Perfect GTO Bluffing

What does a perfect GTO bluffing strategy actually look like in today’s games? How often should you bluff according to the GTO solver? Let’s discuss how to correctly craft your bluff range in a given situation to create a winning betting strategy in all NLHE games.

Even before the days of GTO analysis, the best poker players intuitively understood that there was a limit to how much bluffing they could get away with.

A well-timed bluff can undoubtedly be very lucrative, but if you start bluffing all of the time, even the most obtuse of opponents will catch on to the exploitation that is taking place.

Conversely, if we are never bluffing, it becomes too easy for opponents to simply fold strong second-best hands when we bet, recognizing that we almost always have an even stronger holding.

The solution? Push play, or continue reading…

Just like Rock, Paper, Scissors, we need to mix up our lines.

If we can build our betting ranges with a good balance of bluffs and value bets, it makes it much harder for our opponent to exploit us. Where a bluff is a bet made with a very weak hand that aims to get our opponent to fold, and a value bet is a bet made with a strong hand (i.e., a value hand) that aims to get called by worse holdings.

A Perfect GTO Bluffing Strategy

GTO solver analysis teaches us that there is a perfect balance between the number of bluffs and the number of value hands that we should bet in a given situation. This balance is referred to as the bluff-to-value ratio or bluff:value.

Having the perfect bluff-to-value ratio not only makes it difficult for our opponent to play against us, it actually makes it completely impossible for our opponent to construct a winning counter-strategy. A perfect bluff-to-value ratio is the equivalent of always choosing each option in RPS exactly one-third of the time.

But what does the perfect bluff-to-value ratio look like?

To understand this, we need to first lay some important groundwork.

A Simple GTO Bluffing Model

It is common to make some simplifications and assumptions when applying game theory to poker. We will be making use of the following common assumptions when discussing bluff-to-value ratios.

1: We are analyzing a river situation

The concept of bluff-to-value ratios applies mainly to river situations. The model we are about to discuss will not apply directly to earlier street scenarios.

We will consider a HU situation where one player (the aggressor) makes a bet against their opponent (the defender) on the river.

2: The aggressor has a “perfectly polarized” range

The aggressor has a betting range consisting purely of value hands and bluffs; that is, perfectly polarized.

The value hands can never lose at showdown, and the bluffs can never win at showdown. The aggressor is first to act (out of position) on the river.

3: The defender has a range of pure bluff-catchers

None of the hands in the defender’s range can ever beat the aggressor’s value hands at showdown. However, all of the hands in the defender’s range will always win at showdown against the aggressor’s bluffs. The defender is last to act (in position) on the river.

The term bluff-catcher refers to a hand that can only win if our opponent is bluffing. In the context of a GTO discussion, a bluff-catcher will also be at least strong enough to beat all of our opponent’s bluffs.

This outlined model, along with all of the assumptions, is sometimes referred to as the perfect polarization model. Take a moment to make sure you have a good understanding of the scenario since it will crop up quite frequently in conversations about GTO poker.

Perfect GTO Bluffing Frequency

When making use of the perfect polarization model, the perfect bluff to value ratio is entirely dependent on the size of the aggressor’s bet.

The easiest way of calculating the perfect bluffing frequency for the aggressor is simply to consider the pot odds that the defender gets when facing a bet.

Take a simple example where the aggressor bets $100 into a $100 pot on the river with a perfectly polarized range.

How often should they be bluffing?

Let us start by calculating the pot odds that the defender is getting.

The defender would be risking $100 to win the $200 pot. They are therefore getting ~33% pot odds on the call (or 2:1, if you prefer ratios).

As the aggressor, we should bluff the same percentage as the pot odds the defender is being offered: ~33% (or one third) of the time. The remaining ~67% (or two thirds) of our betting range should be value hands. If we instead use ratios we can say that our bluff-to-value ratio should be 1:2 (one-to-two), which is simply the pot odds ratio switched around.

It is impossible for our opponent to exploit us if we play this way given the proposed situation.

Of course, knowing the optimal bluffing frequency does not automatically mean we understand how, or why, it works! Let us take a look at that now.

How Does A Perfect Bluffing Strategy Work?

Remember in our example that the defender holds a bluff-catcher, which means that they will only win if the aggressor is bluffing.

Think for a moment about the following questions: Should the defender call the river with their bluff-catcher? On what factors is the decision dependent?

The answer depends purely on the defender’s pot odds.

The defender can call profitably if they expect to win more often than their pot-odds percentage. Let us break it down.

If the aggressor is bluffing more than one-third of the time, the defender should always call because it will be +EV (profitable) for them to do so. The aggressor is bluffing too frequently according to game theory.

If the aggressor is bluffing less than one-third of the time, the defender should always fold because calling will be -EV (unprofitable). The aggressor is not bluffing frequently enough according to game theory.

If, however, the aggressor bluffs at the perfect frequency, exactly one-third of the time, there is nothing that the defender can do to exploit the aggressor. It is only if the aggressor deviates from the optimal bluffing frequency that the defender is able to generate an exploitative counter-strategy, in which the defender either always calls or always folds.

The following table shows the three possible scenarios along with the implications of the defender’s EV (or expected value).

Can You Beat Perfect A Bluffer?

Let us play devil’s advocate for a moment and try to increase the defender’s EV by playing around with their strategy. We know that folding more will not help the defender, since the EV of folding will always be zero.

Instead, consider the defender’s EV when they call to see if you can increase their profits.

There are two possible outcomes that can occur when the defender calls the river with a bluff-catcher. The following is an example of how we calculate the EV of this simple poker spot.

The amount the defender wins when the aggressor is bluffing is perfectly balanced by the amount the defender loses when the aggressor is value betting. We have demonstrated that the expected value of calling the river with a bluff-catcher is exactly $0!

No matter what the defender does in this scenario, their EV will always be zero. Even if the defender always calls, always folds, or mixes up their calling and folding ranges arbitrarily, their EV will always be zero.

We usually express this by saying that the defender is indifferent between calling or folding with their bluff-catchers.

This is not to say that the defender’s calling frequency is not important. For example, if the defender chooses to fold every single time, this is something that the aggressor can potentially exploit.

A GTO Bluff Example

Many of the discussions in the book GTO Poker Gems are based upon real solver models. We will start by employing the perfect polarization model and running it through a GTO solver.

It is not necessary to run these solves yourself since we will provide all of the required information. However, we have made the GTO+ solver files available for all purchasers who are interested in a deeper dive.

Here are the starting ranges we used in Solver Model 1: Perfect Polarization. Note that the ranges are not designed to be realistic but rather to represent the perfect polarization model as simply and accurately as possible.

Note that the aggressor’s bluffs here are any 5x hand that does not have a diamond flush by the river. On the other hand, the defender’s range always makes a pair of tens which always beats the aggressor’s bluffs, but loses to the aggressor’s value range.

Here is a breakdown of how the solver is playing the river as the aggressor. If you are unfamiliar with the concept of combos in poker, the term combo is used when discussing how many ways a type of hand can be made. For example, there are six possible ways to be dealt a given pocket pair preflop, so there are six combos of each pocket pair.

Notice that the solver is bluffing exactly one-third of the time when making a pot-sized river bet.

4 Bluffing Tips

• We should bet a mixture of bluffs and value hands on the river. (This is known as betting a polarized range.)
• The larger our river bet sizing, the more frequently we should be bluffing.
• Value bets should account for the larger portion of our range, even when using large sizes.
• The GTO bluffing frequency for the aggressor is the same as the pot odds percentage offered to the defender.

Confused? Don’t Panic!

Avoid getting bogged down with precise bluffing frequencies. Even being somewhere in the right ballpark with your bluff-to-value ratio will make you a lot tougher to play against.

For more on the topic of understanding and integrating major GTO poker principles into your own strategy, be sure to grab my new book GTO Poker Gems. I distill years of solver analysis into actional insights that you can start using right away. Learn more and grab your copy here, or grab GTO Poker Gems directly from Amazon for the paperback or Kindle version.