In the game of chess, expert players spend a considerable amount of time studying the final stages of the game, known as the endgame.
By understanding which endgame board positions are favorable, they can make decisions in the earlier stages of the game that slowly lead them toward a winning endgame position.
In poker, our endgame is the river. Our end goal, where possible, is to reach the river with a well-constructed polarized range since we know these are more profitable on average than condensed ranges. Of course, it is not entirely our decision since it will depend on the community cards. Sometimes we will have no choice but to play a condensed range.
By making careful decisions about our range on the earlier streets, however, we can funnel ourselves towards river situations where we have a well-constructed polarized range as frequently as possible.
What Is A Polarized Range?
A polarized range is comprised exclusively of strong value hands and bluffs, and no hand strengths in between.
As a simple visualization, say a player had exactly three hands in their range: AA, 99, and 22. On a board of AK653, a polarized betting range would bet AA (as value) and 22 (as a bluff), but check with 99 since it’s middling and potentially has some showdown value.
The opposite side of the spectrum would be a depolarized, linear, or merged range, which would also include some medium-strength hands while aggressing.
GTO Polarization On Earlier Streets
Clear pairs of polarized and condensed ranges only really exist on the river (and occasionally on very dry turns).
It is still common to use terms such as โpolarizedโ and โcondensedโ to describe earlier street situations, and we will do that in this book. What we are really seeing on flops and turns, though, is an early version of those specific equity distributions as they begin to form. We do not see them in their purest manifestations until the river.
Discussing a polarized range on the flop is like looking at the range through a distorted lens. We see some of the basic characteristics of a polarized range beginning to form, but the outline of the range still lacks definition. There could still be a number of mid-strength hands within this polarized range for example. We will expand on how these ranges form in the next chapter.
These characteristics of the newly-formed ranges are still often enough for us to be able to make solid predictions regarding what a solver strategy would look like, and whether we should start working towards a condensed or polarized river range with the various hands that we hold.
And to be clear, this all applies whether you are in a live environment, online, or via an online casino us.
The Solver’s Bet Sizing When Polarized
In the previous chapter, our analysis of river situations demonstrated that it is impossible to predict bet sizings by looking purely at range-versus-range pot equity. It is the equity distribution that gives us clues regarding which bet sizings will be incentivized. We will use similar logic for flop and turn decisions.
As a general guide, a range that has the nutted equity distribution will often take on the role of aggressor and will make use of large bet sizes while working towards a polarized river range.
Unlike a perfectly polarized range, the aggressor will hold a selection of fairly strong hands that can extract value, but will still lose to a number of hands in the defenderโs range. These are candidates for using smaller bet sizes.
Since the defender might be able to exploit betting ranges that do not contain any nutted hands, the aggressor is required to mix some nutted combos into the smaller bet-sizing ranges for range protection.
If a range has a large density of thinner value hands that prefer small bet sizings, a larger number of the stronger hands are required for range protection. A range that is more polarized, and contains fewer mid-strength hands, can thus use the larger bet sizes at a higher frequency, given that less of the strong holdings are required as smaller bet sizes for range protection.
The GTO Betting Frequency With Polarized Ranges
Our analysis of river situations in the previous chapter also revealed that it is impossible to accurately predict the correct betting frequency purely from range-versus-range equity. This rule also holds true for flop and turn scenarios.
This is not to say that there will be zero correlation. Looking at the big picture, ranges with more pot equity do bet more frequently on average. Being aware of our pot equity can still be worthwhile. But it is definitely not a given that a range is bet more frequently (or even at all) just because it is a favorite in terms of pot equity.
It is probably more accurate to say that a range is bet at a high frequency simply if it contains many hands that have the right characteristics for betting.
Taking a simplified approach, there are two reasons why we bet individual hands:
- Building the pot in case we win (value hands and semi-bluffs)
- Folding villain off of their share of pot equity (bluffs and mid-strength hands).
Ranges aside, any time we are betting or raising with an individual hand, it is worth considering which of these two categories our hand fits into.
Regarding the second point, even top pair hands that are strong enough to extract thin value on the flop and turn may generate a higher EV when our opponent folds their equity share rather than makes the call. It simply depends on how much pot equity is being folded. It is the difference between splitting the pot up almost evenly when our opponent calls, or taking down the entire pot when they fold.
The larger the amount of equity we can fold out, the more likely it is we prefer a fold than a call. Betting for the sole purpose of folding our opponent off their share of the pot is a concept usually referred to as equity denial.
Equity Denial: Betting to capitalize on the fact that our opponent will fold out their equity share. This is typically done with weak and mid-strength hands, despite the fact that these combos may already be the best hand with some frequency.
Simple Polarized Solver Models
Let us put what we have learned thus far into practice and predict how frequently certain models will bet on the flop, and which bet sizes they will typically prefer.
In the following flop situations, we are out of position, and the analysis is based upon a simple solver model that makes use of a small and large bet size.
A loose description of the equity distribution is usually enough to begin making solid predictions regarding GTO strategy. However, as an extra option, it is possible to see the precise ranges by downloading the available GTO+ solver models linked in the book GTO Poker Gems.
Scenario: Nutted equity distribution and some air, nothing in the middle.
This is the perfect example of a range that likes to bet, since we can formulate a polarized range by the river very easily. Flop ranges are not usually this polarized so soon, but we have kept the models extremely simple for clarity.
Because our range does not contain too much trash, we can bet most of it without becoming too bluff-heavy on the later streets.
The solver uses the large bet sizing with a 95% frequency and never uses the small sizing. The high betting frequency might seem surprising when we consider that the overall range only has 36% pot equity, but this is the power of a polarized range!
The 5% checking range is pure air with zero strong hands for protection. Range protection is not required in this case because our opponent never bets when checked to.
If we tweak the model by adding some trash hands into our opponentโs range, the solver then protects the flop checking range with some strong hands. The solver still bets very frequently overall, but not quite as often since some of the value hands get checked.
Scenario: Nutted equity distribution with a large amount of air
The solverโs betting frequency now drops dramatically to around 17%. It is simply impossible for the solver to bet all of the trash hands without becoming overly air-heavy by the turn and river.
Remember, our goal is to set up a well-balanced polarized range by the river. It is better to ditch most of those very trashy hands sooner rather than later. Thus, the solver has no choice but to check trash hands with a very high frequency.
Since the value hands are nutted, the solver always picks the larger bet sizing when betting.
Assuming we check the river, the solver advises our opponent to bet in position despite having a condensed range. It seems condensed ranges do not always play purely for defense! More on this in the next chapter.
Scenario: No nutted equity distribution, but big range advantage deeper in the range along with some air.
It is a little harder to start forming a clean polarized range here, since we do not have the nutted equity distribution. If we bet too large, we run the risk of losing too many chips against the stronger hands in our opponentโs range.
hat said, there are still plenty of second-best hands with which our opponent can call if we size our bets carefully.
etting those hands for value also allows us to fire some of our air hands on the flop. Remember that GTO play wants us to continue as frequently as is mathematically possible.
As anticipated, the solver only makes use of the smaller bet sizing and fires around 24% of the time.
If we increase the number of weaker hands in villainโs range (decreasing the defenderโs overall equity), the solver will advise that we use a higher betting frequency (while continuing to use the smaller bet sizing). Conversely, if we decrease the number of villainโs weaker hands, the solver will start to recommend that we check the flop with a 100% frequency.
We can see that with this specific model, there is a correlation between pot equity and betting frequency. We are more likely to see this type of correlation when dealing with a deeper range advantage than a nutted range advantage.
Scenario: Range with the nutted equity distribution, but significant range disadvantage deeper in the range.
The equity of our range is now only around 35% due to the deep range disadvantage. The lack of pot equity, caused by this weakness in the deeper part of our range, explains why the solver bets with a very low frequency here.
Despite this, we have some hands in our range that have the correct characteristics for betting, even though our rangeโs overall pot equity is low.
First, we have the nutted equity distribution which allows the solver to make use of the larger bet sizing with some frequency (4%).
Second, some of our non-nut holdings are still strong enough to dominate the weaker holdings in villainโs range. For this reason, the solver also makes use of the small bet-sizing range 8% of the time.
Although our strongest holdings appear mostly in the large bet-sizing range, the solver mixes them into the smaller sizing for range protection. Our weaker middling hands are 100% pure checks however since they do not function well as part of the larger bet-sizing range.
The Gems
- A nutted equity distribution usually means large bet sizes.
- An advantage deeper in the range usually means smaller bet sizes.
- We bet at a higher frequency if our range contains many hands that have the correct characteristics for betting.
- Hands bet either to build a pot or for equity denial.
- Pot equity is more likely to be correlated with betting frequency for deeper range advantages.
Getting More GTO Range Strategy
The contents of this article are largely directly from chapter 7 of the book GTO Poker Gems. The entire book simplifies years of GTO solver work, analysis, and exploration into the macro nuggets and actionable advice. Save yourself from the frustration of doing endless solves with zero idea how to parse the output, and instead read GTO Poker Gems to get up to speed quickly.
