Hi guys,

I'm wondering if anyone can provide a clear explanation as to why your 3betting range should be polarized when you have a flatting range. I.e. predominantly on the button and the big blind. I have read this maxim in several books, but none of them are able to explain the logic and reasoning behind it, other than something like "you are flat-calling high equity hands that don't want to get 3bet" - but this alone does not explain it.

It's somewhat simpler to understand why your 3betting range is linear when you do not have a flat calling range - for example in the small blind. If you are only 3betting or folding, then of course you can simply 3bet a linear range that provides good board coverage.

On that note - what does everyone think of calling ranges preflop? I had a major shift in my game and win rate the day I dropped the flat calling range from all positions other than the button and big blind and have been an advocate of 3bet or fold ever since. Interested to know what other people think.

Cheers,

T

Modern Theory of Poker explains this concept well:

Every time you bet, you force your opponent to make a decision and since you get to decide what your betting range is, if you build it in a way that the correct decision against you is very different depending on which part of your range you hold, then your opponent will be unable to consistently make good decisions and, as a result, will lose EV.

In general you want to build the pot with value and extract maximum fold equity with bluffs, and pot control/keep ranges wide with medium strength.

If you only raise good hands and flat medium hands then your opponent's decisions become easier and you become easier to exploit. They can simply fold to your raise and bully your castrated flatting range.

But it's not that cut and dry. In some cases, if ranges are wide enough, the 3betting range becomes more linear (or somewhat merged). When ranges are super wide they'll no longer be able to bully your capped flatting range or overfold to your wide value raise. This is often the case in HU poker or even some BTN vs BB 6max charts.

Hi tombos, thanks for the reply.

It's interesting that you mention that book, as it is one of the books I was referring to when I mentioned that it outlines the issue but does not explain it thoroughly. To clarify - I am talking only about preflop and would like to know why, in many books - including Modern Poker Theory by Michael Acevedo, it is claimed that a player's preflop 3betting range should be polarized when then have a flatting range. I.e. the button and the big blind because, at equilibrium (as Acevedo shows in his GTO preflop charts) they are the only positions that have preflop flatting ranges - all other positions are 3bet or fold.

I just want to understand the reasoning behind the fact that a position having a flatting range preflop means that its 3betting range should be polarized, as it's not immediately obvious to me why that should be the case. I understand what you're saying about 3betting in general with polarized ranges, and absolutely that part makes total sense.

If you only raise good hands and flat medium hands then your opponent's decisions become easier and you become easier to exploit. They can simply fold to your raise and bully your castrated flatting range.

Yes, the 'capped range' is of course an issue when flatting in the button and the big blind - I don't see how having a polarized 3betting range addresses it.

Reread that quote by modern theory, slowly and carefully. It's paraphrasing the Fundamental theorem of poker.

Polarized raises are the default; linear raises are the exception. The reasons you'd want to polarize your preflop 3bet are the same reasons you'd want to polarize a river shove. By using hands they really don't want to fold to and hands they really don't want to pay off in the same range, you force them into mistakes.

Your flatting range is stronger with a polarized strategy because you remove some of the weakest hands through bluffs, and check back some of the strong/medium strength hands that a linear strategy would have otherwise raised.

Typo:

Hi tombos, thanks again for the response. What you're saying does make some sense, especially this part:

"Your flatting range is stronger with a polarized strategy because you remove some of the weakest hands through bluffs, and call some of the strong/medium strength hands that a linear strategy would have otherwise raised."

So you're saying that the fact there is a flatting range means that the above is the correct way to play the 3betting range? It does make sense and I am surprised it is not explained in the books as clearly as you explained it here.

Also, is this always the case? For example, if you compare the ranges in Acevedo's book for 6max cash, the button 3bets/calls a whole load of hands that the C/O folds against a Lojack open:

https://prnt.sc/v0t4kd

https://prnt.sc/v0t4xs

What are your thoughts on those ranges and how they reflect what you're saying?

Thanks again for your help, I really appreciate it.

T

The BTN is using a polarized (or slightly merged) 3bet strategy. You can see them raising more with hands lik K9s/A8s and flatting more with hands like KQs/AJs. It's harder to see when ranges are tight.

The CO is using a pure linear raise/fold strategy. This is likely because Acevado disabled the option for the CO to call. In equilibrium the CO would have a very tight flatting range, but the extra EV from this is negligible.

It's not always the case. As I explained in my first response, there comes a point where ranges are wide enough that the defender can "afford" to have a more linear (value-heavy) 3bet range, and a more capped flatting range. For example the BB vs BTN defence in Modern Theory is actually very linear.



But the BB vs BTN defence on Zenith (which uses a much larger 3bet size and a a tighter calling range) is quite a bit more polarized:





So obviously there's more than one good strategy in that spot.


If you take a look at some of the prebuilt ranges in pio, it shows Cepheus' HU 3bet range is quite linear, as you would expect when ranges are wide:



But a modern "solver approved" HU 3bet range is a bit more polarized (or slightly merged?):




----

Now I know that this probably just makes you more confused than anything. The main takeaway is that raises are polarized by default when you have more than one continuing range. That's baked into the game theory. But it's a rule of thumb rather than a law. The closer to the river you get, the more polarized and less merged raises become.

Hi tombos, thanks again for your excellent help and giving this your attention and thought.

I understand totally what you mean about raising being polarized when you have more than one continuing range. Also, I see how ranges become more polarized the closer to the river the hand gets - but doesn't this assume that there has been betting on every round? For example if IP is checked to on the flop, and then bets and gets called on the flop turn and river, he has bet a polarized range on every street (assuming he is playing correctly). I.e. he would be more inclined to check back middle strength hands like second pair on any street (except maybe the flop in some cases). Also, if OOP had raised any street, that too would have been with a polarized range, and if IP merely called in response, then his range then becomes linear/condensed?

I went and got the exact section of the book where Acevedo talks about polarized preflop 3betting ranges. It goes like this:

"If you have a flat calling range (mostly from the button or IP) then your 3-bet range has to be polarized because you are flatting high equity hands that don't want to get 4-bet. Therefore, your 3-betting range will consist of your best hands plus the next tier of hands that are not great calls, have equity or good blockers and can offer good board coverage.

If you don't have a flat calling range (mostly in the HJ, CO and SB) then your 3betting range must be linear. If you are playing a 3-bet or fold only strategy, you want to put only your best hands in the 3-betting range and fold everything else."

So his argument in the first case appears to be that if you have a flatting range in a given position then your 3-betting range has to be polarized, because your flat-calling range contains good hands that don't want to get 4bet. What I don't understand is why this means your 3betting range should therefore contain your best hands plus the next tier of hands that are not good enough to go into the calling range, but have equity/blockers/board coverage. I can see of course that the 3betting range is polarized, and the bluffing part of this range provides balance to the overall range. But why can't you instead simply 3bet your best hands and retain the same capped calling range? Is it because your 3betting range becomes too value-heavy?

The reason it's confusing is because, in the second paragraph, Acevedo goes on to say that if you are playing a 3bet or fold strategy, then you should put only your best hands in the 3betting range and fold everything else - which of course appears to contradict the logic behind the first paragraph. I.e. it states that it is fine to have a value-heavy 3betting range, and also it contradicts what you have been saying in earlier messages about the fundamental theorum of poker etc.

Sorry, I know I must be causing you a lot of headaches and that you will feel we have already been through what I'm asking - but I find these contradictions impossible to resolve in a logical way.

Thanks again,

T

Simlify it down to 1-10, 10 being the nuts and 1 being air.

Let's say the polarized GTO strategy is to fold 1-3, bet 4-5,9-10, and flat 7-8.

The GTO linear strategy is to raise 6-10 and fold the rest.

Either of those options is fine. But what you want to do is raise 7-10, and call 4-6. Your calling range will often be too weak. Your 4-6 won't get to realize much equity, and will likely get bullied off the pot against a good opponent.

It's not about the equity of each individual hand, it's about the range construction as a whole.

6 is a fine call so long as it's protected by other strong hands like 7 and 8. 4 is a fine raise so long as it's balanced by 9 and 10. The value of a hand must be judged within the context of its range.

Okay that does make sense. Thanks a million for your help!

T