Most of the literature out there gives examples for when we want to adopt a polarized strategy. i.e we hold AK or QJ on K92m. I'm finding it hard to find answers about when we will want to check flops or bet thinly to deny equity (in what I'm gathering is a depolarized strategy or the depolarized part of our range).

For example, if we hold 88 on K22, we're most likely going to want to be small to deny our opponent's overcards from realizing their equity. But, we can't really bet turn and river for value after being called. It's in these spots where it makes the most sense for opponent to raise aggressively, since we will have to fold some parts of our range that have SDV. If we are near polarized, our opponent has little incentive to raise aggressively, since we can fold our weakest holdings and continue with our nuttier ones.

Additionally, if we are playing a polarized strategy, when we check, our opponent can seemingly bet any amount, no matter how small, and we will fold (which many uNL players have grasped onto... i.e. bet whenever checked to). Clearly this can't be correct. In fact, if we never b, b, x/c for example, our opponent should always bet with any two cards to guarantee that he wins, regardless of his SDV. And if this becomes villain's strategy, we should always check/raise river instead of betting, since we know villain is going to put something in the pot with his air; a bit paradoxical.

I'm finding that, without understanding what our goal is in these areas, I often find my ranges in these spots to be highly exploitable (i.e. I usually find myself b, x/c, x/f, etc.). I've tried experimenting by betting flop and check/calling turn and river, and though I sometimes catch some spewy bluffs, I lose value overall when villain checks behind. Here are most of the lines where I feel pretty lost:

OOP as PFR
- b, x/c, x/c
- b, b, x/c
- x/c, x, x/c versus x/c, x, b versus x/c, x, x/r
- (Any x/r lines basically)

IP as PFR
- b, x, c
- b/c, x, c
- b/c, x, b
- x, c, b

OOP as PFC
- x/c, x, x/c
- x/r, x/c, x/c
- x/r, x, b
- (Any x/r lines basically)

Hopefully this all makes sense. Thanks for the help.

I'm not sure I agree. If you have a polarized betting range, then your betting frequency is often quite low, as you have lots of mid-strength hands that check-call. Maybe 50% of your checking range continues vs a bet.
It's probably more common that your checking range is weak if you use a small size and bet at a high frequency with a more merged range that includes lots of thin value hands.
e.g. If you decided to bet polarized on K22, then you're checking hands like K9 and QQ, and then you're calling with these hands as bluff-catchers. If you bet most of your range on K22, including hands like K9 and QQ, then your checking range (which is only a small number of combos) is super-weak, and will check-fold more often. It's just that in the first example, you might be checking 60% of your range and then continue with half those combos, but in the latter you might only check 5-10%, but fold almost everything in that 5-10% to a bet.
That is to say, with the depolarized betting range, you have a higher check-folding frequency, but you're not checking much in the first place, if you see what I mean.

Hi Arty, thanks for replying. I meant to get back to you sooner, but I got caught up.

That quote you selected mainly has to do with the problem I am having on the turn and river. For example, if our betting range is polarized OTF, then OTT we typically only have hands that are far ahead or behind--at least as far as I can discern. So in other words, I'm finding that my checks consist almost entirely of 1-and-done holdings, which seems very bad and is incredibly frustrating.

I can't figure out why we would want to have check/calls in these spots (besides traps) and which hands we would use for them. I've tried including some traps and what often ends up happening is I seem to either lose a ton of a value or get outdrawn. And furthermore, only having traps and air in my checking range incentivizes my opponents to always bet, and bet small.

Otherwise, I completely follow with what you're saying about check/folding frequencies. I think my main problem is figuring out how to manage the dichotomy of having both a value range and a bluff-catching range at any point in time. Almost any time I have both (say as the PFR instead of cold caller, BB defender, etc.), I have an extremely miserable time against aggression almost whenever I check.

First I would recommend you simply ignore the idea of polarized or not polarized. They are somewhat useless concepts for understanding betting decisions.

The terms are mostly good as a short hand for describing ranges to an audience that ia familiar with them.

When you are deciding what line will be the most profitable you need to consider all variables avaialble to you. It's not just the strength of your hand and where it falls into your range.

Even a "default" strategy for a hand in a given situation is dependent on the variables in that situation.

Overall things should help you consider whether to bet or check a hand in a given situation:

Effective stack sizes
Pot size
Board texture
Board interaction with your range
Board interaction with villain's range
Previous action
Potential future board cards and their interactions with your range
Potential future board cards and the interactions with villains range
Blockers to your value range
Blockers to villain's value range

Also another thing to keep in mind that though it is rare versus human players that have exploitable leaks it's possible that checking and betting have equivalent EV so that it might be right to bet and check the same hand in the same situation.

I starting thinking in terms of polarization because it helped to explain in my mind why, especially, we have different bet sizes and frequencies on certain boards. But all this makes a lot of sense... in fact just returning to thinking about the most profitable way to play a hand was a bit of a kick in the head.

But, in that sense, I suppose my question becomes: how do we decide the most profitable lines when we have many marginal holdings in a certain situation? How can we bring hands to showdown without our opponent realizing all their equity or bluffing us off our hand super frequently.

I seem to be having a great deal of trouble further quantifying my problem... but the gist of it is that I can’t understand how we’re supposed to protect vulnerable lines (the lines I outlined). Without this protection I find myself calling large bets on the earlier streets only to fold river—which feels like a huge leak. The only answer I can come up with is that we have to trap sometimes, but I can’t figure out how often, how, or where to put these hands in.

This part hasn't really been touched yet. Here's what I think about uncommon lines:

I play a mix of no limit holdem and limit holdem. When an opponent takes an uncommon line in no limit, I tend to assume that it's a trap a high % of the time, especially if the line gets lots of chips in the pot(usually betting or check raising the flop(common lines) is the best way to get chips in the pot of course, but sometimes letting other players build the pot for you when you hold a monster is the best play). When an opponent takes an uncommon line in limit holdem, they don't get the same credit; I tend to showdown often vs such opponents because of the risk:reward ratio and the uncertainty of ranging them.

The uncertainty factor is present in no limit, but since the bets are much larger, the price of the information is much higher; this creates a situation where both of these bad things happen: (a) the uncertainty factor causes us to include hands that *shouldn't* take this uncommon line in the opponents range(such as bad bluffs and or weak value hands); (b) the betsize *accidentally* validates these bad bluffs and or weak value hands. The result is that bad players(the root of the uncertainty factor) taking non standard lines and making big bets/raises becomes a huge liability for us.

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I agree with the others that these are rudimentary models for what poker ranges look like.

betting ranges can be more or less polarized(think K22 flop vs 876 flop; my draws have much more realizable equity in the latter, and thus I consider the latter range to be less polarized). However, as default we should have hands in our betting range that both (a) profit when called(a value <pot) and (b) fold to a raise. These hands provide a third layer of ev in our betting ranges(tripolarized imo lol; 1: strong hands; 2: draws, 3: thin value hands).

postflop checking ranges can differ in composition depending on previous street action. Sorry but I don't have a comprehensive post written up in my head for this topic this morning.

Sure. I can understand that. In a more general sense, again, we just have different betsizes because those betsizes are the most profitable for those hands. I would say it's somewhat uncommon in practice to have multiple betsizes with the same hand on the same board (though in theory it's could be possible to increase the EV of the entire strategy). No one really knows the best line with a large majority of hands. Solvers are as close as we can get at this time. The solvers solutions are certainly much better than the guess work we humans have been doing with toy games etc.


Like Bob said a lot of it comes down to risk vs reward which is difficult to quantify exactly but some of the guidelines pointed out above can give you a framework to help guide your judgement of those while you're playing. Getting more information on your opponents can make those judgment calls all the more effective.

In broad strokes I generally try to decide if my hand benefits more from getting to showdown or ending the hand immediately.

Then I try and estimate how much that is going to cost me given various actions and whether those actions leak information about my current holding.

For a rough example generally pairs benefit from seing showdown. If my pair is marginal I need the weight how much equity certain classes of hands have against me now, what villain will do with certain classes of hands, how much of villain's range is comprised of those classes, and how much it may cost me to reach showdown vs given lines and the board texture.


Sometimes the answer is you can't. Sometimes not being the aggressor is the best option you have because other options are worse. Also remember equity isn't everything. For example sometimes betting with a marginal hand can be better because it prevents villain from bluffing you later in the hand either by folding out potential bluffs or hiding the strength of your hand with the strength of your range.

basically after I bet the flop and check the turn, it's a draw(weaker draws get checked more often), or it's a draw that made a weak pair(very position dependent ie ranges matter), or its a value hand that regressed.

after I bet the flop and turn, but check the river, I check a portion of the middle of my range between (junk = bluff) and (bet fold for value), as well as a much smaller portion between (bet call) and (bet 3 bet) that is intending to check raise.
if i start with a flop bet in position hu vs a blind, and then check the turn, I have a very showdownable range that includes mixed strong value checks that can call big river bets or bet when checked to, as well as a decent mix of draws, generally.

more specifically, if I had bet pot on the flop, my turn check range looks quite different than if I bet 1/2 pot on the flop. Pot sized bets indicate strong value ranges and a relatively high number of draw combos. 1/2 pot bets indicate (a) a pair or better that doesn't need protection(few overcards, so basically Ace or King high flops) complemented by relatively few draws; (b) a dynamic flop that is a serious threat to top pairs and overpairs, which causes a smaller flop bet complemented by relatively few draws.
in the blind: I like to donk bet the more dynamic flops for value and with draws, but I do have a check raise range as well as check call/fold ranges. I check static flops 100% hoping to check raise strong hands and strong draws, and keep the pot small with the rest.