Good poker players have long attempted (and sometimes succeeded) in harnessing the power of bet-sizing tells. The idea is that the bet sizes our opponents choose may give away important information about the types of hands they are holding.
As a simple example, imagine an opponent who always bets full-pot when strong, but half-pot with weak hands and bluffs. Generating a winning strategy would be quite simple here. We would simply fold our bluff-catchers when facing large bets, and defend actively against the smaller bet size.
If you are thinking that telegraphing clear information about our hand through bet sizing does not sound very “GTO,” you would be 100% correct! It is about as GTO as eating an Oreo every time we make the nuts.
So how exactly are we supposed to avoid giving away information through our bet sizing?
Editorial note: The following strategy article is based on a chapter from the Red Chip book “GTO Gems” authored by SplitSuit and coach w34z3l. If you’d like to purchase a Kindle version or hard copy, please visit this sales page or Amazon.
A Single-Size Solution?
The logical first question that many poker players ask is: What happens if we simply bet every single hand with the same bet sizing?
At first glance, it might seem that the problem is solved. After all, our opponent is going to have absolutely no idea what type of hand we hold if we always pick the same sizing.
Historically, many players believed that this is the definition of balance in poker.
Unfortunately, this is not a good definition of balance, since we can prove quite easily that a single-sizing strategy can be exploited.
The aggressor always bets $50 into a $100 pot on the river with a perfectly polarized range. They bluff 50% of the time and value bet 50% of the time. Are they balanced?
Take a moment to try and answer these questions. Can we exploit the aggressor here? How?
It is certainly true that the defender has no clue what the aggressor has at any given moment. It is a 50/50 coin flip whether the aggressor has a bluff or a value hand. However, this does not mean that the aggressor is balanced.
With a half-pot bet size, the aggressor should be employing a 1:3 bluff-to-value ratio. The aggressor should be bluffing 25% of the time and value betting the other 75% of the time. This is because the defender is being offered 25% (or 3:1) pot odds.
As it stands, the defender can exploit the aggressor by calling with all bluff-catchers, because the aggressor is bluffing too frequently from a GTO standpoint.
We clearly need a new definition of balance, because always using the same bet sizing is not quite ticking the boxes.
A Definition Of Balance
Let us look at a more accurate definition of balance in poker:
Do not worry too much if this definition does not immediately resonate. Expect a 3 am “aha moment” an unspecified number of days from now.
In the meantime, there are a couple of key lessons that we can extract from this definition.
GTO play is the best exploitative strategy against a perfect GTO opponent.
Some sources appear to imply that exploitative and GTO poker are opposite ends of the spectrum and that each represents a completely different approach to the game of poker. It is not uncommon for debates to break out online regarding whether the best poker players should use GTO or exploitative strategies.
But what is exploitative poker? It is a strategy that always seeks to maximize our EV through exploitation, regardless of whether it makes us unbalanced in the process. What happens if we try to maximize our EV against a perfect GTO opponent? We end up playing perfect GTO poker ourselves.
In other words, GTO poker is a type of exploitative poker.
This frees us enough to understand that the sole objective of any poker player should be to exploit their opponent as hard as possible. GTO poker is simply just one manifestation of exploitative poker. It is the scenario in which both players are so good at exploitation that neither has any incentive to deviate from their current strategy.
Balanced play is a byproduct, not our main area of focus.
When we exploit weak opposition, the end result is that we end up playing an unbalanced game (albeit for a good reason). When we exploit a perfect GTO opponent, the end result is that we automatically play a perfectly balanced game.
In other words, balance is a byproduct of playing exploitative poker well. Attempting to make balance our main area of focus is actually approaching the problem backward. We are not trying to be balanced purely for the sake of being balanced.
If we instead focus on developing strategies that maximize our EV, the degree of balance in our strategy will simply be a response to how skilled our opponent is. Generally speaking, the more skilled our opponent, the more balanced our own game will become when playing the highest-EV counter-strategy.
If we push exploits too far against good opposition, we run the risk of them being able to efficiently counter and significantly reduce the EV of our overall game-plan. We give an example of this in Chapter 4 of “GTO Gems,” in which each player adjusts their strategy to exploit the other. In that example, neither player is trying to be balanced. However, their game plans automatically and progressively become more balanced as they compete.
Balanced Play Means Multiple Bet Sizings
While the idea of only using a single bet size may have initially appeared logical, balanced play actually requires the use of multiple bet sizes in order to maximize EV. We can illustrate this with a simple thought experiment.
Imagine a simple river situation where we are the aggressor with two different types of value hands in our range:
Nuts: This is the stone-cold nuts and the defender can never win when they call.
Thin Value: This is a reasonably strong value hand, but not invincible. Although the defender can call with second-best holdings, they will also have some stronger hands in their defense range.
What does your intuition tell you about our bet-sizing plan here?
A logical answer would be:
- Our nutted holdings maximize their EV by betting large.
- Our thin value holdings maximize their EV by betting small.
- Bonus points if you mentioned that the smaller sizing might need some range protection.
Now imagine we try to force all of these holdings into a single bet size. We run into one of the following two problems.
- If we always use the small sizing, our thin value hands would do well, but our nutted holdings would be missing out on extracting additional EV with a larger bet size.
- If we always use the large sizing, our nutted hands would do well, but our thin value hands would lose too many chips in situations when they are behind, lowering their overall EV as bets.
It is actually impossible for us to maximize our EV by only using just one bet size here.
The big takeaway is that, not only does using multiple sizings not make us unbalanced, but using multiple sizings is mandatory if we want a balanced strategy.
A Simple Multiple-Sizings Solver Model
Let us set up a very simple GTO solver model based on the above premise.
It is a river model with the following features:
- The aggressor has some strong value hands, some thin value hands, and some bluffs.
- The defender has a selection of bluff-catchers along with some slightly stronger hands.
- The defender’s bluff-catchers only beat the aggressor’s bluffs.
- The defender’s stronger holdings generally beat the aggressor’s thin value hands but lose to his strong value hands.
- The solver has the ability to bet either $50 or $150 into a $100 pot (i.e., a smaller bet sizing and a larger bet sizing).
Here are the ranges:
After running the solve, we get the heat map below which shows the distribution of the different actions the solver takes. This type of output is commonly used by solvers to quickly display all strategic options at a glance.
We can see that the solver does make use of both different bet sizings, as predicted. The half-pot sizing is used 30.7% of the time while the overbet sizing is used 21.7% of the time.
Keep in mind that the solver will only use a certain bet sizing if it is possible to maximize the EV of that player’s strategy by doing so. If this is not the case, the solver simply will not use that bet size.
Analysis of Chosen Sizings
Let us see if we can get a better understanding of which sizes are being chosen by the solver and why. We can break the hands down into two categories, those that use pure strategies and those that use mixed strategies.
Category 1: Pure Strategies
77, 33, 22 (full houses and quads). These all use a pure overbet strategy. This makes sense since these hands can never be beaten.
Weak Ax (one pair). These hands all use a pure strategy with the small sizing. This also makes sense, because these hands do not want to lose too much if they run into the stronger holdings in the defender’s range.
AA (full house). The most interesting pure strategy result here is perhaps the pocket Aces. This hand uses the small bet sizing with a 100% frequency despite never losing to any of the hands in the defender’s range. The reasons for this is discussed in Chapter 11: Blockers Decide The Close Spots of “GTO Gems.”
It is true that smaller bet sizings (and checks) potentially need some stronger hands in them for range protection. However, this is likely not the main reason why AA is a pure small bet within our current model.
Category 2: Mixed Strategies
AKo & AKs (strong top pairs). These are mixed across both of the small bet and overbet lines. This means the EV of both lines must be the same.
Take a moment and try to answer the question: Why is the solver seemingly indifferent here?
Looking closely at the model, we see that AK occupies a unique location in terms of how the ranges of both players interact. Unlike the other hands in the aggressor’s thin value category, AKo beats some of the defender’s stronger hands (AJ and AQ). However, unlike the aggressor’s strongest holdings, AK loses to the defender’s A7 (two pair).
Ace King when it hits top pair is therefore solidly in the middle ground. It is not an obvious small bet like weak Ax hands, but it is clearly not an obvious overbet candidate since it loses to some of the hands in the defender’s range (i.e. A7). Consequently, it makes sense that this is a hand the solver would choose to mix.
However, this does not explain why A2s and A2o are also mixed into the small bet-sizing range. These seem like obvious candidates for overbets since they can never lose to any of the defender’s range. They must share some similarities with pocket Aces, which is explored in Chapter 11: Blockers Decide The Close Spots of “GTO Gems.”
The air hands are also mixed strategies, for reasons that should now be familiar. The solver mixes the air hands in order to maintain a balanced bluff-to-value ratio across both the small sizing and overbet sizing.
The solver does not select the air hands at random as in earlier models, but favors certain bluff combos such as 65.
- It is impossible to play GTO poker without the use of multiple bet sizes.
- The sole objective of any poker player should be to exploit their opponent as hard as possible.
- Without multiple sizings, some of our hands will not be able to maximize their EV by playing at their preferred sizing.
- Strong holdings often bet large, but they also need to be used in smaller bet sizing ranges for range protection.
- Bluffs should appear in all bet-sizing ranges using the appropriate bluff-to-value ratio.
Do not be afraid to vary your bet sizings if there is a good reason for it. Using multiple sizings does not necessarily mean that your opponents will be able to exploit you.