How To Properly Balance A Flop Cbet Range

2 weeks ago I received this question from one of you fellow readers, and I thought it was a great one to cover in a future post. I already had the topics planned for the first 2 weeks of the year, but now is the time we tackle this very deep and important question from our friend Giovanni. Take a look at his doubt below:

This is a very important theoretical issue, and one that I don’t remember seeing covered by popular creators or even in advanced training sites. So let’s dive into this.

And important initial disclaimer is that the bluff terminology for betting on the flop can be theoretically controversial. We typically think of a bluffing hand by picturing a river context where equity is 0 and the only way to generate EV is by generating fold equity. On the flop however, it’s perfectly possible for an unpaired hand to generate EV by simultaneously getting called by a worse hand and getting folds from better hands (or at least decent equity hands that could improve). In this post, I’ll ignore the more advanced details, and I’ll categorize an unpaired hand that bets the flop as a bluffing hand.

A second disclaimer is about the strategical context of the discussion. When Giovanni uses sentences like “how far I want to go” and “how is the amount of bluffs chosen” in conjunction, I immediatelly assume he is speaking from a theoretical perspective. There are multiple ways you can build an exploitative strategy, and in that particular context what determines how far you want to go is the size and shape of your opponent’s imbalances. So for the purpose of this post, I’ll assume he is referring to a balanced range construction. More specifically, how to properly balance a flop cbet range. 

But before answering how to balance a flop cbet range, we should talk about what is actually required to be able to say “I’m balanced”. What needs to occur?

From a theoretical standpoint, a balanced strategy is a strategy that can’t be exploited – your opponent cannot make more money by deviating from the equillibrium response. It’s in this context that the most important concept in poker theory arises: indifference.

It’s exactly by generating indifference in our opponent’s response that we can arrive at an equillibrium, in which case we can then say we are “balanced”. If we construct our strategy in a way that our opponent’s hands make the same amount of money with multiple different actions – poker definition of a hand being indifferent – then we are guaranteeing that the equillibrium principle cannot be violated. Well, if different actions make the same amount of money, then the opponent literally cannot capture more EV by changing his strategy – doing so would just lead to the same expectation from before the change. 

From that follows that the ultimate requirement for a strategy to be called balanced is it’s capacity to generate indifference in the opponent’s response.

Going back to Giovanni’s question, the most simplified answer to “how far you want to go” is: exactly until indifference is produced. 

Think about it this way: imagine you are there, BTN vs BB on A73r, and you start crafting your strategy by betting only value hands. At that point, you’re not generating any indifference – your opponent should fold everything apart from his strongest hands. Calling with backdoor hands, weak pairs and even decent bluffcatchers is simply not profitable against a value-only range. Such strategy, however, cannot be the equillibrium strategy because if your opponent is almost never calling you, all of your bluffs can make an insane amount of money by betting, so you can improve your expectation by betting your bluffs (recall that you started always checking those).

As you start to increase the amount of bluffs you bet, however, the EV of calling with marginal hands for OOP starts to increase. By facing a weaker range, they can realize their equity more often, mostly by seeing the river (and showdown) more often, as you now start to check back turn sometimes, fold to flop and turn check-raises, and so on. You keep including more and more and more and more bluffs to your flop betting range, until some hands in the OOP’s range finally reach indifference – calling is now 0EV, just like folding. It’s at this point that you have approached equillibrium, and you’re close to “having enough bluffs that you can’t bluff anymore“.

Noticed how I said “approached” in the last sentence. Here is where things get a little more complicated. What I have ommitted in previous paragraphs is that, while generating indifference is in fact a requirement for reaching equillibrium, I didn’t say how much indifference, or to which hands.

If you have studied poker for long enough, you will probably have noticed that in solver solutions indifference exists in pretty much any node; however it happens to some hands, not all.

In the example Giovanni gave, the cbet strategy from the BTN produces indifference in specific regions of hands from the BB’s range, such as off suit high cards, like KTo; offsuit backdoor straight draws, like 98o, T9o; and suited backdoor flush + straight draw, like Q4s and Q5s. At the same time, hands like K6s, K8s or KJo are pure calls. 

For practical purposes, it’s impossible to generate indifference in all of your opponent’s hands. You can see this happening in the perfectly polarized x bluffcatcher river toy game, where the bettor has nuts or air, and the bluffcatchers can only beat a bluff. In that circumstance, all bluffcatchers become indifferent against a bet, simply because there is maximum information disadvatange and they all have the same properties – same equity and same blocker effects. Such thing basically doesn’t happen in real poker – any range will be composed of different hand classes, with different equities and different removal effects, and the information asymmetry will never be this big. 

How does the BTN find the proper cbet strategy then? Wouldn’t it be possible to build a strategy that generates indifference to all the K high region? Or even the 7x region? Or even the Ax region?

Yes, it would be possible to build a strategy that makes any region indifferent (in theory). The only part of the puzzle missing here is that, while multiple possible strategies can generate indifference in your opponent’s response – preventing the equillibrium principle to be violated from his perspective – only one of them will be the highest EV one for you.

If you build a strategy that successfully generates indifference to some region of hands in your opponent’s range, but then there is another strategy that targets a different region and makes you more money, then an equillibrium has not been reached, as you could simply change your own strategy to target that other region

and increase your EV. Here is where the formal definition of the nash equillibrium comes in handy: “A Nash Equillibrium is a set of strategies for all players such that no single player can improve his expectation from the game by unilaterally changing his strategy“. It’s only an equillibrium when you also can’t change your strategy to a better one.

What I want you to take from all of this theoretical discussion is this: building a flop cbet strategy (and actually any betting range at all!) is about figuring out what’s the most profitable region of hands from your opponent to target and make indifferent. In the iconic book The Mathematics of Poker, the author brilliantly simplifies the solution to this problem with the following quote (Chapter 20):

Now, what does all of this have to do with “how many bluffs I can have” in my betting range?

Well, the answer here is that you simply need as many bluffs as necessary to make the targetted region indifferent. Targetting different regions in different boards with different range strengths will require different range constructions, different bet sizings and, of course, different bluff:value ratios. On an A73r board, the flop betting range for a small size should contain 52,8% bluffs (defined here as an unpaired hand):

On a similar but different board, like A92 two tone for example, even when keeping the same bet sizing, the composition already changes, dropping 6.5%: 

Some important notes here:

• At the end of the day, this is a (long and complex) mathematical problem: for a hand to make 0 dollars when calling a bet on the flop, it follows that the sum of all the possible outcomes that arise from the flop call has to be equal to 0. The amount you lose by calling flop to fold turn for example (assuming you can’t continue profitably vs a double barrel) has to be compensated by the amount you win when your opponent checks back the turn. Therefore, not only the flop range construction matters for the purpose of producing indifference, but also all of the frequencies and range compositions of subsequent nodes – how much you double barrel, the composition of the turn cbet range, how much you fold river after checking turn, and so on.

• The exact bluff to value ratio will be dependant on the betsizings utilized in the game tree. Bluffing on an early street has 2 primary purposes: 1) bring enough give ups from the current street to the next, as to give the opponent incentive to call the bet on the current street; and 2) bring enough bluffs from the current street to be able to balance the value bet region on the next street. Well, how many bluffs you’ll need on the next street to balance your value region will be dependent on how big you are going to bet going forward (and how many value bets you can expect to have). 

Summarizing – you put bluffs into your betting range until you generate indifference in the targetted region. The targetted region is the region that, when made indifferent, produces the highest EV strategy for you. Such region is usually “the strongest that you can” (make indifferent) – the stronger your range is, the more you’ll be capable of targetting higher equity hands in your opponent’s range. 

Ok. 

After reading all of this, I’d imagine you’re not necessarily excited about it. After all, it seems complex and not very practical. It doesn’t provide you with an easy-to-use strategical upgrade that could lead to higher performance at the tables.

And I agree. Poker theory can be very complex if you go deep enough. Unfortunately, in this case there are no easy answers like “the bluff to value ratio on the flop is 2:1”, or “bet 75% of your air and 90% of your draws”. The truth is that how much you want to bluff on the flop varies with the range dynamics, board textures and the sizings utilized; and there is pretty much no way for you to figure it out on your own without looking into a solver solution. 

If you want to get better at your flop cbet execution, then the analytical/theoretical path is not sufficient. It will give you an understanding of what’s going on, which is intellectually pleasant, but it can’t provide you with a framework that allows for easier implementation in-game. The proper way of developing your execution skills, particularly for scenarios like this that repeat themselves over and over, is by using drills.

By practicing with drills, you won’t need to know whether the bluff to value ratio on AK4tt is 1.2:1 or 1.5:1. If you engage in enough repetitions, then with time your brain will pickup on the patterns of range construction, and new heuristics will be formed automatically, like “4x hands are high frequency bets on AK4tt”. You won’t know, from a global perspective of your whole strategy, how often you’re bluffing on that board. But your micro execution – what you do with the individual combos in your range – will be very solid, which will get you close to your initial goal: a balanced range construction. 

I’ve been advocating for the utilization of drills since I touched my first GTO trainer, in 2018. I cannot overstate how these programs are incredible and powerful when the context is improving in poker. By practicing common spots, 1 hour a day, 5 days a week, you will be able to significantly accelerate the process of building heuristics – which can take a very long time to form if you’re simply reviewing a few hands per day and browsing sims. 

One important thing to demystify about using drills as an improvement tool is that they are not effective if you don’t intend on playing GTO. A lot of people have this idea that if their goal is to play exploitative, then drills are not going to be useful for them. I’m very confident in saying that this is 100% not true. In fact, it’s the opposite.

Having very solid heuristics about how ranges should be constructed theoretically will make you a much strongerexploitative player. You’ll know exactly what it takes to be balanced in the most common spots, which will allow you to quickly and more accurately spot imbalances in your opponent’s strategies. Practicing with GTO drills makes you better at exploits, not worse.

The only thing you have to be careful with and keep in mind when you open your tables to grind is the potential development of a robotic execution. A lot of people go through this issue where their execution at the tables starts to become extremely inflexible due to an unconscious tendency to simply mimic what’s been practiced. They see their hand and a random board, and they immediately resort to the RNG to figure out their action. 

Don’t allow this to happen to you. The knowledge you’ll be building in your training time with drills is supposed to be used as a baseline framework for execution, not necessarily the final answer. Make sure to use this framework as a very solid first step in your strategy execution; not the only step. If you do this, I guarantee you’ll become a very strong player much sooner than you thought possible. And flop cbetting will be the easiest thing in the world.

I If you want to learn more about indifference – in my opinion the most important concept in poker theory – check out the video below from my channel. I explain the process of determining which region of hands you should target through toy game examples: 

Why Solver Would Never Lose a Fight

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See you next week. Until then – keep it simple.

Saulo