EV than 3-betting for value, we shall assume that this is the case, even if we can’t determine the individual EVs for flatting or 3-betting accurately.

In addition to the numbers we crunch out using this model, we will use logic and sound poker sense where we can. For example, we can assume that if flatting sets you up for playing postflop with a hand that is the favorite against the raiser’s total range (e.g. QQ against a ~15% UTG range), you should be able to extract some EV postflop (e.g. when you flop an overpair or a set with QQ).

2.2 Flatting versus 3-betting with QQ heads-up in position against a ~15% UTG-range

We let Alice openraise from UTG with out default ~15% UTG range:

A9s+ AJo+
KTs+ KQo

194 combos

Scenario 1: Alice 4-bets or folds against a 3-bet
First we let Alice use the optimal 3/4/5-bet strategy corresponding to a 15% UTG range out of position. From the overview over optimal 3/4/5-bet strategy pairs with the raiser out of position (see document presented earlier in this article), we see that Alice then 4-bets {QQ+,AK} for value, 4-bets {AQ,AJs-ATs} as bluffs, and folds everything else.

We now use Pokerazor to calculate the EV for flatting and the EV for 3-betting QQ for value. We get:

EV (flat) =+2.49 bb
EV (3-bet) =+3.11 bb

We remember that there is 1.5 bb dead money in the pot from the blinds (we assume they always fold). So by flatting, we on average pocket the blinds plus 2.49 – 1.50 =0.99 bb from UTG’s stack. This is intuitively obvious, since we play postflop with a hand that is 70% favorite against Alice’s total range:

When we 3-bet QQ, we make 3.11 bb in total. 1.5 bb from the blinds and 3.11 – 1.50 =+1.61 bb from UTG’s stack. This is +0.62 bb relative to flatting, so 3-betting is more profitable than flatting when we ignore postflop betting (remember, both players are checking to showdown when they see a flop).

But here we should add a manual adjustment based on poker sense. There are two arguments for flatting being better than 3-betting in practice when the model EV difference is as small as here:

  • We should be able to make more than +0.62 bb postflop with QQ after flatting versus UTG’s total 15% range
  • The blinds will sometimes get involved with ranges we have very good equity against

So the +0.62 bb head start that 3-betting has over flatting in our model should be easy to overcome in practice, since we can extract value from postflop betting. For example, we will often flop an overpair (or a set) on an uncoordinated flop where Alice elects to continuation-bet her whole preflop raising range into us on the flop. And we’re a big favorite against this range.

We therefore conclude:

Flatting QQ in position against a tight ~15% openraising range should be more profitable than 3-betting and planning to 5-bet all-in after a 4-bet

Of course, this is against Alice’s optimal defense strategy against 3-bets where she 4-bets a value range + some 4-bet bluffs, and folds everything else (including most hands we beat). But what if we let Alice deviate from optimal play, and tell her to flat the 3-bet with various medium strong hands that are forbidden to play out of position in the optimal strategy?_

Scenario 2: Alice 4-bets, calls or folds against a 3-bet
This defense strategy is common among weak players, and you will see lots of flatting with weak hands out of position at loose-passive tables. There you will often see the raiser flatting 3-bets heads-up and out of position with decent aces, medium/low pocket pairs, and various suited/coordinated high/medium cards. Let’s give Alice permission to flat 3-bets with the following range out of position: {JJ-99,KQ,KJs,QJs,JTs}.

Note that the only change we make relative to the optimal strategy is to allow Alice to flat some hands in addition to 4-betting optimally. So she will still have 4-bet bluffs in her 4-betting range. This is not totally “in character” for a loose-passive player, but we keep the 4-bet bluffs in our strategy to make it simple to study the effect of flatting (since adding a flatting range is the only change we make).

So Alice’s new defense strategy against 3-bets heads-up and out of position becomes:

– 4-bet {QQ+,AK} for value and {AQ,AJs-ATs} as bluffs
– Flat {JJ-99,KQ,KJs,QJs,JTs}

Pokerazor gives us the EV for playing QQ in position behind Alice’s new loose-passive strategy:

EV (flat) =+2.49 bb
EV (3-bet) =+3.67 bb

EV for flatting QQ against Alice’s range is of course the same as before. But when Alice introduces some medium strength flatting hands to her defense strategy, the EV for 3-betting increases (from +3.11 bb to +3.67 bb).

The difference between flatting and 3-betting for value was +0.62 bb in favor of 3-betting when Alice used the optimal strategy. When she adds a flatting range, the difference increases to +1.18 bb in favor of 3-betting.

In the previous simulation we used some qualitative arguments to conclude that flatting should be able to “catch up” to 3-betting in practice because of postflop betting. We can probably conclude the same thing here, since the difference still is only ~1 bb.

But the modeling we have done with a flatting range for Alice is of course not a realistic model for a loose-passive player. So we will not draw strong conclusions about the profitability of flatting versus 3-betting. Instead, we conclude that:

Against a raiser who defends against 3-betting partly by flatting a range of medium strange hands out of position, the EV of 3-betting QQ for value increases relative to the same raiser not flatting.

Then we’ll have to use judgment to decide whether the raiser is flatting sufficiently many/sufficiently weak hands to make 3-betting better than flatting in practice when we have a hand that we flat as a default. As a final simulation, let’s give Alice an extremely loose-passive strategy with lots of flatting and no 4-bet bluffing:

– 4-bet {QQ+,AK} for value
– Flat {JJ-22,AQ-AJ,ATs,KQ,KJs-KTs,QJs,JTs,T9s,98s}

We get:

EV (flat) =+2.49 bb
EV (3-bet) =+2.66 bb

3-betting still makes more than flatting, but the difference is less than when Alice defended optimally. So giving Alice an extremely wide flatting range is seemingly not an argument for value 3-betting QQ. Or?

This is an interesting result, and we’ll look into it more closely. One thing that has happened here is that Alice has stopped 4-bet bluffing. And a significant chunk of our EV for value 3-betting comes from 5-betting and forcing Alice to fold her 4-bet bluffs after putting 27 bb into the pot. When Alice stops 4-bet bluffing, our value 3-bet with QQ sets us up for getting all-in against Alice’s value range {QQ+,AK}. Against this range our QQ is a 40% underdog, so we’re losing chips as of the moment when Alice 4-bets her value range and forces us to get the rest of the stack in as an underdog (without getting any compensation from picking up the pot against her 4-bet bluffs):

This means we have to be cautious when we 3-bet loose-passive players aggressively with “thin” value hands. We expect to make a lot of money from their folding or flatting against our 4-bet, but when they 4-bet, it might be best for us to fold our hand, even if it started out as a value 3-betting hand. Always 3-betting {QQ+,AK} for value and getting all-in when 4-bet is a fine standard line to take, but what if we have elected to 3-bet JJ for value against a loose player who flats a lot of 3-bets with a weak range out of position?

We can test this by repeating the last simulation, but this time we have JJ. Alice 4-bets {QQ+,AK} as before (no 4-bet bluffs) and flats this wide range {JJ-22,AQ-AJ,ATs,KQ,KJs-KTs,QJs,JTs,T9s,98s} against our 3-bet. Let’s first play JJ as a value hand and 5-bet it all-in against a 4-bet:

EV (flat) =+2.04 bb
EV (3-bet) =-4.39 bb

Ouch! Playing JJ as a value hand against a loose-passive player that never 4-bet bluffs makes our 3-bet a losing play, even if he flats out 3-bet with a wide and weak range preflop. We now get all-in against a range {QQ+,AK} that does not have a single hand we’re a big favorite against. So if the choice is between 3-betting JJ for thin value (planning to get all-in if 4-bet) and flatting, flatting is clearly best.

But there is a third option we can choose against a loose-passive player who flats a lot of 3-bets out of position, 4-bets a tight value range, and never 4-bet bluffs. We can simply 3-bet for thin value against his flatting range, but fold those (few) times he 4-bets us with his strong value range!.

We now 3-bet JJ for value (against the hands that call us), but fold to a 4-bet. We get:

EV (flat) =+2.04 bb
EV (3-bet and fold to 4-bet) =+2.52 bb

Bingo! 3-betting is now +EV, and more profitable than flatting (in our model). Next we can use judgment to determine whether flatting or value 3-betting/folding to a 4-bet is best in practice. 3-betting is probably our best option, since a hand like JJ is easier to play postflop heads-up than in a multiway pot (a 3-bet will probably isolate the raiser while flatting will often pull inn more players). The same argument can of course be used for QQ, but there are more good flops for QQ than for JJ.

Note that in the optimal strategies we have used throughout this article series, the term “3-betting for value” has been equivalent to 3-betting with the plan of 5-betting all-in against a 4-bet. But against a player who flats extremely loose against a 3-bet, but only 4-bets his strongest hands (and no bluffs), we might be better off 3-betting for value against his calling range, but folding those few times he has a strong value hand and 4-bets us. This is obviously an exploitative line that we should only use with reads. This type of player is fairly common in soft low limit games, so pay attention!

We saw in a previous simulation that QQ is too strong to fold against a tight 4-betting range, but with hands like JJ, TT, and perhaps also AQ (that blocks AA, QQ and AK in Villain’s value range) a 3-bet-for-value-but-fold-to-4-bet line could be the best line. We then deviate from optimal 3/4/5-betting to exploit the tendencies of a known loose-passive player.

Note that 3-betting for thin value in this way also as a bonus effect: We will usually isolate the raiser and get to play him heads-up postflop (since he calls far more often than he 4-bets). Isolating is good for us with hands like JJ, TTT and AQ, since they are more difficult to play in multiway pots (which we will often get when we flat) than QQ is.

Summary of modeling of flatting QQ in position
Below are some of the things we have learned from this series if simulations of playing QQ in position versus a ~15% UTG openraise:

  • Flatting QQ is probably more profitable than 3-betting for value when the raiser has a tight ~15% openrange that she defends optimally against 3-bets
  • 3-betting QQ increases in value relative to flatting when the raiser adds a flatting range of medium strong hands to her defense against 3-bets
  • But 3-betting for value with QQ against a ~15% UTG range is not necessarily better against a loose-passive player who flats a lot against 3-bets, but never 4-bet bluffs
  • Against that type of player we can 3-bet for thin value (against the range that flats us) with QQ and probably also some weaker hands like JJ, TT and AQ, but we might have to do exploitative folding against 4-bets to make this profitable (at least with JJ/TT/AQ)

Remember that all simulations done here are done with a tight openraising range. This is a range that is easy to defend correctly against 3-bets, so 3-betting with QQ (and probably also AK) is not a big earner for us. Therefore, let’s do one last simulation where we have QQ against Alice with a ~25% CO openraising range that she defends optimally:

Flatting vs 3-betting with QQ against optimally defended ~25% CO openrange

EV (flat) =+2.65 bb
EV (3-bet) =+9.28 bb

EV for flatting increases a little bit from +2.49 bb to +2.65 bb compared to flatting against a 15% UTG range. The EV for 3-betting makes a big jump from +3.11 bb to +9.28 bb. The reason is obviously that Alice’s value range now includes some hands (JJ, TT and AQ) that are crushed by our QQ. We conclude that against a loose openraising range it’s obligatory to 3-bet QQ for value.

Then we are done with our discussion of flatting versus 3-betting for value with QQ against an openraiser. Next we’ll do a model study of flatting vs 4-betting for value with JJ after openraising on the button and getting 3-bet by a player in the blinds.

2.3 Flatting versus 4-betting with JJ heads-up against a 3-bet from the blinds

The scenario is:

– We openraise JJ on the button
– Bob 3-bets us from the blinds
– We flat the 3-bet, or we 4-bet for value (calling a 5-bet)

We remember from Part 3 that Bob’s 3-betting range from the blinds against a button steal raise is:

– {TT+,AQ+} for value
– {66-22,A9s-A6s,K9s-K8s,QTs-Q9s,J9s-J8s,T9s-T8s,98s-97s,87s,76s,65s} as bluffs

In this range the weakest value hands TT/AQ effectively work as 5-bet bluffs, and Bob does not use dedicated 5-bet bluffing hands (like the Axs 5-bet bluff hands he uses in position).

We now use the same preflop and postflop models as previously. We either flat JJ and let the hand get checked down, or we 4-bet for value and call a shove.

Pokerazor gives us the EVs for flatting and value 4-betting:

EV (flat) =+4.32
EV (4-bet) =+5.91 bb

As we guessed in Part 3 both alternatives are nicely profitable for us, and the difference between them isn’t large. So we can play JJ both ways. Note that even if 4-betting has a head start of 5.91 – 4.32 =+1.59 bb relative to flatting, we might be able to catch up because of postflop betting.

In this spot we can use reads to help us decide. If you think Bob will make big postflop mistakes if you let him see a flop with all of his 3-bet bluffs, flatting could be better for you than 4-betting and making the rest of the hand automatic (Bob will shove his value hands and fold his bluffs, so he has no decisions to make, and neither have you). But if you think Bob will be able to outplay you postflop (or at least give you some tough decisions), just make it simple for yourself and 4-bet to end the decision making process right there.

Since we have begun looking at flatting of 3-bets on the button, let’s do the same simulation for AQ. This is a hand we immediately can see is a profitable flatting hand against Bob’s range, this his total 3-betting range is full of hands (the 3-bet bluffs) that we are a favorite against. But using AQ as a value 4-betting hand is probably too thin:

EV for flatting vs value 4-betting with AQ:

EV (flat) =+0.63
EV (4-bet) =-0.84 bb

We have an easy conclusion:

Value 4-betting AQ against the optimal blind defense strategy is not profitable. Flatting the 3-bet is marginally profitable in our model. In practice, flatting should be more profitable than in the model, since we’re playing postflop with position against a range we’re a small favorite against:

So we should have more opportunities to outplay Bob postflop than he has to to outplay us, and our postflop EV should be positive if we play well. But note that this requires more than a simple fit-or-fold strategy postflop. Calling the 3-bet with AQ and then folding to Bob’s c-bet on all flops where we don’t have a pair or a good draw will not be a good strategy for us. We have to be prepared to do things like floating without a pair or draw, or raising all-in on the flop as a semibluff. Not every time of course, but on some flops (and we’ll use flop texture and our knowledge about Bob’s range to determine which flops).

3. Blind versus blind

Our last topic in this article is the blind vs blind scenario:

– It’s folded to the small blind, who openraises
– The big blind 3-bets, flats, or folds

This is a heads-up scenario with the raiser (Alice) heads-up and out of position against an opponent (Bob) who defends by optimal 3/4/5-betting or flatting, so we can use the theory from previous articles. The only difference is that when Alice and Bob are in the blinds, the bet sizing changes a little. For example. if Alice openraises pot from the small blind, she raises to 3 bb and not 3.5 bb. Similarly, Bob’s pot-sized 3-bets become 9 bb and not 12 bb. This changes the value/bluff ratios in the 3-bet and 4-bet ranges somewhat.

We can make things simple by assuming that the optimal ranges we designed with both players outside of the blinds will work in the blind vs blind scenario as well. But this is a good opportunity to repeat the mathematics and the method for constructing optimal strategy pairs, so we’ll build them from the ground up.

Those of you that don’t want to memorize more ranges can use the previous strategy pairs. You then use the overview document and use Alice’s openraise percentage to pick a corresponding optimal strategy pair:

3.1 Bob’s optimal defense percentage

We begin with the fundamental principle of defense:

Bob has to defend enough to prevent Alice from stealing profitably with any two cards

Then we use some additional assumptions:

– Alice openraises her default 35% button range from the small blind
– Bob 3-bets his best hands for value
– He flats with he best hands not good enough to 3-bet for value
– Han 3-bet bluffs with the best hands not god enough to flat
– And then he 3-bets some Axs hands, planning to 5-bet bluff against a 4-bet
– Alice 4-bets or folds against a 3-bet

Our assumptions about stack sizes and bet sizes are:

– Both players start with 10 bb stacks
– Alice openraises pot (3 bb)
– Bob 3-bets pot (9 bb)
– Alice 4-bets to about 3/4 pot (20 bb)
– Bob 5-bets all-in

The assumption about Alice’s openrange is simply a choice we make. But opening 25-40% is typical for a good, aggressive player in the big blind, depending on how well the big blind defends. So assuming a 35% opening range for Alice in the small blind should give us a strategy pair that will work well for most small blind players.

From the overview over optimal strategy pairs we see that Bob’s 3-bet range varies little when Alice’s openrange goes from 30% to 40% (for example, Bob’s value range is {JJ+,AK} against the 30%, 35% and 40% opening ranges). So it makes sense to use a 35% opening range and then assume that the strategy pair we end up with is a good starting point for most small blind openraising scenarios.
We remember that when Bob had position on Alice outside the blinds, there was no minimum defense requirement for his total defense. We constructed his optimal 3/4/5-bet strategy, and then we said that Bob also would flat the hands in “IP flat list”. But when Bob is the only player between Alice and the pot, he has all of the blind defense responsibility. So let’s find out how often Bob needs to defend to prevent Alice from stealing profitably with any two cards:

Alice raises to 3 bb and risks 2.5 bb (remember, she has already posted a 0.5 bb small blind) to win the 1.5 bb pot. Her effective pot odds on a steal raise are 1.5 : 2.5. She needs to win more than 2.5/(1.5 + 2.5) =62.5% to have an automatic profit with any two cards.

Conclusion: Bob needs to defend at least 100 – 62.5 =37.5% by 3-betting and flatting

3.2 The relations between opening range, 3-bet range, 4-bet range and 5-bet range

Now we go through all the steps we went through when we outlined the 3/4/5-bet theory in in Part 1. The only difference is that we’re using different bet sizes, pot sizes and pot odds in the blind vs blind scenario:

What is Alice’s optimal 4-bet%?
The process begins when Alice openraises some range (we’re assuming the default 35% button range) that is known to both her and Bob. When Bob 3-bets, Alice has to 4-bet enough to prevent him from profitably 3-bet buffing with any two cards.

Bob’s 3-bet risks 8 bb (9 bb minus the big blind he posted) to win a 3 + 1 =4 bb pot, so his effective pot odds for a 3-bet bluff are 4 : 8 =1 : 2. He will automatically make a profit if Alice folds more than 1/(2+1) =1/3 =33%. So Alice’s optimal defense against Bob’s 3-bets means she defends 33% of her opening range with a value/bluff ratio we’ll find in a moment.

What is Bob’s optimal value/bluff ratio for the 3-bet range?
When Alice 4-bets to 20 bb, she risks 17 bb more (20 bb minus her 3 bb raise) to win a 3 + 9 =12 bb pot. The effective pot odds for her 4-bet bluffs are 12 : 17. So she profits from a 4-bet bluff with any two cards if Bob folds more than 17/(17 + 12) =59%.

Bob can’t allow this, and he defends optimally against Alice’s 4-bets by defending 100 – 59 =41%. He should then 5-bet all-in with 41% of his 3-betting range and fold the remaining 59%. We round this to 40/60, and end up with the same 40/60 value/bluff ratio we have used in previous articles.

What should Bob’s 5-bet range look like?
We know from Part 1 that the Axs hands (A5s-A2s) work well as 5-bet bluffs. They block Alice’s AA/AK/AQ hands, and they have about 30% equity when called, even against a strong calling range of good aces and big pairs. For example against {QQ+,AK}:

When Bob 5-bet bluffs an Axs hand all-in and gets called, he has ~30% equity in a 200 bb pot where he has invested 91 bb with his 5-bet (a 100 bb stack minus his 3-bet to 9 bb). From this pot he gets back ~0.30 x 200 =60 bb on average, so his net loss when his 5-bet bluff gets called is 91 – 60 =31 bb.

The pot before the 5-bet is 20 bb (Alice’s raise + 4-bet) + 9 bb (Bob’s 3-bet) =29 bb. So Bob risks 31 bb to win 29 bb. His effective pot odds on the 5-bet bluff are 29 : 31. Bob thus needs to win at least 31/(29+31) =52% of the time.

This means that Alice needs to call Bob’s 5-bet at least 48% of the time to prevent him from 5-bet bluffing with automatic profit. We round this to 50%. Alice’s value/bluff ratio for the 4- bet range is then 50/50 (and not 60/40 as in previous articles).

As discussed in Part 1, Bob adds enough Axs 5-bet bluffs to make Alice indifferent towards calling or folding the 5-bet with her weakest value hands.

3.2 Summary of Alice’s optimal 3/4/5-bet strategy from the small blind in a blind vs blind scenario

Alice opens her default 35% button range:

A2s+ A7o+
K2s+ K9o+
Q6s+ Q9o+
J7s+ J9o+
T7s+ T9o+

458 combos

When Bob 3-bets, Alice defends 33% of the time with a 4-bet. She then plays 0.33 x 458 =151 combos. She uses a 50/50 value/bluff ratio, so she 4-bets 75 combos for value and 75 combos as a bluff.

75 value combos is approximately the value range {88+,AJs+,AQo+} =78 combos. She now picks an equivalent amount of bluffs, for example {AJo-A7o,ATs-A7s} =76 combos. Here we have used Ax hands for blocker value (reduces the probability that Bob has one of the value hands AA/AK when when he 3-bets.

– Alice 4-bets {88+,AJs,AQo} for value
– Alice 4-bets {AJo-A7o,ATs-A7s} as bluffs

And this is Alice’s total defense strategy against Bob’s 3-bets after she has openraised from the small blind. Over to Bob:

3.3 Summary of Bob’s optimal 3/4/5-bet strategy from the big blind in a blind vs blind scenario

Bob first finds his value range. He uses hands that are at least 50% against Alice’s value range {88+,AJs+,AQo+}, and this gives him the value range {JJ+,AK} =40 combos.

Then we find the optimal number of 5-bet bluffs for Bob. When he 5-bets all-in, Alice has to call 80 bb more to win a 100 bb (Bob’s stack) + 20 bb (Alice’s raise + 4-bet) =120 bb. So her effective pot odds are 120 : 80 =1.5 : 1. To profit from calling with the weakest hands in her value range, she needs at least 1/(1.5 + 1) =40% equity.

Bob then picks Axs hands from the top and works his way from A 5 down to A 2 . From the equity calculation below we see that Bob has to use all the 16 Axs hands A5s-A2s to make Alice’s weakest value hands break even:

So Bob 3-bets the following total value range, including 5-bet bluffs, planning to 5-bet all-in after a 4-bet: {JJ+,AK,A5s-A2s} =56 combos.

Bob should use a 40/60 value/bluff ratio, so he needs 60/40 =1.5 times as many bluffs as value combos. Bob then picks 1.5 x 56 =84 bluff combos. We’ll make a list of these, but first we define his flatting range. Regardless, Bob’s total 3-bet range contains 56 + 84 =140 combos. This is 140/1326 =10.6% of all hands.

His flatting range needs to be wide to get to 37.5% total defense, so he will flat some of the hands we used as 3-bet bluffs outside the blinds. So we design a separate list of flatting hands to use in the blind vs blind scenario. We can call this list “Blind vs blind flat list”.

To defend 37.5% Bob needs to flat 37.5 – 10.6 =26.9% of all hands. This is 0.269 x 1326 =357 combos, and we can put together this range in various ways. Below is one way to do it:

Blind vs Blind flat list:

  • Pairs: TT-22 =54 combos
  • Suited aces: ATs-A6s =20 combos
  • Offsuit aces: AJo-A7o =60 combos
  • Suited Broadways: KQs-K8s,QJs-Q8s,JTs-J7s =52 combos
  • Off-suit Broadways: KQo-K9o,QJo-Q9o,JTo-J9o =108 combos
  • Suited connectors: T9s-T7s,98s-96s,87s-86s,76s-75s,65s =44 combos
  • Offsuit connectors: T9o-T8o =24 combos
  • Total: 362 combos

Note that we here have only used mathematics to tell us how many hands we need to flat to prevent Alice from opening any two cards with automatic profit. We have not given though to which hands we are able to play profitably after flatting them, and how we should play this range postflop (but we will have more to say about that in a later article series about optimal postflop play).

Using this flat list and the previously defined value range, now only have to pick our 3-bet bluffs (we need 84 combos) from the remaining (and rather trashy) hands. For example, we can use {A6o-A2o,K8o,Q8o} =84 combos.

Now we finally have one possible defense strategy for Bob, designed with optimal 3/4/5-betting against Alice’s 35% openrange from the small blind, and designed to prevent her from having an automatic profit from stealing:

  • 3-bet value range (including 5-bet bluffs): {JJ+,AK,A5s-A2s} =56 combos
  • 3-bet bluff range: {A6o-A2o,K8o,Q8o} =84 combos
  • Flatting range: {TT-22,ATs-A6s,AJo-A7o,K8s+,K9o+,Q8s+,Q9o+,J7s+,J9o+,T7s+,T8o+96s+,86s+,75s+,65s} =362 combos

This total strategy is a handful, particularly the flatting range. But in the next article series about optimal postflop play (“Optimal Postflop Play in NLHE 6-max”) we’ll see than postflop play with a wide range after flatting preflop becomes easier when we use a systematic approach based on principles from game theory.

Note that if we need to, we can construct a 3/4/5-bet strategy pair for any openraise percentage Alice uses from the small blind. we only picked a 35% here, and this strategy pair will be a good default to use in a blind vs blind battle with an unknown small blind. But we could also have made a list of optimal strategy pairs for various small blind openraise ranges like we did in Part 2 for the scenario where both players were outside the blinds.

4. Summary:

We have done a series of numerical simulations to estimate the EV of flatting and value 3-betting for hands in the region between obvious value hands and obvious flatting hands. We did this by calculation the EVs of flatting and 3-betting with QQ against a tight ~15% UTG opening range.

The simulations showed that flatting a very strong hand like QQ can be correct when the raiser has a tight range. We also found that 3-betting becomes mandatory against wider ranges, for example with QQ against a ~25% CO opening range.

We also did some simulations to study the effect of the raiser flatting out of position. Even if this increases the EV for value 3-betting, we also have to take into consideration how often the raiser 4-bet bluffs. Against a loose-passive raiser who flats a lot of 3-bets out of position but never 4-bet bluffs, we can use a “hybrid strategy”. we then 3-bet “thin” value hands (for example JJ), planning to fold to the raisers squeaky tight value 4-bet range. The rationale behind this is that we profit from the raiser’s folding and calling, but on the rare occasions he 4-bets us, we are crushed and can fold. Note that we are exploiting his lack of 4-bet bluffing by making safe folds.

Then we we studied the scenario blind vs blind where the small blind openraises and the big blind defends in position by optimal 3/4/5-betting and flatting. we saw that the big blind has to defend a very wide range (37.5%) to prevent the small blind from profitably stealing with any two cards. Of course, the big blind then has to play his wide flatting range well postflop, and we’ll discuss this further in the coming postflop article series.

I am planning to publish a Part 8 in this preflop series some time in the future. This will be a practical part where we look at how our strategies perform in practice. I’m thinking about grinding a decently large sample of low limit NLHE hands where I focus on playing close to the core strategy we have defined in this preflop article series. This should give us an idea about how our core strategy performs at the limits most of the readers play.

I have already tested the optimal 3/4/5-bet strategies at the middle limits ($400NL to $1000NL), and they work very well as solid defaults, and as a starting point for exploitative adjustments against players I have reads on. But at the middle limits I of course mix up my play a lot, depending on my opponents, so for testing purposes it would be better for the readers to see how the strategies perform against unknowns at the limits they play.

I will not give a date for Part 8, but it will be some time after we have finished the theoretical series about optimal postflop play. The series “Optimal Postflop Play in NLHE 6-max” comes next. There we’ll use strategies and ranges from this preflop series and see how principles for optimal play can be used postflop, using our default preflop strategies and preflop ranges to set up postflop scenarios to study.

Good luck!
Bugs – See more at: http://en.donkr.com/forum/optimal-3-bet-4-bet-5-bet-strategies-in-nlhe-6-max—part-7-533567#sthash.xn4CohAV.dpuf


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