Disclaimer: This strategy article is very lengthy and in-depth. If you don’t have the time (or patience) to read through this information, this probably isn’t for you. Also, you’ll need to thoroughly comprehend most of the general poker concepts prevalent within the small-to-mid stakes level, to completely understand these ideas. Being more specific, if you relatively fall somewhere between the online stakes of $1/$2 to $10/$20, you’ll ultimately be the niche that’s perfect for this article. I’m not saying that this article won’t benefit everyone, but just be aware that most of the concepts presented should be used predominately within that arena. You’ve been forewarned!
Ranges. Ahh, good ol’ ranges. If you’re one of the few that doesn’t know what a range is, it’s simply a collection of different poker hands that a player can hold at any given time. Orchestrating your thoughts around ranges at the poker table is a very important concept, because during play we’re always trying to get a grasp for the types of hands that an opponent may be holding against us. Being able to accurately estimate your opponent’s ranges, and also dissect and manipulate your own, are arguably two of the most essential differences between those who dominate the micro stakes world, and those who crush at the mid-to-high stakes level. A straight-forward approach to the game will no longer be successful at these levels, and players need to be able to make crafty manuevers in order to assist their adversaries in making mistakes. Hopefully, a deep discussion about the complexity of range manipulation should help entice those errors.
In what could essentially be deemed part two of my series on ranges, (see part one if you haven’t already) we’ll be diving deep on several topics. I’ve already commented briefly on the importance of range balancing, but in this article I’ll be giving even more precise analysis on how to do so. We’ll be discussing the times in which you should be using ranges, range notation, along with polarized and unpolarized ranges. To help make some of the more intricate ideas a bit more intuitive, I’ll be using diagrams that I’ve created through Microsoft Paint (I apologize if they’re terrible) to help illustrate a few of the more general topics. I also shouldn’t forget, that as we analyze ranges and their uses, one of the most important theories to understand is how to exploit them. This topic will be covered in great detail.
So let’s get started!
Understanding When Ranges Should Be Used
It goes without saying, but nearly everyone has at some point been completely baffled at what an opponent at the poker table exposed to them. Whether it was through a stone-cold bluff, or through a very well-timed check-raise, we’ve all be uniquely deceived by our opponent’s play. In poker, this frequently occurs, because we NEED to deceive our opposition in order to be most successful. If we didn’t, they would always know what we have, and easily exploit our tendencies.
In order for us as poker players to make great decisions, we need to pay attention to what our opponents’ tendencies are, what cards they present to us during specific situations, and how frequently they take lines with similar holdings. The last thing a poker player wants to do is guess, or arguably worse, become predictable, and by paying attention and dissecting a range that’s no longer necessary. We’ll be able to acutely modify our actions to help merge our ranges with others, and also easily indentify when our opponents are providing us with useful information to heighten our sense of security. I’ll even go as far as saying, that without understanding a range, you’ll never be able to play deeply analytical poker. It’s that important.
Let’s start by giving an example:
We’re in a local $5/$10 No-Limit Hold’em game and we just sat down. We sat down with the norm, $1,000. We look at the . Everyone has folded to us, and we raised to $40 from the cutoff seat. The button and small blind fold. An opponent, whom we’ve never played against, re-raises from the big blind to $120. He has $2,000 in front. The action is back on us. What do we do?
Well, it’s really not very tough debate. Unfortunately, we don’t know much about our villian’s tendencies, so we’re naturally inclined to fold. Why might you ask? It’s because of what our experience about this particular situation has taught us, and our understanding of ranges. Typically, we know that in order to re-raise us from the big blind, generally you’ll need a stronger hand than usual to be willing to play a big pot out of position. We also should note, that the big blind has no information on us either. If he didn’t have a strong hand, and played back into an unknown opponent, he could be making a very costly mistake if our range is indeed quite strong. In all likelihood, his range generally consists of
QQ-AA, and AK, both suited and unsuited
with the possibility of a few lower pairs and the addition of AQs. (On a sidenote, I’ll be using range notations frequently throughout this article. In example, A2s+ would mean all suited aces with a deuce through king kicker, while T4s+ would mean all tens with a four through nine kicker. 33-AA would mean all pairs between threes and aces.) The big blind could be making this move with a variety of other holdings, but since we don’t have those reads, we typically resort to the most generic range possible.
The bold information above is all the security we need to make a good fold. Even if our adversary decides that he only calls our $40 raise half the time for deception with something as strong as AA, making pocket aces less likely in his three-betting range, (also coined a weighted range) the rest of his range still dominates us. At best, we’re 50-50 against an ace-king.
When situations such as these arise, all we can do as players is make the best decision possible. Although our opponent could be holding something we dominate, such as the , adding those hands into the range of our opponent without certainty would greatly complicate our calculations. As illustrated above, although our villian may occassionally mix up his play against us with a semi-bluff of that nature, it’s highly unlikely that they’ll frequently include those types of hands into their range. The best we can do, is to know that our opponent is capable of such a move, and keep this in mind for future play. We can’t afford to add this information to our calculations, because not only does it greatly complicate our solutions, but it doesn’t really improve the end result by much.
Uses For Range Notation and Visualizing Range Structure
We already understand that we can characterize a range by designating a group of hands, just like:
22-JJ, A2o-A10o, or TT+
but while this range notation is certainly useful in making resourceful calculations away from the table, most are immediately curious as to how this can be used during play. Well, I’ll be the first to admit, it’s not very helpful at all. Instead, by illustrating through the use of a diagram, we will be able to peek into the unique visualization of the more general principles and theoretical concepts of range manipulation. And yes, they can be used while in action. If we ever want to be brave and dive into some of the more sophisticated mathematical formulas, we’ll need to convert back to the textual description of a range to do so.
When using charts to diagnose range structure, often times it’s not necessary to be very precise. Since we’re usually commenting on some of the more common principles of a range, the extra precision of plotting actual points and creating a visual masterpiece won’t help us much. Although I do enjoy math, I’m no longer intrigued by creating perfect, mathematical artwork. And to be honest, I’m not very artistic anyway.
Let’s go over another hand to see how a range structure can be illustrated.
We’re on the button in a $5/$10 six-max game, and elect to raise to $30. The small blind folds, and the big blind calls. The pot is now $65.
The flop is:
The big blind checks. We bet $40. The big blind calls. The pot is now $145.
Now, we can begin to understand our opponent’s range by understanding his actions thus far. There is a variety of different hands that our villian is likely to have. Since he simply called our raise, it’s unlikely that he has something as strong as a set. Although it’s possible, we’re pretty confident that he would’ve three-bet JJ-QQ, and something as small as a pair of ducks may have been in his folding range. However, hands such as a strong jack, a straight-draw, a flush-draw, a pocket-pair, a weak jack, and a complete airball are all very viable options. These hands all fall in the weak to medium-strength category, so we’ll plot them as such. If he has a hand that completely missed, he could be floating us, however that’s typically unlikely since he’ll be out of position for the remainder of the hand. Therefore his range typically looks something like:
As you can see, the structure of our opponent’s range is heavily weighted towards weak and medium strength hands. Since our opponent did decide to call our bet, we eliminated some of the weaker hands (air, a deuce, etc.), and concentrated the bulk of his hands in the “average” area. If we were to plot our hand strength on this graph, it would fall just to the right of the area under the curve. Although top-pair weak-kicker certainly isn’t a hand we want to get carried away with, we should realize that against our opponent’s average range, we’re actually doing quite well.
Our opponent bets $120. What do we do?
Oh no! What a terrible turn for us. This card happens to hit our opponent’s range quite well, because now our villain could hold yet another flush draw, a made straight, or two pair. Although our pair of queens still may be best, it changes our decision dramatically after he led into us with close to a pot-sized bet. It also changes his range structure significantly:
And now, since we’re facing bad pot odds, a big bet, and an area under the curve that’s more weighted towards the range we can’t beat, we fold. Hopefully, that makes sense, and helps you comprehend how range structure can change instantly. These types of representations assist in making the correct decisions at the table, if you can visualize them quickly and easily.
For now, let’s move on to more important stuff.
Polarized v. Unpolarized Ranges
In the general sense, the term polarized simply refers to the separation of something into a distinct group, usually involving two groups that are uniquely related. In terms of poker, polarization is defined by categorizing your hand into one of two unique categories — strong and weak. When a range is polarized, since our hand only falls between two distinct genres, it generates a massive gap in the structure of our range. This may be better understood through the use of another chart:
As we can see, there’s a huge gap in between our weak hands and our strong hands. As most players do, when we’re faced with a decision where we need to bet, usually we either have a very strong hand, or a weak hand where the only way we can pick up the pot is to bluff. On the other hand, in situations where our opponent represents strength, and we have a hand of average value, we typically resort to calling (since raising would only allow us to be called by a better hand.) So if we always bet or raise when we have air, a weak hand or the nuts, and call with cards of moderate strength, this creates the trademark polarized range.
When our range is polarized, it makes it very easy for our villians to make decisions against us. Consider this — If our opponent has a hand that falls squarely in the middle of our diagram, he only needs to weigh the proportion of hands in the “strong” category to those in the “weak” category. Ideally, it doesn’t matter what his actual hand is. If we happen to have more hand combinations that fit under the weak area of the curve, rather than the strong area under the curve, his decision becomes trivial; he calls us more often than not.
Polarized ranges are categorized by containing many more bluffs than strong hands. Since there’s only so many ways to have the best hand, this makes complete sense. However, if we want to make our opponent’s decision much tougher, we’ll need to de-polarize our range so that we can be holding a larger variety of hand combinations of varying strengths. Although we normally take aggressive actions with bluffs and strong hands, we’ll need to occasionally mix things up for balance and deception.
Let’s look at ways in which we can de-polarize our range.
$5/$10 NLHE 6-max. Effective stacks: $1,000.
We’re in the big blind. The first four players fold. The small blind elects to raise to $35. We call. The pot is now $70.
Villian bets $50. What do we do?
Although calling certainly isn’t a terrible play, if we’re looking to vary our play and influence the structure of our range, raising is a much better option. Although we currently only have a flush draw, in the instances when we actually had a set or a complete bluff, we would likely consider the same action because we would prefer to get value from all of our opponent’s pairs, draws, and strong aces. If we’re bluffing, we don’t mind ending the hand immediately. The ace is a great scare card, and may allow our villian to fold his weaker holdings.
By entering the semi-bluff into our raising range, we’ve managed to greatly influence the hands of medium-strength (draws) on our graph. This significantly de-polarizes our range, and makes the decisions of whether to call or raise very difficult for the small blind. Let’s also mention, that since our villian will have to act first on the following streets if he does elect to continue, playing a massive pot out of position shouldn’t be on his wish list. This makes it very tempting for us to frequently bluff the small blind, regardless of our actual holding, because of their propensity to fold without a hand of justified value.
If you consider another flop, , with the same action by the small blind and the same action by us, we could represent two entirely different ranges. In this instance, there a no draws present, so the only hands we would be raising with would be sets and completely air, which would make our range polarized. It would be very uncharacteristic for us to raise with a calling hand such as the , since we’re not going to be called by nearly any hand that’s worse than ours. Although that would be deceptive, it would be very risky in terms of expected value to make such a play frequently. This situation is important to understand, because different board textures greatly influence the composition of a range.
Exploiting A Polarized Range
We understand what a polarized range is. Polarized ranges involve weak hands, medium strength hands, and strong hands. These three groups then split into two separate entities — a weak/strong betting/raising range, and a medium-strength calling range. So how do we exploit someone who has a polarized range? Depending on what we find with the composition of an opponent’s polarized range, we’ll need to either call more frequently, fold more often, or raise. (We’ll make this decision after we evaluate our hand strength vs. our opponent’s hand, and whether or not we believe our opponent can stand up to pressure with his estimated holding.)
The ratio of weak hands to strong hands will be the focus of how to exploit a polarized range. Although this article is mostly based on mid-to-high stakes games, I’ll use a dichotomy between the micro-stakes world, and the small-to-mid stakes level to help illustrate this point.
In micro-stakes games, it’s a regular occurance to find players who only 3-bet with a small percentage of hands. Typically in the range of 3 percent, this collection of hands includes only QQ, KK, AA, and AK, both suited and unsuited. Because of the nature of micro-stakes games, players can get away with such a small three-betting percentage because there are enough players willing to pay them off with lesser hands. However, players who are observant will quickly realize that the easiest way to exploit these players is to fold. Since their ranges are strictly polarized with strong hands, unless you’re holding a four-bet value hand such as KK or AA, the best course of action is to avoid danger.
On the other end of the spectrum, players in the small-to-mid stakes realm begin to add a variety of different semi-bluffs (suited connectors, suited aces, etc.) and wider value hands (such as 99-JJ) into their three-betting range. This is often because better players are able to quickly recognize important tendencies, such as a big blind folding percentage, or how often you attempt to steal from late position. They adjust accordingly, and energy is intentionally focused on balancing their play, because it’s the only way to maintain a signficant edge and exploit your opponents’ weaknesses.
If you happen to be in a situation where you’re facing an opponent who makes a bet on the river, and you believe their range is polarized, you’ll need to estimate the amount of hands in both the weak and strong categories to make an intelligent decision. Let’s analyze another hand, then take a look visually.
$2/$5. Effective stacks: $500.
We raise to $30 on the button. Villain calls in the small blind. The big blind folds. The pot is $65.
Although we didn’t flop a monster, we certainly did flop a playable hand. We now have a gutshot straight draw with an overcard to boot. Either an ace or a four makes a hand, although we would hate for it to be a club. We’re betting.
We bet $50. Villain calls. The pot builds to $165.
Not the best card, but not the worst either. Now we have a little more showdown value. Check, check.
Check. Our opponent now bets $110. What do we do?
Let’s analyze this situation closely, and dissect our opponents range. It’s unlikely he holds a set, because the flop brings immediate danger to that hand, which he would respond to. There are both straight and flush draws available, and seeing as though we raised from the button, our range is littered with those possibilities. If our opponent had a set, he would be more inclined to raise, in order to charge us for our draw. Can our villain have a queen? Sure, but they would probably have to hold something like the with a flush draw. Possible, but also unlikely. Maybe two pair? Eh, there aren’t many viable options here, maybe 7-5s or 2-3s, but even then, since we raised on the button and could hold higher cards to a potential straight, these hands don’t have much value post-flop and could be dominated in the right circumstance. Something like 4-6s is reasonable, and may have turned some unlikely straight, but that’s also improbable.
However, we’re rather certain our opponent’s range is polarized. So let’s see if we can make a better decision from a diagram.
Using our estimates from above, the bulk of our opponents range comes in the form of weak to average hands, with the former filling most of that category. Looking closely, there are a ton of hands that are weaker than ours — a busted flush draw, a straight draw, a pair+draw, or nothing. We also know, that if our opponent had a hand that beat us, such as a pair of 6s, 8s, 9s, tens or jacks, not only should he have played these hands differently, but he also could’ve easily checked back on the river with showdown value. The surface area of the strong hands in our opponent’s range is dramatically smaller in comparison to the weak hands, and since there is such contrast, we’re forced to call.
So what can our opponent do to ensure there isn’t such disparity? Well, for starters, he can completely change his line, so that his range doesn’t become so unbalanced at conclusion. Secondly, our opponent could also add the hands that we mentioned before (such as 66-JJ, excluding 77) to his value betting range. Although these options are feasible, they both present their own individual issues. If our range is strong, adding additional hands to the value betting range that are beaten by us anyway would only bleed money. Changing your line is tough also, because it’s hard to plan against our moves on future streets. So what can the villain do to balance his range?
If he limits the amount of times he fires with weak hands, his areas under the curve for both his strong and weak hands can be congruent — meaning his weak range will be identical to his strong range, making our decision much more daunting!
But what if we don’t have much of a hand at all? They’ll often be times in which you’ll notice that your adversary has a polarized range that is unbalanced, but you’ve gotten to the river, and your cards don’t allow you to do much about it! In this specific circumstance, very tough games often require a bluff-raise.
(Note: Before getting into bluff-raising, as I mentioned at the top of this article, these types of moves should be used in games of a higher magnitude, where players are capable of intelligent thought processes and rational decision-making. There’s no need to go around bluff-raising calling stations. Hopefully that goes without saying, but in the case that you weren’t aware, you’ll truly only be bluffing yourself.)
A well-timed bluff-raise can work to perfection, especially if you’re the type of player who frequently raises with the goods. As your opponents begin to understand that you’re river aggression signals strength, adding in a disguised bluff can increase your bottom line. However, since we’re on the topic of polarized ranges, you’ll want to know that by bluff-raising, you’ll also be creating a polarized range for yourself. Since you’ll probably call a river bet with some of your more marginal hands, your raise will signal alarm bells for your opponents. You will either have the nuts, or you won’t. You’ll leave yourself open to exploitation if you don’t get the frequency correct. Optimal bluffing frequencies could be another topic in and of itself, and we’ll leave that for another date and time.
How to Force A Polarized Range
Up to this point, we’ve gone into detail about ranges, visualizing them, polarized vs. unpolarized versions, and how to exploit them. However, it order to use all of our knowledge, we need to ensure our opponent polarizes their hand. Some keen readers may have taken the liberty of realizing that by betting ourselves, we’ll in turn force our opponent to either call, or raise, which generates the two groups we need to make an informed decision. While this is true, this can often present a problem. Our opponent can just fold, which allows him to maintain balance. But even if he decides to just call, his range can still remain unpolarized. Although calling generally makes a range weaker, great players will also make it a habit to call with strong hands, to inhibit polarization.
So what can we do to allow our opponent to polarize his range? We’ll need to induce a bet. If we can inspire our opponent to put more money into the pot, his bets should frequently be polarized. Although this can be tough to do, against aggressive opponents you can check-call their bets to keep your range hidden, while theirs will be polarized. Hand-reading will be an important skill, but hopefully, you’ll incorporate range structure into your analysis.
Ranges are a very complex subject. Although I didn’t touch too much on the topic of merging different ranges, Part I of my series on ranges certainly covers everything you’ll need to know.
Once again, good luck at the tables.
Hopefully I’ll see you soon!