Optimal 3-bet/4-bet/5-bet strategies in NLHE 6-max Part 2

1. Introduction

In “Optimal 3-bet/4-bet/5-bet strategies in NLHE 6-max – Part 1”, we discussed optimal 3/4/5-bet strategies for NLHE 6-max, based on principles from game theory. We only studied the scenario where one player (called Alice) open-raises from some position outside the blinds, and it’s folded to another player (Bob) who has position on Alice. We then used game theory principles to construct optimal strategy pairs for Alice and Bob when Bob elects to 3-bet.

The response for the article was good, and I got the impression that the the topic was interesting to many. I therefore decided to produce a mini article series (4 parts planned) about NLHE 6-max preflop play. The plan for the series is to discuss preflop standards based on a combination of sound poker sense and principles from game theory. In Part 2 we start with default ranges for openraising. Then we’ll generalize the theory from Part 1, and make a list of optimal 3/4/5-bet strategy pairs for opening ranges varying from 15% to 40%, with the raiser out of position.

We’ll also make some improvements in our implementation of the theory from Part 1. For example, we’ll use the blocker effect to Alice’s advantage when choosing her 4-bet bluffs, and we’ll give Bob a more balanced list of candidate hands for 3-bet bluffing. Finally, we’ll give Bob the option of calling raises (flatting) in position, and we’ll give him a default flatting range. Bob now has a complete set of “tools” to use when playing in position against Alice’s openraises.

When the generalized and improved strategies for openraising and heads-up 3/4/5-betting with the raiser out of position have been discussed in Part 2, we’ll move on to heads-up 3/4/5-betting with the raiser in position (e.g. 3-betting from the blinds) in Part 3. We’ll define a complete set of strategies to use both for Bob (folding, flatting the raise out of position, optimal 3/4-/5-betting), and for Alice (folding, flatting the 3-bet in position, optimal 3-/4-/5-betting). Our discussion of this scenario automatically provides us with strategies to use in blind defense.

Note that when the 3-bettor is out of position, flatting of 3-bets becomes a more profitable option for the raiser. Out of position, we elected to let Alice 4-bet or fold after getting 3-bet, since it’s problematic to flat 3-bets with medium strong hands and try to play them profitably out of position with 100bb starting stacks. But when Alice can have position on Bob for the rest of the hand, she can defend a wider range of hands profitably after a 3-bet.

Thus, position makes it easier for Alice to profitably flat 3-bets with a range of medium strong hands that are too weak to 4-bet for value (for example, JJ, AQo, KQs). In Part 3 we’ll look at the hands she should flat, and we’ll use principles for optimal 3/4/5-betting to construct a total defense strategy against 3-betting when Alice has position on Bob. Since optimal strategies come in pairs, our work will also produce a total blind defense strategy for Bob.

But before we place Bob out of position in Part 3, we’ll work through the implementation of all theory with Bob in position in Part 2. Since our goal with this article series is to construct a complete (or close to it) set of default preflop strategies, we’ll also define standard openraising ranges in this article. We start Part 2 with a review of the theoretical concepts from Part 1, and then we define default ranges for openraising. I expect most of the readers to have openraising under control, but defining a set of core ranges is useful, because:

– It makes it easier for us to make assumptions against unknown raisers
– It makes us more conscious about our own opening ranges

When we have defined default opening ranges and optimal strategies for 3/4/5-betting, both in and out of position, we’ll have defined a “model game” with strict preflop strategies. In reality we won’t follow the standards rigidly, since we obviously want to continually adapt to our opponents when we gather reads on them. But this default model game gives us solid standards to use against unknowns, and also against known strong players that we can’t easily exploit. A set of standard preflop strategies will also make it easier for us to model preflop scenarios mathematically, for example if we want to estimate the EV for some preflop line. Then we can plug in our default ranges and strategies (if we haven’t got other assumptions/reads) and do the math.

Defining solid preflop standards for openraising and 3/4/5-betting, based on game theory principles, will give us a much better understanding of what optimal (or at least near-optimal) preflop play is. In my opinion this is the most useful result of all this work. Exploiting weak opponents is (per definition) the same as moving away from optimal play to profit maximally from his mistakes. A good understanding of optimal play makes it easier to exploit our opponents. First, knowing what optimal play is makes it easier to spot opponent mistakes (e.g. their deviations from optimal play). Second, when we adjust to exploit these mistakes, we know both what we are adjusting away from and in which direction we should go.

The latter is something we’ll discuss further in Part 4. My plan is to use Part 2 and Part 3 to construct default strategies, and then we’ll talk more about how to use them in Part 4. There we’ll look more closely at the difference between default strategies/optimal play and exploitative play. We want to use exploitative strategies against weak opponents whenever we can, since this is generally more profitable than optimal play. But against strong opponents that are difficult to exploit, we want a set of solid standards to fall back on to prevent them from exploiting us. So we need to think about when to use one or the other, based on who we’re playing against. In Part 4 we’ll also test our strategies numerically, usingPokerazor simulations with various assumptions about our opponents.

Finally, Part 1 generated some interesting forum discussion, for example about our definitions of value hands/bluffs, and how these are chosen. We’ll return to this topic in Part 4, but first we’ll finish all the work and define our default preflop ranges and preflop strategies in Part 2 and Part 3.

The structure of Part 2 is:

  • Summary of the theory behind optimal strategy pairs for heads-up 3/4/5-betting with the raiser out of position. We’ll also point out areas where we’ll improve on our previous implementation of the theory (for example, using blocker effects when choosing 4-bet bluffs)
  • Default ranges for openraising
  • Generalization of the results from Part 1 for optimal 3/4/5-betting heads-up with the raiser out of position, using opening ranges varying from 15% to 40%

We’ll use heads-up scenarios with 100bb starting stacks, unless otherwise mentioned.

2. Summary of optimal 3/4/5-bet theory with the raiser out of position

We used the following model:

  • Both players start with 100bb stacks, both are outside the blinds, and Bob has position on Alice
  • Alice openraises pot (3.5bb) with some opening range
  • Bob 3-bets pot (12bb) with a mix of value hands and 3-bet bluffs
  • Alice responds by folding or 4-betting to 27bb (slightly less than pot =37.5bb) with a mix of value hands and 4-bet bluffs
  • Bob responds by folding his 3-bet-buffs and 5-betting all-in with a mix of value hands and 5-bet bluffs
  • Alice responds by calling with her value hands, and folding her 4-bet bluffs

The strategies we defined were based on the following mathematical relations (see Part 1 for details):

  • Alice needs to defend 30% of her opening range to prevent Bob from profitably 3-betting any two cards
  • The optimal ratio of value hands to bluffs in Bob’s 3-betting range is 40/60
  • The optimal ratio of value hands to bluffs in Alice’s 4-betting range is 60/40
  • Bob should have enough 5-bet bluffs in his 5-betting range to make Alice’s weakest value hands break even when they call the 5-bet (and we elected to use Axs hands as 5-bet bluffs)

Here we define “value hand” as a hand we plan to keep reraising until we get all-in. A “bluff” is a hand we fold to a reraise (when we’re 3-betting or 4-betting), or a hand we 5-bet bluff all in.

Then we defined optimal strategy pairs from Alice and Bob in two scenarios:

1. Alice raises a ~15% range from EP (UTG or MP)
2. Alice raises a ~25% range from CO

For both scenarios we did the calculations in full detail to show how you can do similar work on your own opening ranges. In this article we’ll generalize these results, and construct a list of optimal strategy pairs that you can use as a “cheat sheet” when 3-betting optimally against any opponent. We’ll list optimal strategy pairs for 15%, 20%, 25%, 30%, 35% and 40% opening ranges, which should cover all the opening ranges you will encounter in practice when engaging in 3/4/5-bet wars outside the blinds.

You can also use this list to estimate optimal 4-betting strategies for yourself when you are the raiser out of position (if you don’t feel like doing the calculations for the exact ranges you are using). For example, if you know that you’re openraising 32% from CO, you can use the strategy pair for 30% openraising when estimating your 4-betting range. In practice, this will be close enough.

Before we define the list of optimal strategy pair for 3/4/5-betting with the raiser out of position, we’ll make a couple of adjustments for Alice’s and Bob’s choice of 4-bet bluffs and 3-bet bluffs. In Part 1 we made some simplifications to make things easier to remember, but here we’ll improve on them:

2.1 Alice’s choice of 4-betting hands

Alice’s value hands follow directly from her opening range plus the requirement that she should defend 30% of this range, using a value/bluff ratio of 60/40. But Alice has a choice to make when selecting hands to 4-bet bluff. She can choose between two methods:

1. The combo method: Alice picks a set of hands to 4-bet bluff
2. The percentage method: Alice 4-bet-bluffs a fixed percentage with all her non-value hands

When Alice gets 3-bet out of position, her response is to never call, and 4-bet 30% of her opening range with a 60/40 ratio of value hands to 4-bet bluffs. So 0.30 x 0.60 =18% of her opening range should be 4-bet for value and 0.30 x 0.40 =12% should be 4-bet as a bluff. For example, when Alice opens a 15% range from early position, this corresponds to 4-betting 0.18 x 0.15 x 1326 =36 value combos and 0.12 x 0.15 x 1326 =24 bluff combos.

Alice then chooses her best 36 (or thereabouts) hands to use as value hands, and the obvious choice is {QQ+, AK} =34 combos. Then she can either choose 24 specific combos to use as 4-bet bluff hands, or she can 4-bet all non-value hands (the remaining 82% of her range when the 18% of value hands has been selected) a certain percentage of the time.

If she chooses the latter, she should use a percentage x that gives her a 60/40 ratio of value hands to bluffs. Formulated as an equation, we get:

0.18/0.82x =60/40
0.18/0.82x =1.5
0.18 =1.5(0.82x)
0.18 =1.23x
x =0.18/1.23
x =0.15 =15%

So Alice should 4-bet bluff 15% of the time with all hands not strong enough to 4-bet for value. This makes 4-bet bluffing easy to implement i practice. We only need to remember one number x =15%, and this 4-bet bluff percentage is the same regardless of Alice’s opening range. In Part 1 we therefore elected to use the percentage method for simplicity. We used a randomizer from random.org for this purpose, as illustrated below:

Example 2.1.1: Randomized 4-bet bluffing

$100NL
6-handed

Preflop:
Alice ($100) raises to $3.50 with K J from UTG, Bob ($100) 3-bets to $12. Alice uses the randomizer, planning to 4-bet bluff if it returns a number between 0 and 15, and otherwise she will fold.:

The randomizer returns 41, so Alice folds this time.

The percentage method works well and is easy to implement, but in practice the combo method will work better. The difference between the two is that the combo method gives us the opportunity to exploit the blocker effect to our advantage. If Alice uses her best hands not strong enough to 4-bet for value, this will ensure Bob’s range is poorer in value hands.

For example, assume Alice raises 15% from early position. In Part 1 we established that Bob’s value 3-bet range against this opening range should be {KK+} plus some Axs hands as 5-bet bluffs. Before the blocker effect is taken into account, there are 12 AA/KK combos in Bob’s value range. But when Alice has AQ (which she does not 4-bet for value), the chance that Bob has AA is reduced to half (there are 3 possible AA combos in his value range when Alice has an ace on her hand). So if Alice uses AQ and similar decent hands at the top of her non-value range, she ensures that her 4-bet bluffs go in those times it’s less likely that Bob has a value hand to continue with. The hand we fear most in Bob’s 3-betting range is AA, and it’s seems obvious that Alice should pick her 4-bet bluffs from the best Ax hands not strong enough to 4-bet for value. For example, AQ blocks the AA/QQ/AK hands in Bob’s range.

In Part 2 we’ll list specific 4-bet bluff combos for all of Alice’s opening ranges in order to exploit the blocker effect. This will require more memorization than with the percentage method, but on the other hand we save time and distractions when we don’t have to click the randomizer while playing.

2.2 Bob’s choice of value 3-bet hands

We defined Bob’s value hands as the range of hands he 3-bets, planning to 5-bet all-in after a 4-bet from Alice. His value range has two components:

– Value hands that profit from getting all-in against Alice’s value hands
– 5-bet bluffs

When building Bob’s total value range, our starting point was to find all hands with at least 50% equity against Alice’s value hands (which followed from her opening range). These are Bob’s value hands. Then we added Axs hands as 5-bet bluffs until it became break even for Alice to call a 5-bet with her weakest value hands. Note the difference between Bob’s value range an his value hands. The latter are the hands that profit when Bob’s 5-bets get called by Alice’s value hands, while Bob’s value range is the total range of hands he’s planning to 5-bet all-in (his value hands plus some 5-bet bluffs).

For example, in Part 1 we saw that when Alice raises a 15% opening range from UTG, Bob’s response is to 3-bet a total value range {KK+, A5s, A4s}, planning to 5-bet all-in after a 4-bet. AA/KK are clearly hands we want to get all-in against Alice’s value range {QQ+,AK}, and then we add Axs hands until it becomes break even for Alice to call a 5-bet shove with her weakest value hand (QQ).

Alice is getting pot odds 128.5 : 73 to call a 5-bet shove, and she needs minimum 73/(128.5 + 73) =36% equity to call profitably. We can make her call with QQ break even by using 7 Axs combos as shown below (we start with A 5 and work our way down towards A 2 ):

Thus, the exact number of 5-bet bluffs in Bob’s value range against Alice’s 15% opening range is {A5s,A 4 , A 4 , A 4 }. In Part 1 we simplified this to {A5s,A4s}, but in Part 2 we’ll use the exact number of 5-bet bluffs.

The next step for Bob is to define a 3-bet bluff range. He should use a 40/60 ratio of value hands to bluffs, so his 3-bet bluffing range should have 60/40 =1.5 times as many combos as his value range. For example, if he uses the value range {KK+,A5s,As4s,Ah4h,Ad3d} =19 combos against a 15% opening range for Alice, he should bluff with 1.5 x 19 =29 combos.

The number of 3-bet bluff combos Bob needs will chance with Alice’s opening range, and Bob can choose between two methods:

– Memorize a list of specific 3-bet bluff combos for each of Alice’s opening ranges
– Memorize a list of 3-bet bluff candidates, and use each of them a certain % for each of Alice’s opening ranges

We chose the latter, and defined the following list of 156 combos to use as 3-bet bluffs:

Candidate list for 3-bet bluffing

Ace high: A9s-A6s ATo-A8o (52 combos)
King high: K9s-K6s, KJo-K9o (52 combos)
Queen high: Q9s-Q6s, QJo-Q9o (52 combos)

The list is based on the fact that Bob wants to 3-bet bluff with the best hands not strong enough to 3-bet for value or call. If Alice always 4-bets or folds out of position, Bob’s choice of 3-bet bluffs doesn’t matter, but in practice we’ll sometimes get called. So we want to use the best possible hands in case the raiser calls our 3-bet and forces us to play postflop.

For example, if Bob needs 29 3-bet bluff combos to use against Alice’s 15% opening range, he can 3-bet each hand on the list above 29/156 =19% of the time. He uses a randomizer to achieve this, as illustrated below:

Example 2.2.1: Randomized 3-bet bluffing

$100NL
6-handed

Preflop:
Alice ($100) raises to $3.5, and it’s folded to Bob who has K 7 on the button. Bob knows from observation that Alice is opening a 15% range from UTG, and his response is to 3-bet a value range {KK+,A5s,As4s,Ah4h,Ad4d} =19 combos for value plus a range of 3-bet bluffs. He uses 1.5 x 19 =29 3-bet bluff combos, which corresponds to 3-betting all hands in the 3-bet bluff list 29/156 =19% of the time. Here he has one of these hands, so he uses the randomizer, planning to 3-bet when it returns a number between 0 and 19:

The randomizer returns 3, and Bob 3-bets pot to $12. Alice folds.

In this article we’ll make a change in Bob’s 3-bet bluff list. The list we designed in Part 1 was easy to remember, but it’s somewhat imbalanced. It only contains Ax/Kx/Qx-combos and few low cards, which makes it hard for us to connect with low flops. The list also contains lots of offsuit hands. We’ll replace this list with a more balanced list that has more suited hands, and also some medium/low connectors and 1-gappers. Designing Bob’s 3-bet bluff list is not an exact science, so we’ll use judgment and sound poker sense.

3. Open-raising

Before we move on to generalizing the theory for 3/4/5-betting, we’ll define a set of standard opening ranges for all positions. A good NL player should never feel like a “slave” to strictly defined preflop strategies, and ideally he should always try to play hands that are profitable, and otherwise fold. But there are good reasons for starting with a set of memorized opening ranges.

It’s obvious that the strongest hands like AA-QQ, AK, etc. are profitable raising hands from any position. But in practice it’s impossible to know exactly how profitable the weakest playable hands (for example A6o, 22, 76s) are in a given situation. Sometimes they will be profitable and sometimes not. Sticking to a default reasonable opening range for each position is probably just as good as trying to find exactly which weak hands can be openraised in a given situation and which can not. Sometimes we will be wrong, folding some playable hands and playing some hands that should have been folded, but usually it won’t matter much (close decisions don’t matter much). When we here say “scenario” we mean the combination of your position, the tendencies of your opponents, the history between you, and stack sizes for everyone involved.

Also, even if you are very flexible with respect to openraising, and always try to adapt to the situation, there will always exist a “core range” for a given situation. The core range is the range of hands you are always willing to open, regardless of the circumstances. For example, you might decide that you’ll never open less than 35% of your hands on the button, regardless of how the players in the blinds play. Starting with a well-defined set of standard opening ranges makes it easier to know what your effective core range is for a given position.

Starting with a standard set of opening ranges also makes it easier to defend against 3-betting, since we easily can memorize optimal defense strategies for our standard opening ranges. Against good players who 3-bet optimally of near optimally, we can fall back on our default optimal defense strategy. Against weak players who either 3-bet way too little or way too much, we can use the optimal defense strategy as a starting point, and then adjust as needed (folding more against a tight 3-bettor, and 4-betting or calling more against a loose 3-bettor). Note that exploitative adjustments against weak opponents become easier when we know what the optimal starting point is.

Thus, the point of starting with a set of standard opening ranges is not to “bind” you strategically, it’s quite the opposite. Building your preflop game on top of solid standard opening ranges will make it easier to adjust. By this I mean that it will be easier to adjust correctly to the situation when you start with a good understanding of what a good default strategy is, and this understanding starts with understanding the opening ranges we’re using. When solid default preflop strategies have been trained, you’ll spend less time at the table thinking about what the default play is, and more time thinking about how to adjust correctly away from default play.

The opening ranges listed below are on the tight side, and you can think about them as “core ranges” that you always open, regardless of the circumstances. You can elect to open looser, but unless the table conditions are extreme, you’ll probably not gain much by opening tighter.

Note that we can’t use game theory principles to find optimal opening ranges, since this is more or less equivalent to solving the game of NL Hold’em in it’s entirety. This is not possible in practice, so our choice of standard opening ranges is based on experience and sound poker sense.

Here is another way to look at it:

Instead of asking what the best standard opening range is for a given position, look at the range you’re using and ask yourself if your range is a good tool for the job. If you had given your opening ranges to the world’s best 6-max grinder and told him to grind your limits using your ranges, would he still be a big winner, even if he couldn’t play the way he wanted preflop? If you think the answer is “yes”, your ranges are probably fine.

3.1 Openraising from early position (EP =UTG and MP)

From the two earliest positions we should use tight default ranges, and I recommend you use a ~15% core range as a starting point from both UTG and MP. I’ll list an EP range here, and then you can choose for yourself how much to loosen up in MP (you should definitely not play tighter than this from MP), and how much to tighten up or loosen up from UTG.

22+
A9s+ AJo+
KTs+ KQo
QTs+
J9s+
T9s
98s
87s
76s
65s

194 combos
15%

From UTG you can drop the lowest suited connectors, if you think this range is too loose. From MP, don’t tighten up, but you can raise some more hands (e.g. K9s, Q9s, ATo, KJo, QJo, etc.) if you think 15% is too tight. But using something around 15% for both the UTG and MP positions is a good place to start.

If you feel uncomfortable having so many medium/low suited connectors in your EP range (they can be difficult to play well out of position), feel free to drop the lowest ones from the range, or replace them with high card hands. For example, you can drop 87s-65s (3×4 =12 combos) and play KJo (12 combos) instead. But don’t take this too far, and be cautious with the offsuit high cards hands (KQo, KJo, QJo, QTo, etc.). These hands are negative implied odds hands that often put you in tough spots postflop, especially out of position, even when you flop what you’re hoping for (top pair, mostly).

Keep in mind that domination is less of a problem for the suited connectors. Also, having a handful of them in your range makes it easier for you to credibly represent strength on low flops (which can be a problem when open-raising a strong range with lots of high card hands). So the suited connectors makes your range more balanced and more difficult to read.

Later, in the discussion about defense against 3-betting, we’ll for simplicity assume we’re using the 15% range above from both UTG and MP, and we’ll refer to both positions as “EP”. This simplification is acceptable, since the optimal strategies don’t change much when we move from, say, 15% –> 13% in UTG, or 15% –> 17% in MP.

3.2 Openraising from CO

Here I recommend a ~25% core range. In CO you’ll get more opportunities to exploit the players behind you, if they are playing too tight. For example, with a tight-passive button player and weak players in the blinds, it’s fine to open 30% and perhaps even more from CO. But start with a core range of 25% or so, and let this be the range you never tighten up from. And if the table conditions are right, you can loosen up.

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

326 combos
25%

3.3 Openraising from the button

From the button I recommend a ~35% core range. Button is the position with greatest flexibility with respect to openraising, and you should be willing to vary your range a lot. Openraise at least 35%, but be quick to loosen up if the blinds are weak. In this context, “weak” means blinds who either fold too much preflop, or who mostly defend by calling.

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

458 combos
35%

Don’t be afraid to openraise a loose range on the button against weak players in the blinds, even if they call a lot preflop. When they don’t punish your loose openraising with 3-betting, you’ll have 3 ways to win the pot:

  • They fold preflop
  • They call preflop, miss the flop, and you win with a c-bet
  • They call preflop, hit the flop, but you win anyway. Either by hitting the flop harder than them, or by drawing out on them later, or by bluffing them out of the pot (for example when a scare card falls on the turn or river).

3.3 Openraising from the blinds

Here we mean openraising from the small blind when everybody has folded, or raising from the big blind in a limped pot. Here I recommend starting with the following set of simple guidelines:

When it’s folded to you in the small blind, openraise your button range if the big blind doesn’t defend aggressively. If he is difficult to steal from, tighten up to the CO range. Don’t open-limp, unless you have specific reasons to think this will be more profitable than open-raising or folding.

When you’re in the big blind, it’s folded to the small blind, and he open-limps, raise the button range to punish his limps. If someone has limped in outside the blinds, raise a tight range for value. The more players have limped, the tighter you raise. The better the limpers play, the tighter you raise. This is logical, since you need a stronger hand to play out of position against many players, or against players who are competent postflop. Now you’ll win fewer pots without a showdown, and you compensate by basing your raises more on showdown equity and less on steal equity.

As a starting point, it’s a good idea to not raise much looser than {99+, ATs+, AJo+, KJs+, KQo} from the big blind out of position against limpers, unless you are heads-up and/or you expect the players behind you to give up easily.

3.4 Isolating limpers

As a starting point, if you have position on one or more limpers outside the blinds, raise with the same range you would have openraised. It’s of course fine to drop the very weakest hands (65s, Q2s and the like), especially against more than one limper, or against a very loose limper. Some of the hands you will be isolating with are technically too weak to play postflop against one or more limping ranges, but keep in mind that you base your raise partly on steal equity. Isolating a limper with a hand like T8s is a semibluff. Sometimes you win preflop, and when you don’t win preflop, you’ll often get heads-up with position on a weak player with a weak range. This will give you many opportunities to steal the pot postflop, and when this isn’t possible, you’ll sometimes make the best hand and win a a showdown.

But as mentioned previously, don’t make loose raises against limpers when you’re in the blinds. The exception is when you have reads telling you that a raise will make it easy to win the pot. Some limp and fold a lot to raises. Others limp and call a lot of raises, but then play fit-or-fold postflop. Pay attention to the players around you, and when you pick up information you can use to your advantage, use it. But against unknown players and loose players, raise a tight range out of position in the blinds in a limped pot.

3.5 Summary of standard opening ranges

I recommend that you memorize all these opening ranges, and also the number of combos in each range. For example, knowing that you’re opening 326 combos (25%) as a default from CO will make it easier for you to defend correctly against 3-betting.

For example, we know that the optimal defense percentage out of position is 30% of our opening range when we defend by 4-betting or folding out of position. 18% should be for value and 12% should be bluffs. If you know how many combos you have in your opening range, it will be easier to get a feel for how many hands you should defend, both for value and as bluffs.

4. Generalizing the theory for optimal 3/4/5-betting with the raiser out of position

We remember from Part 1 that optimal strategies for 3/4/5-betting come in pairs: A raise/4-bet/call 5-bet strategy for the raiser, and a 3-bet/5-bet strategy for the 3-bettor. In Part 1 we estimated these optimal strategy pairs after a ~15% EP-raise and a ~25% CO-raise

In Part 2 we’ll generalize this theory in two ways:

  • We’ll list strategy pairs based on 15%, 20%, 25%, 30%, 35% and 40% openraising
  • We’ll include flatting in position as a strategic option for the 3-bettor

As previously mentioned, we’ll also list specific hands that the raiser will use as 4-bet bluffs (the combo method) to exploit the blocker effect. We’ll always keep the strength principle in mind:

– With your best hands: Raise for value
– With your next best hands: Call
– With hands that aren’t good enough to raise or call: Fold or bluff

Which hands make up your “best hands”, and your “next best hands” will depend on the situation you’re in. For example, the value of a NLHE starting hand in position behind a raiser will vary with both our absolute position and the raiser’s range. But regardless of the situation, we’ll choose our value hands form our best hands that we are willing to get all-in with against our opponent’s value hands (for example {QQ+,AK}). Then we pick our calling hands from the best hands that aren’t strong enough to get all-in preflop. Finally, we pick the best of the remaining hands to use as bluffs.

Our 3-bettor Bob now will get a flatting range in position, and we start by listing all of the “tools” at Bob’s disposal against Alice’s openraise. As previously mentioned, we’ll make a new list of 3-bet bluffing hands (which we’ll name “IP 3-bet air list”), more weighted towards balance and suited hands than the simple list we used in Part 1. We’ll also list the 5-bet bluff hands Bob 3-bets, planning to 5-bet all-in as a bluff after a 4-bet (“IP 5-bet air list”). Finally, we list a range that Bob flats in position (“IP flat list”).

4.1 Ranges for 3-bet bluffing, 5-bet bluffing, and flatting in position

IP 3-bet air list

A9s-A6s
K9s-K6s
Q9s-Q6s
J9s-J6s
T8s-T7s
97s-96s
87s-86s
76s-75s
65s

100 combos

IP 5-bet air list

A5s-A2s

16 combos

IP flat list

22+
ATs+ AJo+
KTs+ KQo
QTs+
JTs
T9s
98s

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

Note that the flat list changes according to which hands we 3-bet for value. For example, against a 15% UTG raise, we use {KK+} as our value range. The flat list then becomes {QQ-22,AKs-ATs,AKo-AJo,KTs+,KQo,QTs+,JTs,T9s,98s} =162 combos.

The flat list is made up of hands that you can always flat as a default after a raise from UTG, MP and CO when you’re on the button. But you should flat somewhat tighter from earlier positions (for example, it’s probably best to fold 98s in MP after an UTG raise). You might also want to tighten up against a very tight raiser (folding hands like AJo, KTs, QTs and 98s after a tight 8% openraise from UTG is fine). Conversely, if you have position on a very loose and bad raiser, it’s allowed to sneak in more marginal flatting hands (e.g. 87s) if you think it’s profitable to see a flop with them in position. So use the flat list as a starting point, and exercise judgment.

The lists for 3-bet bluffing and 5-bet bluffing can be easily memorized to make them easier to apply at the table. I use this 3-bet list at the limits I play ($400NL to $1000NL), and I use it together with a randomizer. Of course we can also pick specific combos from the 3-bet bluff list, but in my opinion it’s much simpler to use a memorized “IP 3-bet air list” plus a randomizer than having to memorize a specific range of 3-bet bluffs for each opening range.

For the 5-bet bluffs I use a simpler method. In the summaries below I give the number of 5-bet bluffs Bob needs for the opening range he’s up against, and then he simply picks hands from the top of the list {A5s-A2s} and works his way from A 5 down towards A 2 . For example, if Bob needs seven 5-bet bluff hands, he picks {A5s, As4s, Ah4h, Ad4d} =7.

I’ve also made a simplifying little trick with the 3-bet bluff list. I put exactly 100 combos in the list, so that we easily can convert between percentages and combos. Let’s say you’re in position behind a raiser, and you know that your value range is {KK+} =12 combos, but you don’t remember how many % you should 3-bet bluff the hands on the list (you’re using a randomizer).

But you know that you should use a 60/40 ratio of value hands to bluffs, so with {KK+} =12 combos as your value range, you need 1.5 x 12 =18 bluff combos. Since the 3-bet bluff list has 100 combos, this corresponds to 3-bet bluffing all hands on the list 18% of the time. So if you pick up Q7s, you click the randomizer, planning to 3-bet if it returns a number between 0 and 18, and otherwise you fold.

You can either have the lists and percentages memorized, or have them in a document on your screen for easy access, but it’s a good idea to use structure/organization to keep things simple where you can. I have memorized everything, and I rarely have to pause and think about these strategies, but sometimes I slip up. Then it’s easy to start with the value range, then count the number of bluff combos you need, and with 100 combos in the 3-bet bluff list, you now also have the percentage to use with the randomizer.

A final word: These lists are not gospel. If you’d rather use hands like KJo, KTo and QTo instead of some of the lowest suited connectors on my 3-bet bluff list, go ahead and change things to your liking. I’ve chosen to use suited hands, since negative implied odds is less of a problem for suited hands when our 3-bet gets called and we’re forced to play postflop. Suited hands also pick up equity on the turn more often than offsuit hands, and this will give you more good spots to 2-barrel.

4.2 Optimal 3/4/5-bet strategy pairs with the raiser out of position

Bob’s lists of flatting hands, 3-bet bluffs, and 5-bet bluffs are given above. What remains to be done is to systematically find Alice’s 4-betting hands (value hands and bluffs) for various opening ranges between 15% and 40% in increments of 5%. Then we find the 3-bet bluff percentage that Bob should use with his “IP 3-bet air list”. Last we find the number of 5-bet bluffs Bob should use, and we’re done.

All calculations are done like in Part 1, so we simply present the results here. Note that we have done some rounding here and there. For example, when openrasing a 15% range, we 4-bet {QQ+,AK} =34 combos for value, while the theoretically optimal number of value combos is 0.18 x 0.15 x 1326 =36. We generally want to play all combos of a particular starting hand the same way. So we don’t pick 2 combos of JJ or AQ to get to exactly 36 value combos.

We have rounded the percentages to use with Bob’s “IP 3-bet air list” to the nearest 5% to get numbers that are easy to remember. It’s not critical to be accurate to the nearest percentage point, and rounding is fine. Another approximation we have done is to let Bob flat the same range of hands, regardless of his exact position behind the raiser (MP, CO or button). We’re assuming he can flat all hands from the flat list profitably from all positions behind the raiser, but in practice Bob should flat a bit tighter from MP and CO. When Bob flats from MP and CO, his position will be worse postflop, and the risk of a 3-bet behind him is higher, so he should flat a bit tighter than on the button.

We use the following notation:

– AJ =All AJ, suited and offsuit
– AJs =All suited AJ
– AJo =All offsuit AJ

Optimal 3/4/5-bet strategy pair with 15% openraising OOP
Alice’s strategy:

  • Openraise 15%
  • 4-bets {QQ+,AK} =34 combos for value and calls a 5-bet
  • 4-bets {AQ,AJs-ATs} =24 combos as a bluff and folds to a 5-bet

Bob’s strategy:

  • Flats the flat list: {22+,ATs+,AJo+,KTs+,KQo,QTs+,JTs,T9s,98s} =162 combos when {KK+} gets 3-bet for value
  • 3-bets {KK+, 7 air} for value, planning to 5-bet all-in after a 4-bet
  • 3-bets 30% of “IP 3-bet air list”, planning to fold to a 4-bet

For simplicity I have used the notation “x air” for Bob’s 5-bet bluffs. For example, “7 air” means that he picks the 7 best combos from “IP 5-bet bluff list” ={A5s-A2s}. So he picks {A5s, A 4 , A 4 , A 4 }. With this notation we only need to remember a number for the 5-bet bluffs, and then we pick the actual hands on the spot.

Optimal 3/4/5-bet strategy pair with 20% openraising OOP
Alice’s strategy:

  • Openraises 20%
  • 4-bets {TT+,AK,AQs} =50 combos for value and calls a 5-bet
  • 4-bets {AQo,AJ,ATs} =32 combos as a bluff and folds to a 5-bet

Bob’s strategy:

  • Flats the flat list: {22+,ATs+,AJo+,KTs+,KQo,QTs+,JTs,T9s,98s} =156 combos when {QQ+} gets 3-bet for value
  • 3-bets {QQ+, 10 air} for value, planning to 5-bet all-in after a 4-bet
  • 3-bets 40% of “IP 3-bet air list”, planning to fold to a 4-bet

Optimal 3/4/5-bet strategy pair with 25% openraising OOP
Alice’s strategy:

  • Openraises 25%
  • 4-bets {TT+,AQ+} =62 combos for value and calls a 5-bet
  • 4-bets {AJ-AT,A9s-A8s} =40 combos as a bluff and folds to a 5-bet

Bob’s strategy:

  • Flats the flat list: {22+,ATs+,AJo+,KTs+,KQo,QTs+,JTs,T9s,98s} =140 combos when {QQ+,AK} gets 3-bet for value
  • 3-bets {QQ+,AK, 12 air} for value, planning to 5-bet all-in after a 4-bet
  • 3-bets 70% of “IP 3-bet air list”, planning to fold to a 4-bet

Optimal 3/4/5-bet strategy pair with 30% openraising OOP
Alice’s strategy:

  • Openraises 30%
  • 4-bets {99+,AQ+,AJs} =72 combos for value and calls a 5-bet
  • 4-bets {AJo,AT-A9,A8s} =48 combos as a bluff and folds to a 5-bet

Bob’s strategy:

  • Flats the flat list: {22+,ATs+,AJo+,KTs+,KQo,QTs+,JTs,T9s,98s} =134 combos when {JJ+,AK} gets 3-bet for value
  • 3-bets {JJ+,AK, 10 air} for value, planning to 5-bet all-in after a 4-bet
  • 3-bets 75% of “IP 3-bet air list”, planning to fold to a 4-bet

Optimal 3/4/5-bet strategy pair with 35% openraising OOP
Alice’s strategy:

  • Openraises 35%
  • 4-bets {99+,AJ+} =84 combos for value and calls a 5-bet
  • 4-bets {AT-A8, A7s-A6s} =56 combos as a bluff and folds to a 5-bet

Bob’s strategy:

  • Flats the flat list: {22+,ATs+,AJo+,KTs+,KQo,QTs+,JTs,T9s,98s} =134 combos when {JJ+,AK} gets 3-bet for value
  • 3-bets {JJ+,AK, 14 air} for value, planning to 5-bet all-in after a 4-bet
  • 3-bets 80% of “IP 3-bet air list”, planning to fold to a 4-bet

Optimal 3/4/5-bet strategy pair with 40% openraising OOP
Alice’s strategy:

  • Openraises 40%
  • 4-bets {88+,AJ+,ATs+} =94 combos for value and calls a 5-bet
  • 4-bets {ATo,A9-A7} =60 combos as a bluff and folds to a 5-bet

Bob’s strategy:

  • Flats the flat list: {22+,ATs+,AJo+,KTs+,KQo,QTs+,JTs,T9s,98s} =134 combos when {JJ+,AK} gets 3-bet for value
  • 3-bets {JJ+,AK, 14 air} for value, planning to 5-bet all-in after a 4-bet
  • 3-bets 80% of “IP 3-bet air list”, planning to fold to a 4-bet

4.3 Summary of optimal strategy pairs for 3/4/5-betting with the raiser in position

We have now listed a set of strategy pairs that cover most of the opening ranges you will encounter as a 3-bettor in position. Note that we’re not claiming that a 35% or 40% range is a good opening range from positions earlier than the button, but we include it anyway. You might meet opponents that play this loose.

Those with good memory can memorize these strategy pairs once and for all. We’ll also organize them in a tidy document that you can keep on the screen while you play:

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

Here I have marked our own EP and CO standard opening ranges with grey, so that it will be easy for you to find your 4-betting ranges from the document when you’re out of position and get 3-bet. But the 4-betting ranges are easy to memorize, so this document will be most useful when you’re in position and need the optimal 3-betting strategy to use against an openraiser.

You can use the HEM stat “Raise 1st” to estimate Villain’s opening ranges for the different positions. You can include the positional “Raise 1st” stats in the HUD, or you can find them in the HEM pop-up when you click on the player.

Here is an example of using HEM stats when 3-betting in position:

Example 4.2.1: Optimal 3-betting based on HEM stats

$400NL
6-handed

MP ($400) raises to $14, CO folds, you ($526) are on the button with J 7 . This hand is on “IP 3-bet air list”, so it’s a candidate for a 3-bet bluff in position. You now need an estimate of MP’s opening range, so that you can estimate the bluff percentage to use with the 3-bet bluff list.

We have a large sample (¨~7k hands) on MP, and his HUD stats look like this:

The number we’re interested in is Villain’s “Raise 1st” from MP. The “Raise 1st” stats are located on the HUD’s last line: UTG, MP, CO, Button, SB, BB from left to right. We find that Villain raises 23% from MP

Then we turn to the summary document we made earlier and look up the strategy pair closest to an opening raise percentage of 23%. We choose the strategy pair for a 25% opening range. Our value range is then {QQ+,AK, 12 air} ={QQ+,AK,A5s,A4s,A3s}, and we use a bluff percentage of 70% for our 3-bet bluff list.

Next we click the randomizer, planning to 3-bet if it returns a number between 0 and 70, and otherwise fold:

The randomizer returns 34, so we 3-bet bluff to $48, and button folds.

4.3 HUD layout with positional “Raise 1st” stats

Most of the HUD layout used in Example 4.2.1 is a standard layout that can be downloaded from the HEM forums. Then I added a line with “Raise 1st” stats at the bottom. The original HUD with explanations of stats and color coding schemes can be found here: NL6max Layout: Optimization.

My modification of the HUD with positional “Raise 1st” stats on a separate line can be downloaded here (right click and choose “Save as”): nlsixmax.xml. The structure of the layout is shown below

5. Summary

In this article we have gone further with the theory discussed in Optimal 3-bet/4-bet/5-bet-strategies in NLHE 6-max – Part 1, and we have given more specific guidelines for how to implement the theory in practice.

We constructed a set of optimal 3/4/5-bet strategy pairs with the raiser out of position for a set of opening ranges between 15% and 40% in increments of 5%. We organized the strategies in a document for easy access during play. We also defined a HUD layout with the necessary stats for estimating an openraiser’s range. This enables us to quickly find optimal 3-betting strategies in position against an arbitrary openraising range. We can also use the table of optimal strategy pairs to estimate our own ranges (4-betting for value or as a bluff) for defending against a 3-bet when we’re the openraiser.

We also defined a set of standard opening ranges that we can use as “core ranges” for our preflop game. The purpose of these ranges is to give ourselves solid defaults, and to make future modeling and analysis simpler. For example, we’ll use the standard opening ranges when working on the theory for 3/4/5-betting with the raiser in position in Part 3. Then the raiser will defend against 3-bets using a combination of 4-betting and flatting, and we’ll find the 3-betting and flatting ranges from our standard opening ranges.

In Part 3 we’ll discuss 3/4/5-betting heads-up with the raiser out of position, for example when button openraises, and small blind 3-bets. The theory is based on the same mathematical principles used in Part and and Part 2, but the ranges will change a bit. The raiser can now defend against 3-bets by flatting in position, and not only defend by 4-betting or folding. Having the option to flat 3-bets in position makes the overall defense strategy more flexible, and we’ll use less mathematics and more good poker sense.

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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