It’s becoming increasingly common to justify decisions at the poker table by commenting on subtle range-vs-range interactions.
“This board favours my range, so therefore I should bet”.
This is despite the fact that the majority of players, even winning players, don’t understand the relevant variables when analyzing range-vs-range interaction. Statements such as the above are simply a smoke-screen for the fact that no decent decision-making process is occurring. I.e, I don’t really know whether to bet here, so let’s just fire anyway and make some vague comment about “range advantage”.
Of course, range advantage is a real concept, and understanding it correctly can increase our capacity for accurate decision-making in many scenarios. Here we will break the concept down into relevant variables and dispel some myths in the process.
The Blind Spot of Range vs Range Analysis
Before we analyze range advantage in greater depth, it’s necessary to start with a warning. The idea of analyzing range advantage goes hand-in-hand with equilibrium or GTO style strategies. I.e, the type of strategies that are advocated by PIOsolver and other GTO solvers. Blindly attempting to reproduce such strategies can lead to a large number of missed exploitative opportunities.
In other words, if we are playing small-stakes or lower in a soft player pool, most of our attention should be centered around finding the best exploitative play. If we find ourselves consumed with thoughts of equilibrium strategies and balanced lines, we are absolutely not doing our winrate any favours.
Range Advantage – Raw Equity
We don’t need to go too many years back in poker history to see some laughably bad “GTO” style videos. This is despite the fact that the video producers may have been consistent small or mid-stakes winners over a large sample. It just goes to show that having a good understanding of GTO poker is absolutely not a pre-requisite for being a crusher.
One mid-stakes coach made a HH review style video where every decision was made solely by analyzing the range-vs-range equity in every spot. Even to this day, many players don’t realise that the approach is tragically flawed. After all, isn’t a range advantage simply where one range has more equity than the other? No, absolutely not. Raw-equity is merely one component of a range. It’s possible for a range to have the most equity and yet still be considered at a disadvantage.
It didn’t take the more profilic GTO analysts too long to establish this. For example, in many situations, solvers often recommended low c-betting frequencies OOP as the PFR, even if the PFR is given a raw-equity advantage. In other spots, solvers seemed to be recommending high bet-frequencies despite the bettor being an equity underdog. So what was happening?
We can perceive that our strategy is clearly not defined solely by the raw equity of our range. Solvers are certainly looking at raw-equity as an important component of a decision, but there are additional important variables that have to be taken into consideration.
Range Advantage – The Unsung Variables
As our brief discussion on cbetting OOP as the PFR demonstrates, position is clearly one variable that needs to be thrown into the mix. Being OOP confers a serious disadvantage, moreso on some textures than others. Stack-depth needs to be considered also. The exact same range set-up can be much more problematic with deeper stacks. We’ll hence continue with different ranges against a bet solely because the effective stacks are different.
It’s not too difficult to contrive a scenario in a solver where one player has an extreme amount of raw-equity, yet the solver advises that he never bets. This can be extremely confusing to players with only a rudimentary understanding of GTO analysis. How can one range have 80% equity and yet be advised to check-range? Our mid-stakes coach mentioned above would have been firing like a monkey. The reason why we can encounter low betting frequencies even with large raw-equity has to do vulnerability. Sometimes a “weaker” range (equity-wise) will bet more frequently than a “stronger” range. This is because the weaker range contains a large number of combinations which are susceptible to being outdrawn. Of course, we are not saying that weaker ranges bet more frequently than stronger ranges on average, simply that the vulnerability of a range needs to be taken into account when determining the ideal betting frequency.
The final variable that absolutely must be considered before strategizing is the equity-distribution. The raw-equity of a range tells us little or nothing about how that range is constructed. For example, if our opponent’s range has 50% equity against us it could mean either one of the following –
1. He has exactly the same range as us.
2. 50% of his hands have us crushed, and we crush 50% of his hands.
Of course, point 2 is an approximation assuming zero redraw possibilities. The concept should be clear however. In both cases our equity reads 50%, but in one situation our opponent has a similar range to us while in the other, he is polarized with respect to our condensed range.
Ignoring position for a minute, in scenario 1, no player has any range advantage. In scenario 2, our opponent usually has the range advantage. But how can he have a range advantage when the equities are at a symmetry? Because polarized ranges are easier to play and more profitable than condensed ranges. One reason why polarized ranges are more profitable is because they have the nutted-equity-distribution. This is a fancy way of saying that one range can have the nuts, while the other can’t. As a general guide, it’s difficult to play aggressively without the nutted-equity distribution even if we have the best raw-equity. Conversely, the nutted player can often play somewhat aggressively even as an equity underdog.
Range Advantage and Bet-Sizing
Bet-sizing is already the least understood area of poker, so when we combine it with in-depth GTO style concepts, poker players are liable to come out with some really idiotic statements.
“We have an equity-advantage, therefore we should bet our whole range small”.
It would be nice to think that if players thought about this for any length of time, they’d begin to perceive that it has no grounding in actual theory. Of course, there are some players out there currently employing such strategies. Such strategies are utilized not because they are theoretically correct, but because they are considered “acceptable simplifications”. I.e a strategy that is not theoretically correct, but does ok, and is easy to execute consistently.
When inexperienced players attempt to copy such strategies they assume that what they are doing must be GTO correct, but this is absolutely not the case. Besides, it’s important to understand that the equity of a range does not indicate the optimal bet-sizing. A statement that correlates range equity with optimal bet-sizing is hence flawed from the outset.
Usually, bet-sizing should primarily be considered through the lens of equity-distribution, not raw-equity. Also seeing as individual combinations within the distribution have different respective equities vs villain’s entire range, multiple bet-sizing ranges must be introduced in order to maximize expectation. Therefore, assuming that we should use just one bet-sizing for the entire range is flawed. Although we consider the equity of the range as a whole, it’s the equities and characteristics of individual combinations within the range which determine the optimum setup of our multiple bet-sizings.
As a rough guide, having the nutted-equity-distribution allows us to use large bet-sizing ranges. It does not, however, imply that our whole range should be betting large; simply the nutted subset of it (along with relevant bluffs). A smaller bet sizing range would still need to be used in most cases unless we were perfectly polarized with respect to villain. Conversely, a range without the nutted-equity distribution will struggle to bet large at any point. Overly large bet-sizings run the risk of isolating themselves vs villain’s nutted-equity distribution. The sizing that a condensed range can hence utilize, is theoretically capped.
Utilization in Practice
We’ve considered some widely unknown and also somewhat complex concepts. We might wonder how exactly we can use this in practice. Improvement can come simply by being aware of the additional facets of range vs range interaction.
Who has the best raw-equity?
Who has the nutted equity-distribution?
How vulnerable are the holdings within each players range? (Looking at the board texture will help).
How will position impact our aggression/defense frequencies?
How will stack-depth impact our aggression/defense frequencies?
When first embarking on a GTO analysis of the game, many players limit themselves to asking the first question at the top of the list. When running analysis on two ranges we should consider all 5 of the above variables in determining who truly has the range advantage.
It can be difficult to address all 5 variables in game. We can augment the process by looking at various range-vs-range interactions beforehand. By the time the flop falls, we’ll then already have a rough idea of where we stand, and how to respond strategically.