All IMHO.

Hey guys. I wrote a similar article about a month ago, but did more research and wanted to release a new version. This is just a pretty standard 3bet article for beginning and intermediate players (and myself, as I write). I think there are at least a few somewhat newer players that will appreciate this post, so I hope you enjoy.

Also, if I screwed up any math or something...sorry. Any math is mostly irrelevant to the article, so I didn't double-check it. This is just supposed to give an idea of the "why" behind 3betting scenarios.

History
cliffnotes for lazy people:
- Everyone 3bets a merged value range.
- Everyone realizes that 4bets are really big in No Limit, and folding JJ preflop sucks.
- Everyone stops 3betting, unless they have KK+, AK.
- Everyone stops calling 3bets, because no one 3bets anything but KK+, AK.
- Smart people started 3betting ATC because nits are hilarious.
- Nits got less nitty and started 4betting.
- Even smarter people invented polarization.

A long time ago, when online games were passive and nits made millions, people were 3betting a merged (depolarized) range preflop. The poker community moved from Limit Hold’em to No Limit Hold’em, and carried with it the belief that the best players aggressively raised their strong hands preflop for value. It didn’t take long for people to realize that 3betting AJ and being forced to fold to a 4bet sucked. So they stopped 3betting unless they had KK+ or AK.

Games became incredibly tight in 3bet scenarios as a result. Folding anything but KK+ or AK to a 3bet was not a rare tendency. As a result, a few 2+2ers realized that mashing the 3bet button would make them…a lot of money. So, they relentlessly pounded the button until the poker community caught on and began to adjust by 4betting light. At this time, there wasn’t much to 3bet theory, except that it was theorized to be good. In a recent interview on Deuce Plays with Bart Hansen, Beluga Whale said that during this time he 3bet almost his entire preflop range, and he certainly wasn’t alone.

It’s important to understand why 3betting ATC was good when it was…and that is because there were two types of players: people who folded to the 3bet OOP, and people who called and check-folded the flop. This is before people realized how lightly they could profitably stack off. It seems obvious to readjust your stackoff range now, but the idea that “this hand isn’t quite good enough to shove” instead of “this hand has X% equity against villain’s 3bet range” was still incredibly prevalent.

Take the following FR Cash game example:
Hero is on the BTN with 8h9h
Villain is in the HiJack with a PFR in unopened pots in the HJ of about 15%. He is folding everything but QQ+, AK. This is about 2.6% of hands. So he’s folding about 83% of the time.

UTG-MP2 folds
Villain raises to 4bb
Hero raises to 12bb
Villain folds

Our hero can raise ATC until villain adjusts and do so profitably. If our villain is only 4betting QQ+ and AK, and will never flat our 3bet, our hero doesn’t ever need to wake up with a hand. He will win 4bb about 83% of the time and his opponent will make 12bb about 17% of the time.
0.83(4) – 0.17(12) = 1.28
Hero will make an average of 1.28bb every time he 3bets the opponent, regardless of his holding. Consider that this situation occurs frequently, and you’ve just reached superuser status. Mind you, the math is very simplified. This is assuming villain never flats and hero never has a hand that can stack off.

Eventually, the games became less tight-passive and people began to 4bet a wider range against players with a wide 3bet%. This was huge for online poker. Before this point, a hand like QTs or 89s didn’t have as much equity as the action of 3betting had in fold equity, thus making the correct play a 3bet. However, once villains adjusted, the fold equity just wasn’t there. These hands now have more equity in their relative strength, couple with positional advantage, than is generated by the fold equity created by the action of 3betting.

This is where the idea of Polarization comes in...


Polarized 3betting and Merged 3betting
cliffnotes for lazy people:
- Against someone who will not flat, but only 4bet or fold, polarize your range.
- Against someone who will flat a wide range, merge your range.


If someone realizes that you are 3betting often, they will adjust. In his article, "Facing a 3bet", knn05 echoed the common knowledge of players moving through the microstakes by saying "generally speaking, calling 3bets in the micros just isn't profitable". This is because as we rise through the stakes, we play against players who know less about the game than we do. Most of the players you play are stuck 3betting a slim but merged value range. Thus, calling 3bets out of position generally means you are playing a hand with a weaker range than your opponent out of position when playing against poor players, and the skill edge you have is not enough to counteract these disadvantages (unless you are deep enough). A strong, aggressive player has been taught the "rule" about not calling 3bets out of position, and so they are compelled to adjust by 4betting light.

This presents us with a couple of things to think about:
1. Even if it's +EV to 3bet someone with ATC, should we?
2. If our opponent adjusts by 4betting a wide value range, how should we readjust?

1. Even if it's +EV to 3bet someone with ATC, should we?
Probably not. You want to take advantage of someone in such a way that he doesn't realize you are exploiting him. If you 3bet him every time he raises, he'll adjust pretty quickly and no longer make the same exploitable mistake. If you get out of line just enough, he'll never realize you're exploiting him.

Also, by 3betting too often you make yourself vulnerable to resteals, whether the 4bet comes from the initial raiser or a third party.

2. We adjust to a wide 4bet by polarizing our 3betting range. If we are 3betting a hand that did not have enough equity to flat call and does not have enough equity to call a shove, then we are taking a hand that was previously a fold (zero EV) and 3betting it (adding EV). With those hands, we are 3betting a very strong stackoff range that will call the 4bet from our opponent (dominating their range). With our air, we can happily fold knowing our opponent made a mistake.

But, you may ask, how is your opponent making a mistake by 4betting AQ when you have Q3s?

Because our range either has AQ dominated, or is complete air. Thus, we are playing perfectly and our opponent is actually making what could be a -EV shove (dependent on how wide he is raising and how wide we are calling). Let's take an extreme example and say we are 3betting only AA, KK, AK, J2s-J6s, Q2s-Q6s, K2s-K6s, that means our range is:
- 4.5% air
- 2.1% nuts

Our range doesn't have to be this tight in most situations, but perhaps consider this range when UTG+1 against an UTG raiser that has a preflop range of 77+, AJ+. 2/3 of the time has us crushed, and makes a mistake by folding. What makes this idea interesting is that almost no one is going to cold 4bet you without the nuts...our range looks incredibly strong because very few players are balanced in this spot. Assuming our opponent doesn't flat the 3bet out of position, we are never making a mistake in the hand and our opponents are. According to Sklansky, that's money in the bank.

If you take a step back and look at the total EV of the situation, you'll realize that while your average profit per 3bet is going to drop (because you'll fold to 4bets 2/3 of the time when villain wakes up with the nuts), you're doing it three times as often. You turn what was 0EV into +EV at the same time you balance your ranges. This is key, and is the reason you don't 3bet a hand that you could otherwise flat with. If a hand already has positive EV in a flat and cannot stack off preflop, and your opponent is going to 4bet or fold, then you give up the EV you already had by flatting and replace it with the EV of the 3bet. As such, you can keep the EV of the flat, but gain the EV of the 3bet by adding hands to your preflop range that were not previously there.

So this is a general idea of what you should choose to 3bet when polarizing your range, and hopefully you understand why you should do it. Note that polarizing your 3bet range against a player who is going to flat your 3bet is suicide, as you can't play postflop poker with complete trash. This theory really hinges on your opponent either 4betting or folding.

Choosing what hands you want to 3bet as your bluff range is difficult, and I'm not going to pretend that I know the answer with any surety. The reason I chose the hands that I did is because:
- They have blockers to the hands most likely to flat our 3bet. TT-QQ seem to be the only hands that many people flat 3bets with oop with 100bb effective, and that's the worst result for us.
- They are suited, just in case.
- They are easy to count. If you memorize the percentages of different stackoff ranges and want to manipulate your bluff ranges to better counteract your exact opponents, the math is pretty simple on the fly. Each suited hand is about one-third of a percent, so you can create a range of hands that are easy to memorize and manipulate, making it so you don't have to think too hard about your frequencies once your range is created.
- They have hilariously low equity against pretty much any stackoff range, making it damn hard to be priced in to call a shove.

But, there is much to be said about being more precise in choosing the bottom of your range. For example, in the UTG+1 v UTG scenario, perhaps A2s-ATs would be a much better range to 3bet. Since our opponent's range is 77+, AJ+ and a rather large portion of the hands he shoves with contain an Ace, having one of the aces in the deck is...probably a very good thing combinatorically. This also offers us equity when he flats with a TT type hand. Since there is no way we can profitably play A2-ATs in that situation 100bbs deep, there's no reason we can't choose it to 3bet instead.

In practice, though, it's very difficult to construct a bluffing range from scratch, simply because it involves figuring out the exact range with which you can call, the percentage you wish to bluff, and then constructing that percent out of the hands immediately below the ones you can flat for postflop equity. So if you're pressured by the time bank across your twenty tables, it might be prudent to construct a few ranges for similar scenarios and tweak them as you go, adding or subtracting hands as necessary.

So, to summarize, polarization is when you have air or the nuts. Polarizing your 3bet range is done to combat someone who will not call your 3bet, but only 4bet or fold. And remember that your opponents are going to be much more likely to flat a 3bet when in position than out of position, which will again be mentioned later in this post. It's pretty important to realize this, regardless of whether you play full ring, six max or heads up, because polarizing by default when out of position is probably just going to turn into spew.


Facing a 3bet
cliffnotes for lazy people:
- Against someone who is 3betting a polarized range, flat.
- Against someone who is 3betting a merged range, 4bet.

Many good players don't know why they are polarizing their 3bet range, and as such don't know how to counter it nor how to know when they should be merging their 3bet range instead. It's excruciatingly simple...if a polarized 3bet range relies on the initial raiser to never call, you should call when facing a polarized 3betting range rather than 4bet.

In episode 109 of Deuce Plays, Beluga Whale presented this idea. Although it seems simple, it's rather astonishing when you've spent several hundred thousand hands folding AJ out of position facing a 3bet. However, if you're certain your opponent has a properly polarized 3betting range, flatting with hands like KQ or AJ will leave you dominating 2/3 or more of your opponent's range. The question is how to balance...

Although flatting 3bets out of position isn't a new idea, it's somewhat new when it comes to reg versus reg situations. What was a difficult spot to navigate becomes very clear when you recognize your opponent's entire range (and how much more difficult the spot is for him than yourself). It's as simple as wanting to play postflop poker with KQ against your opponent's Q2.

Beluga Whale also discussed some common postflop situations. For example, your opponent will expect you to ship preflop with most strong hands that contain a Ace or a King, so flopping top pair will often mean generating a huge pot while your opponent is drawing dead. Once your opponent sees you flatting AJ and KQ type hands, he may begin to shut down on all two-broadway boards...in which case you can start flatting suited connectors out of position and, as Beluga Whale said...win every pot.

So, this leaves us with the question as to whether, facing a polarized range, you should ever 4bet. Should we be flatting a merged value range and remain balanced by never 4betting? Or should we 4bet a polarized range right back, and flat a merged middle-value range? My guess is on the latter of the two, but this is certainly just a guess. This would allow us to profitably continue with more hands than never 4betting would, as we would profitably 4bet hands as a bluff that we would otherwise fold. If you fracture your rnage into 4betting polarized and flatting merged, hands like suited connectors and small-mid pocket pairs become pretty crucial in the process. If you have the right dynamic, you can flat both of these facing a 3bet with correct stack sizes and perhaps 4bet suited Ax hands as the bluffing portion of your 4bet range. If you can't flat the 3bet profitably with your PPs and SCs, you will probably be in a situation in which you are 4betting all in instead of 4betting 2.5-3x your opponent's raise...in this case, you might want to 4bet shove the top of your range and balance with suited connectors and small pocket pairs (each of which has about 35% equity against most player's stackoff ranges).

The answer to whether or not to 4bet at all against a polarized range is most likely highly dependent on effective stack size and the ratio of nuts to air in your opponent's 3betting range. To be honest, I think someone who has been able to do more research on this subject should take over the mechanics of 4betting a polarized range at 100bbs...or if we should do this at all.


In Position and Out of Position
cliffnotes for lazy people:
- Generally, people flat often in position, so merge your range as a default.
- Generally, people 4bet or fold out of position, so polarize your range as a default.
- Most decent players understand the two previous statements. Expect them to play accordingly as a default.


The difference between 3bet dynamics caused by the relative position of the initial raiser and 3better is caused by people's willingness to call 3bets in position as opposed to the disgust caused by flatting out of position. Strangely, this causes something of a backwards dynamic, as proven above. The larger the pot, the less position matters. Though the 3better takes control of the hand and has position, this matters less the larger the pot is bloated by preflop aggression. But this isn't to say it's incorrect to 3bet in position...I say this only to illustrate the beautiful contradictions of the game.

Most strong players know this, and those who know how to both polarize and merge a 3betting range often choose to polarize in position and merge when out of position, as they expect to face flats when out of position and 4bets when in position. The way to combat this is to do the exact opposite...until they adjust, which is when you'll have to readjust...

This is something that Beluga Whale didn't get into...should we be flatting as much as we do in position when 100bbs deep? The pot is already bloated to about 20bb when we flat the 3bet, which greatly depreciates the affect of our positional advantage. And we're most likely seeing the flop with a weaker range than our opponent, as we 4bet the top of our range and flat the middle while our opponent enters the flop with both the top and middle of his range. Against players who are 3betting hands like 99 or KJ when out of position, we should be more inclined to 4bet a polarized range than we should be to flat.


Full Ring, 6max and Heads Up
cliffnotes for lazy people:
- Full ring and 6max are basically the same.
- Realize that you aren't in position when you 3bet Heads Up...

If you're structuring your ranges correctly, in that they are fluid and structured individually based on your opponent and your image (as opposed to being read off of a chart), then there isn't much a theoretical difference in the logic behind structuring your 3bet range between 6max and Full Ring. Obviously, ranges will be tighter in Full Ring than they will be in 6max...but that's basically all there is IMHO.

Heads up, everything changes. You'll never face a 3bet out of position, and you'll never be able to 3bet in position (other than by limp-raising). This means that you can, in most cases, just dump the idea of 3betting a polarized range. Most opponents are going to be flatting far too wide for a polarized range to remain profitable. However, playing Heads Up Cash is a fantastic way to practice on your BB v Steal game at the Full Ring and 6max tables (and, of course, vice-versa).


How effective stack sizes change the 3bet 4bet dynamic

Effective stack sizes have a drastic effect on what and how often you should be 3betting. For example, take a hand from our 3betting range at 100bb: K2s. In a HU SnG with effective stack sizes of 10bb, we can minraise-fold this hand on the button as a part of a polarized BTN strategy, and possibly 3bet-shove it for value facing a raise. Or, at 10bbs, we could profitably just shove all in with it. With 100BBs, we are 3betting with it as the bottom end of a polarized range. At 250+ BBs, we might be overcalling with it with the intention of over-flushing a suited connector. It's just interesting to note the dance our ranges play with the SPR.

There's just far too much to cover here...but a few things to note are the effects stack sizes have on suited connectors and small-mid pocket pairs, and how our 4bet ranges will change.

Let's begin with extraordinarily shallow stacks in a heads up scenario. Mers has a great video about the Full Tilt Heads Up Super Turbos in which he polarizes his opening minraises with a wide limping range. This works so well because, out of position, most 3bets are going to be 3bet shoves when incredibly shallow (they are certainly very committing regardless). Because his opening range is polarized, when Mers is faced with the 3bet he never has a difficult decision and gets it in with a very strong range relative to his opponent. What we can take from this is that the last possible raise can't be polarized, for obvious reasons. When Mers minraises his BTN, his opponent is already facing an SPR similar to that of a 3bet or 4bet in a 100bb game. So, Mers' initial raise can, in a sense, be construed as the only polarization which can take place. By limping in this situation, we are making a very similar play to that of flatting a raise in position. This is mostly just an interesting tangent to ponder...

An extension of that thought is how you perceive someone's initial raise in a 100bb game. Everything begins with a merged value range, and that range is then dissected into air, middling equity and monsters once our opponent presents a tighter range with a raise. Again, not much to be gained except an interesting perspective.

As for 3betting in such a short game, it's a mistake against a polarized range such as the one mentioned above, just like 4betting with a wide range is incorrect facing a 3bet from a polarized range at 100bbs. This holds true, at least, until stacks get so shallow that there is so much dead money caused by forced bets that it's impossible for our opponent to polarize a range correctly. Basically, at 10bb, just pretend that your opponent's opening raise is a 3bet and act accordingly in terms of structuring your range (widening your range to correctly match your opponent's, obviously).

Insane_Steve wrote a great article about 3bet shoving with about 25bbs, in which he breaks down the equity of small PPs, low SCs, mid SCs, weak Ax, and complete air against different types of opponents. To summarize:

- Against an opponent you suspect is not calling your 3bet very often, your edge in 3bet shoving comes from fold equity. On the off-chance you are called, it is best to have a pair or a middling suited connecting hand than a bad Ace.
- Against an opponent you suspect will call your 3bet shove somewhat wide but not a lot, your edge is still in fold equity, but suited conntectors drop a bit in value and marginal Aces increase in value.
- Against an opponent you suspect will call with a lot of his raising range, your EV in shoving comes from the fact that a middle Ax hand or a low pocket pair is a favorite against whatever trash he's calling with. Suited connectors should not be shoved against these opponents.
- 3bet shoving any pocket pair over a 3x raise with 25bb effective is almost never a mistake.

I think we have 100bb play pretty much covered, but it might be worth saying that hands that we were 3betting for value at 10bbs effective are now being 3bet as a bluff. Small PPs move from a 3bet for value at 25bbs to a flat for set-mining. We are no longer reshipping suited connectors as a 3bet, but instead flatting them with our small-mid pocket pairs. But once 3bet by a wide, merged range at 100bbs, we can consider reshipping suited connectors as a 4bet bluff for the same reason we 3bet them at 20bbs. If you really take the time to learn play at different stack sizes, you see the connection between SPR and the structuring of your ranges in such a way that makes all that preflop drama much simpler.

When stacks get deep, we are usually forced to depolarize our range as people are going to flat 3bets on a regular basis. But, we can set up a healthier SPR with our suited connectors and other hands that benefit from initiative and fold equity. In episode ten of Duece Plays, Beluga Whale discussed how the equity of the second nuts (and all non-nut value hands) works like a bell curve against stack depth. To illustrate the concept, ask yourself if you would ship bottom set at 100bbs. How about 200bbs? Tree-Fiddy? 500? At a certain point, the second nuts carries negative implied odds. This should affect the way we structure our preflop range. As the stacks get deeper, you should be focusing on setting up the SPR for its effect on decisions in later streets. 3betting becomes less about the benefit of fold equity and more about balancing ranges and remaining unreadable.

That's all I've got for now...look forward to many "tl;dr" replies. Have a great one, and I hope there was at least a nugget of information for the troopers that made it all the way through.

great post. ty

thank you. i've read most of it and will read the rest later, but that was very helpful. made me realize alot of mistakes i'm making

nice article

thanks for contributing

VL;RIA

Very long, read it all. Great post.

thanks for the post. very helpful.

Awesome article, man, thank you.

You're very welcome. I'm glad to hear it's helping people out. =)

thanks so much

Great article. Thanks

this is good stuff. hidden, too.

very well written.

Good read. Thank you.

Great post. Lots of creative thinking regarding adjustments and ranges.

THANK YOU THANK YOU THANK YOU...

I have been a 'semi pro' STT player for about a year now... I am just starting to expand my game because STTs suck (a lot of variance, and relatively simplistic gameplay). This article taught me a lot and directed me to a lot of other really important articles. Thanks again!

actually surprised to find a good and useful poker related thread in 2p2

thank you!! Great post! a MUST read

Thanks much for the replies.

Also, as for whether to polarize+flat or only flat when faced by a polarized 3bet oop, I JUST saw a video by balugawhale where he explained that he believed his opponent's range was polarized and so he was flatting AA.
So my guess is that he would argue flatting 100% of your continuing range is correct.

Glad to see this is helping people out.

PS. lol @ a theory post being posted in the theory forum being hidden. It's sad cause it's true.

Maybe the best strategy post I have read here. Excellent work, thank you very much.

I have been thinking lately about min/small 3betting IP 100bb deep, but have not yet bothered to try it out at the tables. If it is done with a carefully balanced range (lots of merged hands), I suspect this could be an interesting move. Maybe I post about it in the near future.

Great job, very clear and concise points.

Very well written article. I have a few questions about it,

In theory, flatting vs a 3bet OOP with a merged range is correct, but against a similarly skilled opponent, do you believe our equity edge outweighs their positional advantage? I'm still in the camp that 4bets or folds oop, and I have a very obvious/exploitable calling range against regs of AQ/JJ/TT, and thats about it. Would you suggest adding QJs, KQ, AJ, etc to a calling range to balance, or rather just adding premiums to the calling range occasionally? Is there a thread addressing calling 3bets oop that you can recommend?

Also, to clarify, when in position, would you never 3b KQ, QJ, AJ, 88, 99, etc against a player who rarely flats oop? I understand the theory, I suppose I'm struggling because I play 100nl (6max), and have been working on a very LAG game that heavily revolves around 3betting the **** out of the nitty regs and fish alike. Looking at today's session of 400 hands, I had a 14.9% 3b, with a 23% 3b from the blinds. I haven't really been focusing on merging or polarizing my 3b range in position, rather just lumping it into 3b for value or as a bluff. Can I have a very wide 3b% while polarizing my range still? Or do you think 100nl regs are weak enough in general that 3betting a merged range IP is profitable?

I have a few more questions, but I'll let other people comment first.

fantastic post, digest worthy

You need to look at it from a playability standpoint and not exclusively from profit it generates. GTO (game theory optimal) isnt necessarily the most profitable line to take, but in the end its optimal.
If you never flat OOP you are really easy to play against and thus not GTO.

Lets take OPs first example of having 89s and 3beting it (although the cards we hold itself dont mean anything since we can make profit with ATC if the criteria is met). For those that dont remember i will quote that part

If villain never flats, we can use this formula [Ft3b * (OR)] – [4b * (3bR)]
Ft3b=fold to 3bet
OR = original(opening) raise (usually 3-4BB)
4b = 4bet
3bR = 3bet raise, usually 3.5 *OR

Since Ft3b+4b=1 (he never calls), we have 4b= 1-Ft3b, and 3bR= 3.5*OR
We substitute those variables in the formula above, and after some easy math and equating the formula with zero in order to find our breakeven point, and then simplifying we get that our breakeven point is when Ft3b=0.77.
That means if you are folding more then 77% to 3bets (and never flatting) i generate profit by 3beting ATC.

**depending on the 3bet size the number may vary from 0.75-0.8

So long story short, if you never flat and have Ft3b>0.75 you are abusable. If you are abusable you are not GTO (although depending on the players and how much they abuse you, you may still generate profit). They are ways of balancing you opening range and keeping your Ft3b<0.70 but its easier by balancing the 3bet calling range instead.

Never is a strong word. If i knew my opponents has Ft3b>0.75 it is automatically profitable to 3bet him, however that doesnt mean its the best way to play the hand. All of those hands are easy to play postflop especially IP. That means that i can make a decent profit without a need to 3bet and thus force my opponent to adjust. Which means i can abuse him some other time with a ****** hand like J2s and expect to generate profit from that play. But thats basically merging vs polarizing and OP covered that pretty well imo.

You can have it if the opponents dont abuse you. With the same method in which we calculated the breakeven point of 3beting, we can calculate the breakeven point of 4betting. If we assume (the same things as we did for the 3beting) that villain never flats, and that 4betting size is 2.5 the size of 3bet, we get that when villain has Ft4b>0.72 its is profitable to 4bet him with ATC.

Lets put these numbers into perspective. You said that you had a 15% 3b. If the opponent 4bets you (2.5 x times your 3bet raise size) and you fold more then 72% of your range, then you are exploitable. 72% of a 15% 3beting range is about 11% and that means you need to either flat or stack-off with 4% of your entire range. Thats 99+, AKo, AQs+ and i dont think you can do that profitably.

However, if the opponent isnt exploiting you and you are getting away with it and generating profit then, by all means, do it. But always be on the lookout if they start making quality adjustments.

And once again i need to stress that GTO isnt the most profitable way to play the game. Its just the unexploitable way of playing.

Where/how did you learn all these stuff?

Thanks for sharing that! It further explains things I knew, but so much better.
The only thing that i'm having trouble with are the effective stacks in a tourny. Whats the smallest stack size can we 3bet if we are polarizing? Of course villian would have equal or greater the stack.