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

1. Introduction

This is Part 3 in the series Optimal 3-bet/4-bet/5-bet-strategies i NLHE 6-max. In Part 1 we outlined the necessary theory and mathematics by studying a simple model: A player (Alice) raises from some position outside the blinds, and she gets 3-bet by a player (Bob) with position on her. Both players start with 100bb stacks, both the raise and the 3-bet are pot-sized, and Alice’s options out of position were 4-bet or fold. We then used mathematics to estimate optimal strategy pairs for Alice’s and Bob’s 3/4/5-bet war.

In Part 2 we generalized this scenario by estimating optimal strategy pairs for a wide selection of possible opening ranges for Alice. We also gave Bob the option to call the raise (flat) in position. In Part 2 we also looked closer at how to implement these optimal strategies in practice, and we finished our discussion of the scenario where the raiser is heads-up and out of position against the 3-bettor.

The plan for Part 3 is to study the opposite scenario, namely when the raiser is heads-up with position on the 3-bettor. We’ll use a model where Alice openraises from outside the blinds, then Bob 3-bets from one of the blinds, and a 3/4/5-bet war arises. We’ll give this scenario the same systematic treatment as the scenario with Alice out of position, and we’ll specify a complete set of strategies for both players, flatting included.

As before, we assume:

– Both players start with 100bb stacks
– The raise and the 3-bet are pot-sized
– The 4-bet is 27bb (a bit less than pot-sized)
– The 5-bet is all-in

This means we can use the mathematics from the previous two articles. To avoid gaping over too much at once, we’ll narrow the scope for this article to the scenario where Alice openraises from the button, and then Bob is sitting in the small blind, or in the big blind after small blind has folded. We’ll use the standard ranges for openraising described in Part 2, and Alice will open our default 35% button range defined there. When Part 2 was published, the plan was to also study squeezing in Part 3, plus 3-betting from the blinds against openraises from other positions than the button. But due to space constraints we’ll move these topics to a future article.

Bob can both flat the raise and 3-bet from the blinds, and flatting the 3-bet now becomes an option for Alice because she has position on Bob. When Alice was out of position in Part 1 and Part 2, we chose to let he use a 4-bet-or-fold strategy. Her options were then to 4-bet her best hands for value, plus some 4-bet bluffs, and otherwise fold. The rationale behind this is that it’s difficult to defend against 3-bets by calling with medium strong hands out of position (i.e. hands not strong enough to 4-bet for value), trying to play them profitably postflop with 100bb stacks.

It’s easy for Bob to peg Alice with a range full of medium strong hands (KQ, AJ, JTs and the like) when she flats the 3-bet, since she 4-bets her best hands for value. Alice then gets a difficult job postflop, trying to play her medium strong hands profitably out of position. Bob both has position, and more information about Alice’s hand (medium strong) than she has about his hand (either a strong hand or a bluff). Bob’s range is easy to play postflop, since he polarized his 3-betting range preflop by 3-betting an optimal mix of value hands and 3-bet bluffs (and flatting his medium strong hands). Polarizing his 3-betting range into strong hands and bluffs makes it’s easier for Bob to know whether he’s strong or weak postflop when his 3-bet gets called, and this makes his postflop decisions easier. Therefore, with a range that’s easy to play well, and with position on Alice’s medium strong range, it’s relatively easy for Bob to outplay Alice postflop.

Therefore we denied Alice the option of flatting 3-bets out of position, even if there aren’t any “laws” that forbid it. But in Part 3, Alice has position, which makes it easier for her to play medium strong hands well postflop. So now she will flat 3-bets with a range of medium strong hands that are not good enough to 4-bet for value (hands like JJ-99, AQ, AJ, KQs, etc), and then use position to play them profitably postflop. Alice will still 4-bet her best hands for value, together with an optimal number of 4-bet bluffs, and then she flats with the next tier of hands that are good enough to play, but not strong enough to 4-bet for value, and she folds the rest. Note that “for value” in this context means hands we’re planning to go all-in with preflop, either by calling a 5-bet (when we’re the raiser), or by 5-betting all-in (when we’re the 3-bettor).

For example, if Alice raises KQs on the button, and Bob 3-bets from the small blind, we’ll see that this is an automatic call for Alice. She has a decent suited and coordinated high card hand, and she has position. But in Part 1 and Part 2, Alice folded this type of medium strong hands to avoid putting herself in difficult postflop scenarios out of position.

The mathematics and the theory behind optimal optimal 3/4/5-betting with the raiser in position is the same as when the raiser is out of position, but Alice’s option to call the 3-bet makes her total defense strategy after a 3-bet more flexible. Therefore, the theoretical work we do in Part 3 will involve a bit more sound poker sense than the very strict strategies we found when Alice could only 4-bet or fold out of position.

When Alice has position and the option to flat Bob’s 3-bets as well as 4-bet, we have to take two things into consideration:

  • Alice now has more strategic choices to make, when she has to define both a 4-betting range and a flatting range after a 3-bet
  • When Bob can get his 3-bets called, his choice of 3-bet bluffs and 5-bet bluffs becomes more important

We defined both an “IP 3-bet air list”, an “IP 5-bet air list” and an “IP flat list” for Bob in Part 2. These were the hands Bob picked his 3-bet bluffs, 5-bet bluffs, and flatting hands from, when he was in position (IP). These lists were based on the following simple principles:

  • Bob 3-bets his best hands for value, planning to 5-bet all-in if he gets 4-bet
  • Bob flats with the best hands not strong enough to 3-bet for value, but strong enough to play profitably
  • Bob 3-bet-bluffs with hands that are a bit too weak to flat (and he also 3-bet bluffs some Axs hands that he plans to use as 5-bet bluffs after a 4-bet)

Bob uses the same principles when out of position, but now he’ll use hands that are a bit stronger on average. The reason is that Alice’s positional advantage reduces the profitability of all of Bob’s hands that are forced to play postflop (after Alice chooses to flat his 3-bet). This means Bob should use stronger hands for both 3-bet bluffing and 5-bet bluffing. For example, in Part 2 we defined QTs as a candidate for flatting in position, but out of position Bob will use QTs as a candidate hand for 3-bet bluffing.

The fact that Bob often gets his 3-bets called also has consequences for his choice of 5-bet bluff hands. For example, we’ll not use Axs as dedicated 5-bet bluff hands for Bob when he is out of position, since these play poorly against the range Alice flats 3-bets with. When Alice only defended by 4-betting or folding, we picked Bob’s 5-bet bluffs from the region of hands not strong enough to flat Alice’s openraise. We chose the Axs hands, since these never have very poor equity against Alice’s value range (that she calls 5-bets with), no matter what it is (Axs has about 30% equity, no matter what Alice calls our 5-bets with). The reason for picking our 5-bet bluffs from this region, was that we didn’t want to use hands good enough to flat as bluffs, thereby wasting their postflop value. Keep in mind that when Alice never flats 3-bets out of position, our 3-bet bluffs will have to play postflop. They will either win the pot right there, or be folded to Alice’s 4-bets.

Since our 3-betting hands never gets to play postflop when Alice is out of position, we prefer to flat with the best non-value hands like AQ, rather than 3-betting them and turning them into bluffs. AQ has decent equity against Alice’s openraising range, but if we use it for 3-betting against a raiser who either 4-bets or folds, it becomes a bluff in practice. We can’t 5-bet it for value (unless Alice openraises an extremely wide range), so our response to a 4-bet is to either fold (and then we have wasted the hand’s decent postflop value), or 5-bet all-in (and only get called by better hands). The same logic can be applied to other medium strong hands like TT, 99, AJ, KQs, KJs, QJs, etc.

Thus, when we have position we assume that there is more value in flatting the raise with hands like AQ and play a pot postflop than turning it into a bluff. And when these medium strong hands are used as flatting hands, we pick our 5-bet bluffs from the next tier of hands, namely those slightly too weak to flat the raise profitably. From this class of hands we picked the Axs hand to use as 5-bet bluffs, since they always have decent equity against Alice’s value range that calls our 5-bet. In a future article we’ll study flatting versus 3-betting with medium strong hands in more detail and compare the EV for the two lines. Until then, we’re simply going to assume that is the best way to play medium strong hands in position.

Back to Bob’s choice of 5-bet bluffs out of position:

Instead of picking 5-bet bluffs from the region of hands slightly too weak to flat Alice’s raise, we’ll extend Bob’s 3-bet value range downwards. The value range will now include some of the best hands that Bob would have flatted in position. In other words, when Alice sometimes calls our 3-bets, we widen our 3-betting value range to include hands from the upper part of the range we would have flatted in position against a raiser who only 4-bets or fold out of position. These are hands that aren’t the favorite when they 5-bet all-in and get called, but they have decent equity when this happens, and they also have good equity when the 3-bet gets called. AQ/JJ/TT (all were flatting hands in position) are obvious candidates, and we’ll discuss this in more detail later in the article.

So we’ll define a new set of lists for 3-bet bluffing (“OOP 3-bet air list”) and flatting (“OOP flat list”) for Bob out of position (OOP). This means more ranges to memorize. But if you already have memorized the IP ranges for Bob’s 3-bet bluffing and flatting in position, his OOP ranges will be relatively easy to commit to memory. They are a bit different from the IP ranges, but not widely different. Just keep in mind that Bob needs stronger ranges out of position, and the differences become easy to understand.

We start Part 3 with Bob’s strategies for 3-betting and flatting from the blinds (e.g. blind defense) after a button steal raise from Alice. Then we turn to Alice, and study how she defends on the button against Bob’s 3-betting from the blinds.

In Part 4 we’ll generalize to scenarios where Alice has openraised from other positions. Later we’ll also generalize the 3/4/5-bet theory to squeezing (3-betting after Alice’s raise has been called by another player). The mathematics behind squeezing is the same as for 3/4/5-betting heads-up, but the percentages and ranges change a bit when the raise has been called in front of us, and we’ll use mathematics to explain why squeezing is so profitable. We’ll also look at the multiway scenario cold 4-betting, which is 4-betting after a raise and a 3-bet in front of us.

The structure of Part 3 is thus:

  • Blind defense heads-up against a button steal raise
  • The button raiser’s defense against a heads-up 3-bet from the blinds

Then well discuss squeezing and cold 4-betting in Part 5. This will be followed by the final Part 6, where we test our strategies using analysis software (Pokerazor), and also take a look at optimal postflop play.

2. 3-betting and flatting heads-up from the blinds

When Alice raises from outside the blinds and Bob is in one of the blinds, the discussion of optimal 3/4/5-bet strategies and flatting is equivalent to a discussion of blind defense. As we’ll see soon, we now have more things to think about than the corresponding scenario with Bob in position. Both in and out of position Bob has the 3 alternatives 3-bet/flat/fold, but when Bob had position, we didn’t specify how often Bob should flat.

We remember that the optimal 3/4/5-bet strategy pair for Alice and Bob with Bob in position followed from Alice’s open-range. Then we added a flatting range of medium strong hands for Bob, based on sound poker sense. But beyond the optimal 3/4/5-betting, we didn’t make any demands about how often Bob should get involved. We gave him a default flatting range, but he did not have to flat those hands.

Before we move on, let’s determine how often Bob gets involved in position after Alice’s openraises when he uses optimal 3/4/5-betting, and also flats with all the hands from “IP 3-bet flat list”. In Part 2 we designed the following set of optimal strategy pairs for various open-ranges for Alice, together with Bob’s lists of 3-bet-bluff hands and flatting hands in position:

Link to download(right-click and “Save as …”): IP_3-bet_summary.doc

For example, if Alice opens 25% from CO, Bob will 3-bet the value range {QQ+,AK,A5s-A3s} =46 combos (including 5-bet bluffs), and then he adds 1.5 x 46 =69 3-bet bluff combos from “IP 3-bet air list”, which is equivalent to 3-betting all hands on the list 69% of them time (rounded to 70% in the document above) using a randomizer.

Bob then uses a total of 46 + 69 =115 3-bet combos and this results in a a 3-bet% of 115/1326 =8.7%. Then he flats the 140 combos on “IP flat list”. Bob now plays a total of 115 + 140 =255 combos, or 255/1326 =19.2% of his hands on the button.

Calculating Bob’s total range for all of Alice’s open-ranges 15%, 20%, 25%, 30%, 35%, 40% used in Part 2, we get:

Alice opens 15%: Bob plays 15.8% (with 3-bet% =3.6%)
Alice opens 20%: Bob plays 17.0% (with 3-bet% =5.3%)
Alice opens 25%: Bob plays 19.2% (with 3-bet% =8.7%)
Alice opens 30%: Bob plays 19.5% (with 3-bet% =9.4%)
Alice opens 35%: Bob plays 20.3% (with 3-bet% =10.2%)
Alice opens 40%: Bob plays 20.3% (with 3-bet% =10.2%)

In practice, Bob should adjust his flatting range somewhat, according to Alice’s open-range, and fold the weakest hands (e.g. QTs, T9s, 98s, etc.) if Alice opens a very tight range. Regardless, his optimal strategy in position follow from two factors:

– Bob’s half of an optimal 3/4/5-bet strategy pair
– Flatting with the medium strong hands Bob considers profitable

2.1 How often do the blinds have to defend against a button steal raise?

Using the same philosophy as above (3/4/5-betting optimally, and otherwise flat profitable hands) when Bob is in the blinds is a start. But as we’ll see in a minute, we have more things to think about. We of course always want to play profitable hands and fold unprofitable ones (basic exploitative play). But with Bob heads-up in the blinds after a button steal raise, we can also formulate a mathematical requirement for how often the players in the blinds need to defend to prevent Alice from profitably stealing with any two cards.

When Alice openraises pot (3.5bb) on the button in a 1-2 blind structure (small blind =0.5 x big blind), she’s risking 3.5bb to win 1.5bb. The effective pot odds are 1.5 : 3.5, so if Alice succeeds more than 3.5/(1.5 + 3.5) =70% of the time, she can profitably open any two cards on the button. The two players in the blinds can’t allow this, so they have to defend combined at least 30% of the time.

We remember from the theory in Part 1 that an optimal 3/4/5-bet strategy pair is designed to make our opponent’s worst bluffing hands break even. So we start the process of finding an optimal(ish) blind defense strategy with the assumption that the blind players should defend 30% combined.

We use a simple model where we assume that the job of defending the blinds is shared equally between the small blind and the big blind. Both blinds defend a certain percentage x (where x is the same for both players), so that there’s a 30% chance of at least one of them defending.

The chance of one particular player folding is (1-x), so the chance of both folding is (1-x)(1-x). Thus, the chance that at least one of them isn’t folding is 1 – (1-x)(1-x), and we want this to equal 30%. We can formulate this as an equation:

1 - (1-x)(1-x) =0.30
1 - (1 -2x +x^2) =0.30
1 - 1 + 2x - x^2 =0.30
x^2 - 2x + 0.30 =0

This is a quadratic equation with solutions x =1.84 and x =0.16 (you can use Quadratic Equation Solver to compute this). Since we require x to be between 0 and 1 (x is a probability), we choose the solution x =0.16 =16%. Let’s check the solution before moving on. With a defense percentage x =16% for both blinds, the chance that at least one of them defends is:

1 - (1 - 0.16)(1 - 0.16) =0.30 =30%

And we conclude:

If the task of defending the blinds 30% against a button steal raise is shared equally between the small blind and the big blind, both players should defend about 16% of the time.

If we combine this with our general desire to defend with the hands that are profitable, we can say the following:

Heads-up after a steal-raise from the button, you want to defend with the hands that are profitable. But of this range is significantly tighter than 16%, you are probably doing something wrong, and/or you are exploiting your opponents’ mistakes.

Let’s pause for a bit and think about what this statement means. In practice you can often get away by defending the blinds tighter than optimal, without introducing a big leak into your game. This is typically the case in soft low limit games. There are two factors at work:

  • When your opponents don’t exploit tight blinds as hard as they should from the button
  • When your opponents also play too tight in the blinds, and/or give up too easily postflop when they choose to defend

In soft games with many passive players, this is more or less what happens. You don’t have to defend optimally (i.e. make it unprofitably for the button to steal with any two) because most players won’t try to exploit this opening if you offer it to them. And if you lose a bit by defending too little against some players, you can get it back when it’s your turn on the button, since your opponents often make the same mistakes as you in the blinds. So errors tend to cancel each other.

But then we’re in the realm of exploitative play where we’re profiting from opponent leaks, and not optimal play, which is the central topic for this article. We want to explore what optimal (or near-optimal) play is for this scenario, so that we can design a blind defense strategy to use against strong players who use aggressive button openrasising for what it’s worth.

If you think 16% blind defense is too loose for the limits you’re playing, and you don’t think you can defend such a range profitably, think ahead. Work on making this standard defense percentage profitable for you, and think of it as preparations for tougher games in the future. Also, you should replace the “fit-or-fold” mantra postflop with a more aggressive style.

The looser your preflop ranges, the more important it becomes to exploit steal opportunities postflop. Keep this in mind when you’re working on your blind defense. For example, when you flat a hand like KJs in the big blind, don’t always check-fold the flop when you miss. Look for profitable stealing spots, based on flop texture (e.g. sometimes checkraising dry flops like A 7 3 ), and based on your opponent’s tendencies (you can steal more against weak players).

Postflop play is not a topic for this preflop article series, but I’d like to point out the coupling between preflop play and postflop play, and that strict fit-or-fold generally isn’t a good strategy to use in heads-up postflop play when both players start with wide ranges. We’ll not go further into this, but I might write an article later about using principles for optimal play postflop.

Postflop play aside, our job is now to design Bob’s strategies for:

– 3/4/5-betting from the blinds heads-up after a button steal raise
– Flatting from the blinds heads-up after a button steal raise

And we want to end up with a total defense percentage of about 16% when Bob is in the small blind, or in the big blind after the small blind has folded. Both blinds defending the same percentage 16% is an approximation, since the big blind should defend somewhat more than the small blind. But it’s a good approximation, and we’ll use it throughout this article.

We build Bob’s strategy step-wise by giving him a total value range of value hands + 5-bet bluffs, a range of 3-bet bluffs (defined as an “OOP 3-bet air list”) and a range of flatting hands (“OOP flat list”). As always, we use the strength principle as a guideline:

  • We 3-bet the best hands for value
  • We flat with the best hands not strong enough to 3-bet for value
  • We 3-bet bluff some hands among those not strong enough to flat, and we fold the rest

Since we’re out of position, the hands we flat and bluff will be a bit stronger than the ranges we used in position (“IP 3-bet air list” and “IP flat list”) in the previous work done in Part 1 and Part 2.

2.2 Bob’s value range for 3-betting OOP against a button steal raise

Before we get into details, let’s look at the big picture, taking into consideration the difference between being in and out of position. Then we use the work done in Part 1 and Part 2 as a starting point for defining Bob’s strategies from the blinds.

We start with Bob’s value hands that he 3-bets for value, planning to 5-bet shove all-in if Alice 4-bets. When Bob had position on Alice, his value hands followed from Alice’s value range, which followed from her opening range (more precisely, the number of hands in her opening range), plus the requirement that Alice could only 4-bet or fold. But with Bob out of position, the strategies are more flexible, since Alice now has the option to flat Bob’s 3-bets.

Let’s start by assuming Alice opens our default 35% button range. According to the list of optimal strategy pairs defined in Part 2, Alice should use a 4-bet value range of {99+,AJ+} =84 combos if she only 4-bets of folds. She then uses {AT-A8, A7s-A6s} =56 combos as 4-bet bluffs to to get a 60/40 ratio of value hands to bluffs.

But now we have to take into consideration Alice’s positional advantage. When Alice has position on Bob, she doesn’t have to 4-bet all hands that are playable after Bob’s 3-bet. She can now choose between 4-betting or flatting. The weakest value hands Alice 4-bets out of position with a 4-bet-or-fold strategy are 4-bet because they gain enough EV from folding out Bob’s 3-bet bluffs, not because they are a favorite against Bob’s 5-bet-range. If the EV she gains from folding out Bob’s 3-bet bluffs is more than the EV she loses from getting 5-bet and being forced to call because of pot-odds, she has a profitable value 4-bet. But in position it might be more profitable to flat this type of hands and play postflop against Bob total 3-betting range.

For example, it’s seems reasonable to flat a 3-bet in position with one of the weaker OOP value hands like AQ, instead of 4-betting and planning to call a 5-bet. AQ should do well against Bob’s total 3-betting range (40% premium hands like AA-QQ,AK and perhaps a few more, and 60% 3-bet bluff hands like A9s, K9s, J8s, etc). So when Alice can play against this total range with position for the rest of the hand, this seems better than 4-betting, driving out most worse hands, and getting all-in against mostly better hands.

If Alice 4-bets AQ, she’ll probably get sufficient pot-odds to call a 5-bet against Bob’s total 5-bet range (we remember from previous articles that we need minimum 36% equity to call Bob’s shove). And since AQ gains a lot of EV from folding out Bob’s 3-bet bluffs, a 4-bet + call 5-bet might be profitable overall. But this doesn’t mean that 4-betting is the best way to play AQ when we have position. When Bob has to play his total 3-betting range out of position postflop (and 60% of this range consists of bluffs) he will get plenty of opportunities to make postflop mistakes that Alice can exploit. So it could very well be that Alice’s alternatives with AQ in position are ranked call > 4-bet > fold. We’ll look into this in more detail with analysis software in Part 5.

At any rate, by flatting 3-bets in position with the weakest hands she would have 4-bet for value out of position, it is reasonable to assume she’ll be able to extract more value than by playing for all-in preflop. After all, she has position and a hand that’s a favorite against the range that 3-bet her. We have talked about AQ here, but the same argument can be used for for AJ, JJ, TT and 99 (which would all be 4-bet value hands out of position after a 35% openraise). We can also flat 3-bets in position with various medium strong suited/coordinated hands like KQs, KJs, QJs, etc.. They have decent equity against Bob’s total 3-betting range, and our plan is to use position to play them profitably postflop through a combination of showdown equity (the ability to make hands) and steal equity.

So when Bob 3-bets, he can expect Alice to flat a lot with medium strong hands (medium pairs, high card hands of the type good-but-not-great, and the best suited/coordinated hands). This means two things for Bob:

  • His 3-bet bluffs should be stronger than in position, since they now often get called. Bob is then forced to play a weak hand postflop
  • The same goes for the hands Bob 3-bets, planning to 5-bet bluff

Compared to 3-betting in position, Bob should now drop the weakest 3-bet bluffs like K6s. And instead of using low Axs hands as 5-bet bluffs (they do poorly against Alice’s 3-bet flatting range), he should use hands that perform better when the 3-bet gets called.

Let’s start by estimating Bob’s value hands and see where this takes us. With value hands we mean the hands Bob 3-bets for value, planning to 5-bet all in, and where he expects to profit from getting called by Alice’s value hands. From the list of optimal strategy pairs we made in Part 2, we see that Bob will use the value range {JJ+,AK} in position against a 35% open-range. The same value range is also used against 30% and 40% open-ranges, so it seems reasonable to use {JJ+,AK} as our starting point for building a value range to use in the blinds against a button steal-raise (which is rarely tighter than 30%, and often looser than this).

What about the next tier of hands? If we move on to TT/AQ, we’re no longer favorites against Alice’s value range corresponding to 35% open-range, so we can’t define TT/AQ strictly as value hands. Remember that our definition of value hand for the 3-bettor (and this definition is mostly a conceptual tool to help us build ranges), is a hand that we 3-bet and 5-bet, expecting to be a favorite against the hands that call our 5-bet. If this is not the case, we define the hand as 5-bet bluff.

To see that TT/AQ can’t be value hands under this definition against a 35% button open-range, note that Alice optimal value range for a 35% open-range can’t be wider than {99+,AJ}. This is the value range she will use if she only defends against 3-bets by 4-betting or folding, and if she also can flat, her value range will be somewhat tighter. Against {99+,AJ}, both TT and AQ are small underdogs as shown below:

And in practice TT/AQ should be somewhat bigger underdogs against Alice ‘s actual value range in position, since she flats some hands, and therefore can 4-bet tighter than out of position when she defends optimally (30% defense when she 4-bets or folds, and a bit more when she 4-bets/flats/folds). For example, Alice might elect to flat with TT-99 and AJ in position. On the other hand, TT/AQ will have good equity against Alice’s flatting range, so TT/AQ can be viewed as value hands when the 3-bet gets called. For example, if Alice 4-bets {QQ+,AK} for value (plus some 4-bet bluffs) and flats a medium strong range {AQ,AJ,JJ-99,KQ,KJs,KTs,QJs,QTs,JTs}, TT and AQ have 60% and 55% equity against the hands that call the 3-bet, as shown below::

We can therefore view both TT and AQ as a “value/bluff hybrid” where we 3-bet for value against Alice’s flatting range, but when we get 4-bet, we turn them into 5-bet bluffs and 5-bet them all-in. Using these hands as 5-bet bluffs makes more sense equity-wise than using Axs hands as 5-bet bluffs. Axs are underdogs against Alice’s flatting range as shown below, and in addition they are difficult to play well out of position postflop in a 3-bet pot:

So we choose:

Bob’s value-range OOP against a button openraise

TT+
AQ+

62 combos

We landed on this range using a combination of theory from previous articles and sound poker sense. From the previous work it’s clear that {QQ+,AK} can always be used as value hands against a normal button range, and we chose to also include JJ based on the strategy pairs we estimated in Part 2. Then we concluded that TT/AQ work as “hybrids” between value hands and 5-bet bluffs. TT/AQ have good equity against the hands that call our 3-bet, so they can be viewed as value hands. But when we get 4-bet, we use them as 5-bet bluffs, so that we don’t have to use weak hands like Axs (poor equity against Alice’s flatting range) for this purpose.

We’ll also specify the hands Bob uses for 3-bet bluffing. First we’ll specify his flatting range, and then we pick his 3-bet bluffs from the hands a bit too weak to flat.

2.3 Bob’s range for flatting OOP against a button steal-raise

We now turn to Bob’s flatting range. We can use his flatting range in position (“IP flat list”) as our starting point and tighten it up a bit to compensate for Bob’s positional disadvantage. Before we list specific hands, we note that we need about 57 combos in the flat list to end up with a total blind defense range of 16%, which is the requirement we estimated previously.

Bob has 62 combos in his value range, and he wants to 3-bet 1.5 x 62 =93 bluff combos to get an optimal 60/40 ratio of value hands to bluffs. So he 3-bets a total of 62 + 93 =155 combos. Since a 16% total defense range contains 0.16 x 1326 =212 combos, Bob needs 212 – 155 =57 flatting combos.

In the Stoxpoker video series Optimal Preflop Play I-III (which we have used as background material for this article series), Matt Janda recommends the following OOP flatting range, which gives us a few more combos that we need:

OOP flat list

99-77
AJs-ATs, AJo
KTs+ KQo
QJs
JTs

70 combos

We have no reason to make any big changes here, so we’ll use this OOP flat list as standard from the blinds after a button steal-raise. There’s also a mathematical argument for flatting with a few more hands than we need to get to exactly 16% total defense. When we defend by 3-betting, Alice has to fold a lot of weak hands preflop, but when we flat, these weak hands get to see a flop. Therefore, Alice “freerolls” flops with many weak hands when we flat preflop, and she now gets an opportunity to flop something with these hands, or bluff us out postflop when both players miss the flop. We’ll return to this concept when we discuss Alice’s defense strategy against Bob’s 3-bet, where she will call a lot and therefore give Bob an opportunity to freeroll flops with his 3-bet bluffs.

2.4 Bob’s range for 3-bet-bluffing OOP against a button steal-raise

Bob has 62 combos in his value-range, so he needs 1.5 x 62 =93 bluff combos. Matt Janda recommends the following list of 3-bet bluff hands against a button steal-raise:

OOP 3-bet air list

66-22
A9s-A6s
K9s-K8s
QTs-Q9s
J9s-J8s
97s+
87s
76s
65s

98 combos

A bit more than we need, but that’s not a problem. Having an “OOP 3-bet air list” with about 100 combos will also come in handy for 3-betting against open-raises from other positions than the button. Then we want to 3-bet tighter, so we’ll use “OOP 3-bet air list” as a candidate list for 3-betting. With about 100 combos in the list we can easily convert between the number of bluff combos we need, and the corresponding bluff percentage that we can use together with a randomizer. For example, if we decide to 3-bet {QQ+,AK} =34 combos for value against an MP open-raise, we know that we need 1.5 x 34 =51 3-bet bluff combos for an optimal 60/40 ratio. So we need 51 combos from the list, and with ~100 combos in the list, this corresponds to 3-bet buffing the whole list 51% of the time (and we use a randomizer for this, as illustrated in Part 1 and Part 2).

We note that we should use all the hands in “OOP flat list” and “OOP 3-bet air list” when Alice openraises on the button, since these lists we designed to give a total defense percentage of about 16% for this case. But if Alice raises from an earlier position, Bob should tighten up a bit. Both because Alice’s open-range now is stronger, and because the players with position on Alice will do some of the job of defending the blinds. Therefore, the responsibility of denying Alice the opportunity to profitably openraise any two is now shared between the players behind Alice and the two players in the blinds. We’ll talk more about this concept in Part 4, and use a simple mathematical model to study the effect of having players with position on Alice when Bob is in the blinds.

Thus, against openraising from positions earlier than the button, we’ll use “OOP flat list” and “OOP 3-bet air list” as candidate lists, and then we use a bit of common sense to reduce the number of hands that we use, according to the raiser’s position. We’ll play somewhat tighter against a CO open-raise, and a lot tighter against an open-raise from early position. In principle, there are two ways to tighten up; the combo method (playing specific hands from OOP flat list” and “OOP 3-bet air list”) and the percentage method (playing all hands on the lists a certain percentage of the time, using a randomizer).

For the flatting hands, it’s obvious that we should fold the weakest hands on “OOP flat list” when we tighten up. Flatting implies we’ll always play postflop out of position, and this makes it important to always use the best possible hands. However, for the 3-bet bluffs this is less important, since we’ll often win the pot preflop. Therefore, to keep things simple I use “OOP 3-bet air list” with a randomizer in scenarios where I don’t need to use the whole list. But I choose my flatting hands by picking the best hands from “OOP flat list”, using common sense.

But we won’t look at blind defense against raises from other positions until Part 4. Here we’ll finish our work with Alice openraising on the button, and then we use all hands from “OOP flat list” and “OOP 3-bet air list”.

Before we move on to Alice’s strategies for defending in position against Bob’s 3-bets, here’s a “cheat sheet” for Bob’s blind defense strategies against a button steal-raise. You can download the document and have it open on the screen when playing for quick access. This strategy can be used as your default both from the small blind, and from the big blind after small blind has folded.:

2.5 Summary of Bob’s defense strategy heads-up OOP against a button openraise

We defend a total of 62 + 98 + 70 =230 combos. This is 230/1326 =17% of all hands, which is a bit more than the 16% we wanted. This is fine, since flatting lets Alice freeroll flops with her weakest raising hands, so in practice we should defend a bit more when we sometimes flat. If both blinds defend 17%, their total combined defense percentage is:

1 - (1-0.17)(1-0.17) =32%

Link to download (right-click and “Save as”): blind_defense_vs_button_summary.doc

3. Defense against OOP 3-bet after openraising on the button

In Part 1 we saw that when Alice open-raises pot and Bob 3-bets pot in position, Alice needs to defend 30% with a 4-bet-or-fold strategy to prevent Bob from exploiting her by 3-betting any two cards. This percentage changes slightly when Bob is in the blinds (it’s cheaper for him to 3-bet), but we’ll keep things simple and use 30% as our starting point.

3.1 Defending an openraise against a 3-bet using 4-betting and flatting with a “call multiplier”

When Alice defends with both 4-betting and flatting in position, she needs to defend a bit more than 30%, since her flatting lets Bob freeroll flops. For example, if Bob has 3-bet a hand like K9s as a bluff in position, he will never see a flop when Alice defends with only 4-betting or folding. So Bob’s 3-bet bluffs never get the opportunity to outflop Alice those times she defends with a better hand. For example when Alice 4-bets TT for value from CO after a 3-bet from Bob on the button.

But when Alice raises TT on the button, Bob 3-bets K9s from the blinds, and Alice defends by flatting, Bob gets additional ways to win. He can outflop her if the flop comes something like K 8 4 , or he might win with a bluff on flops that contain one or more overcards to Alice’s TT, for example A J 7 . Thus, Alice’s defense strategy in position gives Bob the opportunity to win some pots he would never have won had Alice used a 4-bet-or-fold strategy. When Bob can freeroll flops this way, Alice needs to defend a bit more than 30% in total.

We can adjust Alice’s strategy to compensate for this effect by using something Matt Janda calls a “call multiplier”. We know that Alice should defend at least 30% of her opening range against a 3-bet, so we start by choosing her 4-betting range, for example 10% of her openraising range. Then we must defend 30 – 10 =20% by flatting to get 30% total. But since flatting lets Bob freeroll flops, we scale up this flatting percentage with some constant factor > 1. Janda suggests using a factor 1.5. So we end up with 1.5 x 20% =30% flatting in addition to 10% 4-betting. We name this constant factor “the call multiplier”.

3.2 Alice’s total strategy for defending her button open-range against a 3-bet from the blinds

Alice openraises our default 35% button range that we defined in Part 2:

Default 35% open-range

22+
A2s+ A7o+
K2s+ K9o+
Q6s+ Q9o+
J7s+ J9o+
T7s+ T9o+
96s+
86s+
75s+
65s

458 combos
35%

When Bob 3-bets heads-up from the blinds, Alice knows that she will defend at least 30%, using a combination of 4-betting and flatting. Alice’s job is now:

  • Choose a value range of hands she 4-bets, planning to call an all-in 5-bet
  • Add an optimal percentage (60/40 ratio of value hands to bluffs) of 4-bet bluffs that she folds to a 5-bet
  • Find the percentage of her opening range she needs to flat to defend a total of 30%, then multiply this number with our call multiplier of 1.5 to find the total percentage of flatting

Alice’s value-range
When Alice was out of position, her value-range was uniquely determined from the requirement that she should 4-bet 30% of her opening range, using a 60/40 ratio of value hands to bluffs. But when she also has the option to flat the 3-bet in position, her value-range is no longer a simple percentage of her opening range, and we have to use some judgment.

If Alice hadn’t used flatting in position, she would have defended her 35% button range by 4-betting {99+,AJ+} for value and {AT-A8,A7s-A6s} as 4-bet bluffs, as we found in Part 2. So when she defends partly by flatting, she will obviously 4-bet tighter than this. Let’s use the value-range {QQ+,AK} =34 combos as a start, and see where this takes us. These hands are obviously strong enough to get profitably all-in against Bob’s 5-betting range as shown below (we remember from Part 1 and Part 2 that we need at least 36% equity to call the all-in 5-bet):

Alice’s 4-bet bluffs
Using the value-range {QQ+,AK} =34 combos, we need 34 x (2/3) =23 combos of 4-bet bluffs for an optimal 60/40 ratio of value hands to bluffs. We then pick the best hands not good enough to flat, for example {ATo,A9s-A7s} =24 combos. Alice’s total 4-betting range then becomes {QQ+,AK} + {ATo,A9s-A7s} =34 + 24 =58 combos. This is 58/458 =13% of her total opening range.

Alice’s flatting range
Alice 4-bets 13% of her 35% button opening range, and she needs to flat 30 – 13 =17% to get to 30% total defense. Then we scale up this percentage with the call multiplier 1.5 to compensate for the fact that Bob now can freeroll flops. We end up with a flatting percentage of 17 x 1.5 =26% of the opening range (35% =458 combos), which is 0.26 x 458 =119 combos. For example, we can use {JJ-88,AQ-AJ,ATs,KQ-KJ,KTs,QJ,QTs,JTs} =120 combos.

Summary
Our estimate of Alice’s optimal total defense strategy heads-up against a 3-bet from the blinds after openraising 35% on the button is:

– 4-bet {QQ+,AK} =34 combos for value
– 4-bet {ATo,A9s-A7s} =24 combos as a bluff
– Flat {JJ-88,AQ-AJ,ATs,KQ-KJ,KTs,QJ,QTs,JTs} =120 combos

Alice’s now defends 34 + 24 + 120 =178 combos. This is 178/458 =39% of her opening range, and top 178/1326 =top 13% of all hands. If you think this is loose for the games you’re playing in, keep in mind that we’re not trying to adjust to the tendencies of the 3-bettor here, we’re trying to make it impossible for him to exploit our button openraises by 3-betting any two cards from the blinds. If the 3-bettor is tight, feel free to tighten up yourself. For example, if you think he only 3-bets {JJ+,AK} for value and never 3-bet bluffs, you obviously should adjust by never 4-bet bluffing and fold your medium strong hands (unless you think you have the implied odds to call). But then we’re in the realm of exploitative play, not optimal play.

Note that even if you choose to not use exploitative play against a particular opponent, your knowledge about what optimal(ish) play is will make it easier to adjust to exploit him. You know that the strategy above is designed to prevent a loose 3-bettor from exploiting you, and then you can drop most of this defense against a tight 3-bettor when you have a strong read you can use to increase your profits. Drop all 4-bet bluffing, 4-bet a tight value-range, and only flat with the very best flatting hands when you think this is profitable.

Another thing worth mentioning is that if you don’t think you can play these button defense ranges profitably against a loose 3-bettor, you can take this as a sign that your postflop play needs improvement. Flatting hands like 88, ATs, and JTs to a 3-bet, and then playing them profitably postflop is not necessarily easy. You will get into many tricky spots postflop, but never forget that your position allows you to “turn the table” to some degree, and let your opponent get more than his fair share of postflop misery.

It’s important to realize that you should not flat 3-bets with medium strong hands in position and only plan to play fit-or-fold postflop. The weakest hands in our flatting range will probably be unprofitable for you, if you never use position to bluff and steal postflop. Aggressive and opportunistic postflop play is therefore a requirement when you try to defend optimally preflop, using a wide flatting range. Your postflop strategy for your flatting range should include a fair amount of (semi)bluff raising and floating.

Finally, note how loose you have to defend when trying to defend optimally, even when you’re starting with a relatively tight button range of 35%. Now think about how ultra-loose you would have to defend if you open something like 50% on the button, and you want to defend optimally against 3-bets. However, if you raise this loose on the button, it’s probably because you’re trying to exploit weak players in the blinds. If this is the case, it doesn’t make much sense to try to defend optimally against their 3-betting (since we don’t expect them to 3-bet very light, per definition).

Therefore it’s fine to use our estimated defense strategy for a 35% button core range also when you’re openraising a looser range in practice. You can think about the button openraising you do above and beyond 35% as “bonus raising”, based on an opportunity to exploit weak players in the blinds. If you’re trying to exploit the blinds, it’s fine to give them an opening to exploit (since we assume they won’t try to exploit us), and then you don’t worry about trying to defend the extra raising hands optimally. You just fold these additional weak hands when you get 3-bet, and you don’t worry about getting exploited until you notice the blinds have loosened up significantly against you. If they start fighting back by 3-betting a lot, it’s probably better to tighten up to something close to the 35% core range and defend this range optimally, than to try and defend a very loose opening range (e.g. 50%) optimally.

This will be discussed further in Part 6, where we’ll talk about optimal versus exploitative play. Until then, train optimal defense of our default 35% button range, and you will be a tough nut to crack for blinds trying to fight back against your button steals by 3-betting you a lot. If you can play well postflop after flatting 3-bets, a player 3-betting you often and light from out of position is likely to find himself in lots of trouble. He’ll often be faced with your optimal 4-betting range (mathematically impossible to exploit), and when you don’t 4-bet, he’ll often get called. When you flat your range of medium strong hands, the 3-bettor is forced to play postflop out of position, often with a worse hand than yours. This will be difficult for him when you play well postflop, including knowing when to steal.

As a thought experiment, think abut how you would like to sit in the blinds against a button player who plays this way. If you fold too much, he will rob you blind preflop. If you get feisty and try to defend with uncontrolled and overly aggressive 3-betting you will run into a wall of optimal 4-betting plus flatting followed by aggressive postflop play where you are out of position with a lot of weak hands in your range. The solution is of course to defend the blinds with a controlled mixture of optimal 3-betting and flatting, as discussed previously in this article, but this will be hard enough against a button player who plays close to optimal both preflop and postflop.

If button is a strong player, think “damage control”. Accept that his position + skills entitles him to make a profit in this scenario. Focus on limiting your losses, and don’t get fancy and try to outplay him from out of position. Stick close to the optimal strategies outlined here, and don’t spazz out. Spewy 3-betting and flatting out of position won’t do you much good against a strong player, but the mathematics of the situation guarantees that you can get away with some bluffing, and the optimal guidelines tells you how much. By sticking closely to a memorized optimal strategy, many of your preflop decisions become automatic, and you can direct more of your attention towards exploiting the weaker players at the table.

3.3 Questions that go away when we’re using optimal strategies

New players think a lot about how to play individual hands, and they can spend a lot of time mulling over relatively unimportant questions that they believe are important.

For example:

I raised JJ on the button, and an unknown player in the small blind 3-bet. Can I 4-bet? Should I 4-bet? What do I do if I 4-bet and get 5-bet? Is it perhaps best to flat the 3-bet?

A consequence of using a range-based way of thinking is that such specific questions about individual hands become less interesting. It’s obvious that JJ is a hand we can play profitably heads-up in position against a small blind who uses an optimal defense strategy, so our choice is between 4-betting for value and flatting. The question above can therefor be replaced by:

Do I want to 4-bet JJ for value or flat as a default? How does my choice affect the rest of my default defense strategy against small blind’s 3-bet?

Above we outlined a defense strategy against 3-bets where JJ was put in the flatting range, but there is nothing that forbids us from 4-betting it for value. We have 43% equity against small blinds estimated optimal value range {TT+,AQ} which we defined earlier in this article. So we have enough equity to call a 5-bet shove from this range (we need more than 36% equity against a 5-bet shoving range to call profitably, which you can easily verify for yourself).

Since JJ is an underdog against the range it gets all-in against (but we have to call the shove because of pot-odds), we see that JJ’s source of profit when used as a 4-betting hand is folding out small blinds 3-bet bluffs. And when we get 5-bet and have to call, we lose back a little bit of that money. However, since there are many 3-bet bluffs in small blind’s range, we might make money overall by 4-betting JJ, even if we’re an underdog against the range that 5-bets us. But even if this is the case (and we can verify whether this is the case with a little math) we might make more money by flatting JJ and playing a pot postflop in position against small blind’s total 3-betting range. This was our choice earlier in this article.

But let’s study 4-betting as an alternative default line for JJ heads-up in position against a small blind 3-bet. If we decide to use JJ as a value 4-betting hand, the rest follows automatically. We 4-bet and call a 5-bet (since this is what we do with all value hands). Then we adjust our 4-bet bluffing range to our new value range, so that we maintain the optimal 60/40 value/bluff-ratio. Finally, we also adjust our flatting range accordingly, so that we end up with an optimal overall defense strategy against small blind’s 3-bet (according to the principles of 30% total defense, adjusted with a 1.5 call multiplier for flatting).

We start with the previous value range for button, {QQ,AK} =34 combos, and then we add JJ and get {JJ+,AK} =40 combos. To get an optimal 60/40 ratio of value hands to 4-bet bluffs, we need 40 x (2/3) =27 bluff combos. We start with the previous bluffing range{ATo,A9s-A7s} =24 combos that we used with {QQ+,AK}. Then we add A6s and get {ATo,A9s-A6s} =28 combos. So we’re 4-betting 40 + 28 =68 combos, which is 68/458 =15% of our total button range.

We then have to flat 30 – 15 =15% of our button range to defend at least 30% total. This number is scaled up using the call multiplier 1.5, so we end up with a total flatting percentage of 1.5 x 15% =22.5%. This corresponds to 0.225 x 458 =104 combos from our 35% button opening range with 458 combos in it. We can choose {JJ-88,AQ-AJ,ATs,KQ-KJ,KTs,QJs,JTs} =104 combos (where we somewhat arbitrarily have removed QJo and QTs from the flatting range used previously).

Our new estimate of button’s optimal defense of a 35% opening range against a 3-bet from the blinds is then:

– 4-bet {JJ+,AK} =40 combos for value
– 4-bet {ATo,A9s-A6s} =28 combos as a bluff
– Flat {JJ-88,AQ-AJ,ATs,KQ-KJ,KTs,QJs,QTs,JTs} =104 combos

The original question How do I play JJ on the button after a 3-bet from an unknown small blind? has now disappeared. Instead we have the answer to how our total default button strategy against a 3-bet changes as a function of how we choose to play JJ in this situation (4-bet for value or flat).

Previously in this article we defined a button strategy where JJ was placed in the flatting range. But that doesn’t mean that you have to flat it. Feel free to experiment with other default defense strategies in position against 3-bets, based on the mathematical relations defined in this article:

– Optimal 60/40 value/bluff-ratio when you 4-bet
– As a starting point, use a total defense percentage of 30% of the opening range
– Adjust this percentage by using a call multiplier (we used 1.5) on your flatting range

Within these limits you can define your default strategies more or less as you please. But of course you should make sure that the hands you include in your value range are actually value hands (i.e. they can profitably call an all-in 5-bet against the 3-bettors 5-betting range). We’ll have more to say about this in a later article, but it’s easy to fall for the illusion that a hand is best played as a 4-betting hand, just because it makes money when we 4-bet it. It might be that the hand makes money from getting Villain to fold his 3-bet bluffs, and that we’re a small underdog when we call a 5-bet. If this is the case, we might make more money by putting the hand in our flatting range and playing a pot postflop with position.

We’ll return to this problem for JJ in a later article and analyze the EV for 4-betting versus flatting on the button after a 3-bet from the blinds. We’ll use the analysis software Pokerazor for these calculations, plug in small blind’s defense strategy, and compute the EV for the two ways we can play JJ after a 3-bet. We already know from ProPokerTools calculations that JJ is a small underdog against small blind’s 5-betting range (but we have pot odds to call the 5-bet). So we know that JJ’s profit after 4-betting comes from getting Bob’s 3-bet bluffs to fold, and then we lose back a small amount those times Bob 5-bets us all-in and we call for pot-odds.

But we’ll show that JJ makes money overall when we 4-bet it as a value hand. But we also know that JJ can be played profitably by flatting against small blind’s optimal 3-betting range (with 60% bluffs in it). So the question we want the answer to is what’s the most profitable way to play JJ in position after a 3-bet. The difference is probably not big, and in that case it’s impossible for us to make a big mistake. And when one alternative is about as good as the other, the decision is not all that important. What’s important is that we adjust the rest of our strategy accordingly, after we have made our choice. And then the what’s-the-best-way-to-play-JJ question simply evaporates.

We see that when we have a hand that works both as a 4-betting hand and a flatting hand, we have to use some judgment and try to choose the most profitable line for the hand. Note that when we’re the raiser out of position, the mathematics of the situation forces us to 4-bet and call a 5-bet all-in as an small underdog, since we now don’t have the option to flat the 3-bet (which is a choice we’ve made). In other words, we 4-bet and call a 5-bet as an underdog because this is more profitable overall than folding to the 3-bet. We have seen examples of this in Part 1 and Part 2. For example when we call an all-in 5-bet out of position with AK from UTG after having 4-bet against a button 3-bettor, even if we know that Villain only 3-bets {KK+} for value, plus some 5-bet bluffs. AK now becomes a small underdog against Villain’s total 5-betting range, but we have more equity than the minimum 36% we need to call, so we automatically go all-in after a 5-bet.

But when we’re the raiser in position, we have the option to flat hands that are small underdogs against Villain’s value range. So we can instead choose to play them postflop with position on his entire 3-betting range, which is heavy with weak 3-bet bluffing hands. In the scenario we studied above, JJ is a small underdog against Villain’s value range from the small blind after our button openraise. So even if we might make money by 4-betting it and calling a 5-bet as a small underdog, we have to think about what’s the most profitable line; 4-betting and ending the hand preflop, or flatting and playing postflop.

At any rate, the strategies we have defined in this article give you solid defaults. And I think even an optimal strategy without overly aggressive 3/4/5-betting will cause you to 3-bet and defend against 3-betting much more aggressively around the blinds than what’s common at the low limits. Train these strategies and play around with them, knowing that the mathematics behind them will protect you from getting exploited preflop.

Some of you might feel uncomfortable playing postflop in 3-bet pots, or after flatting preflop, using these strategies. Take this as a sign that you need postflop training. Stick to the optimal preflop strategies for 3/4/5-betting and flatting in blind stealing and blind defense, and force yourself to deal with the tricky postflop situations as they come. Getting better postflop is a matter of practice, and there are no shortcuts. Don’t be afraid to make mistakes, as long as you learn from them afterward. Keep in mind that when your preflop strategies are mathematically sound, you don’t have to worry about big preflop leaks, and you can focus on your postflop decision making when plugging leaks.

4. Summary

We have discussed 3-betting heads-up from the blinds against a button steal raise, and the raiser’s defense against this. We have designed default ranges for 3-betting and flatting in this scenario, both for the 3-bettor in the blinds and for the raiser on the button.

When flatting is an alternative for the raiser, the choice of 4-betting range becomes more ambiguous, and we therefore used more judgment than for the corresponding scenario with the raiser out of position (discussed in Part 1 and Part 2). Some of the raiser’s medium strong hands can be played profitably both by 4-betting them and flatting them in position after a 3-bet. For these hands we have to choose an alternative based partly on judgment.

In addition to 3/4/5-bet strategies with an optimal value/bluff ratio, we also took into consideration that the players in the blinds need to defend at least 30% to deny the button raiser the possibility of making a profit from stealing with any two cards. This mathematical requirement for minimum blind defense is not something we have discussed previously, but it’s always the case that the players sitting after the raiser have a collective responsibility for denying the raiser an opportunity to raise any two cards profitably. When button is the openraiser, all of this responsibility falls on the two players in the blinds. We used a simple assumption (both players in the blind defend the same percentage) to estimate an optimal defense percentage of 16% for the players in the blinds, heads-up against a button steal raise.

In Part 4 we’ll generalize the theory of 3-betting from the blinds to include scenarios where the raiser has opened from an arbitrary position (button, CO, MP or UTG). We’ll also talk more about the collective responsibility of defending the blinds sufficiently often. We’ll show that it’s mostly button openraising that forces the blinds to defend very aggressively, and that we can play much tighter against raises from earlier positions, without opening ourselves up from getting exploited by loose open-raising.

After that we’ll talk about two multiway 3-betting scenarios in Part 5, namely squeezing (3-betting after the raise already has been called), and cold 4-betting (4-betting after a raise and a 3-bet).

Then we’ll end this NLHE preflop article series with Part 6, where we test our strategies with the analysis software tool Pokerazor, and also discuss optimal play versus exploitative play, and when we should use one or the other. In Part 6 we’ll also discuss blind vs blind scenarios where the small blind openraises and the big blind defends by 3-betting and flatting, and we’ll use this scenario to give a taste of optimal postflop play.

So we’ll end up with a preflop series in 6 parts, and when we’re done, we’ll have touched upon most of the heads-up preflop scenarios, and some selected multiway scenarios.

Good luck!

Bugs – See more at: http://en.donkr.com/forum/optimal-3-bet-4-bet-5-bet-strategies-in-nlhe-6-max—part-5-533565#sthash.ZwlU6ch6.dpuf

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