GTO Aggression in Poker

w34z3l• 16,902 Views • on 6/5/15

Application of GTO (game theory optimal) when we are the aggressor. How can poker GTO aggression improve your overall results and make you a better player? Implementing things like big overbets in your game can be difficult at first but is guaranteed to increase your profits if done correctly.

This article will

discuss how we can use game theory principles to create balanced ranges when we are the aggressor. Having a balanced range as the aggressor will ensure that we cannot be exploited, but does not necessarily constitute the best line of action in any given circumstance.

Keep in mind that we will take a shortcut approach to understanding real game theory analysis. This is common amongst modern poker players although many fail to realise that the following calculations are based on a heavily simplified model of poker and don't necessarily represent perfect GTO poker solutions. However, they should serve as a useful introduction to a GTO concepts and increase our effectiveness in many situations where we are the aggressor.

We would typically resort to balanced aggression when:

Our opponent is also very balanced
We don't know our opponent's tendencies
We have no specific population read which will allow us to make an exploitative decision vs an unknown.

GTO: Bluff:Value Ratio

The first step to calculating balanced ranges is to understand bluff:value ratios and how to balance them. A bluff:value ratio describes the proportion in which bluffs to value hands appear in a certain range.

If we have a bluff:value ratio of 2:1, it implies that we are bluffing twice as frequently as we are value betting. Logically, 33% of our range would be value-hands and 67% of our range would be bluffs in this case. Calculating the correct bluff:value ratio is very straightforward on the river, but gets increasingly complicated the earlier the street we are on. As such, we will start with river situations.

The proportion of bluff:value hands in our range is a function of thebet-sizing. Generally speaking the larger we bet, the higher the percentage of bluffs we should have in our range. We can calculate the ratio by considering the pot-odds our opponent is getting and how often he needs to be good to make a call.

A bluff:value ratio describes the proportion in which bluffs to value hands appear in a certain range.

Example 1 - We make a pot-sized bet on the river. How often does our opponent need to be good for calling to be correct?

In this case our opponent would be investing 1pot-sized bet(PSB) to make a total of 3PSB. He is investing 33.33r% of the total pot and so needs to be good at least 33.33r% of the time in order to make the call.

Example 2 – We make a pot-sized bet on the river. How should we construct our bluff:value ratio if we want to be unexploitable?

We calculated previously that our opponent needs to be good 33% of the time to call. Very simply we allow him to be good by bluffing 33% of the time. (There are one or two assumptions made with this example (the “simplifcations” mentioned earlier.)

We assume that our value hands are always good and our bluffs always lose, which may not always be the case in practice. In other words, our opponent always holds a bluffcatcher and we are perfectly polarized.)

If we were to bluff more often than 33% our opponent would be incentivised to call every single bluff-catcher (he would be good more than 33% of the time), whereas if we were to bluff less than 33% our opponent would be incentivised to fold every bluff-catcher (he would be good less than 33% of the time).

Our opponent can call/fold with any frequency he likes, and there is absolutely nothing he can do to exploit us. We are now balanced.

Assuming we bluff 33% of the time something interesting happens with our opponents expected-value. It doesn't actually matter what he does, his expected value remains exactly the same.

We can demonstrate this with a quick EV calculation.

Assuming he folds every time = EV is obviously 0 (we don't need a calculation for this)

Assuming he calls every time ---->

(33.333 * 2bb) – (66.6666% * 1bb) =

0.6666r - 0.6666r = 0bb EV

Our opponent can call/fold with any frequency he likes, and there is absolutely nothing he can do to exploit us. We are now balanced.

Earlier Streets

Unfortunately we can't game theory optimal

simply apply our current bluff:value calculation to earlier streets. This is because GTO poker always takes into account what may happen on later streets. In other words, we can't calculate what our flop bluff:value ratio is without knowing what our river bluff:vaue ratio is first. In order to know this we will also need to know which sizing we will be using on the river.

For simplicity's sake we will use pot-sized bet on flop turn and river. We will work back from the river and calculate what our turn bluff:value ratio should be and also our flop bluff:value ratio.

A useful starting point is understanding what percentage of our flop range will be strong enough to value-bet the river after firing flop and turn. We will think of all ranges as a proportion of our initial flop range.

All % uses are a percentage of the range we reach the flop with!

Let's imagine we run some calculations and establish that roughly 10% of our flop-betting range will be strong enough to 3-barrel and fire the river for value. We are also aware that since we will be betting pot-size on the river we will need a bluff:value ratio of 1:2.

If we are value-betting 10% of our total flop-range then we will be bluffing 5% of our total flop-range. Of all the hands we reach the flop with, 15% of them will be firing the river in this example

GTO: Turn Bluff:Value Ratio

On the turn we are also betting pot-size. But now we can no longer simply use a 1:2 ratio because we need to account for the river action which will follow. So how exactly should we adjust our range?

When using GTO principles we can essentially think of any situation where we fire a balanced range as a “win” for us, regardless of whether we are bluffing or value-betting. We have already calculated that our opponent's EV does not change based on his action. So in a sense, all of those 15% of hands we are betting river with can be considered “value-bets” on the turn.

In other words, any hand we raise the turn with (whether it be a value bet or bluff) with the intention of firing the river, can now be considered a “value-hand” for the purposes of calculating bluff:value ratio on the turn. The hands we consider “bluffs” on the turn are those which will fire the turn and then proceed to give up on the river.

With this in mind we can now calculate our turn bluff:value ratio. 15% of our hands will go on to fire the river so we need to balance this with 7.5% “bluffs”. (Exactly the same ratio for 1PSB, 1:2 bluffs:value).

In other words, any hand we raise the turn with (whether it be a value bet or bluff) with the intention of firing the river, can now be considered a “value-hand”

So to break down our turn strategy (remember these are percentages of our total flop-range)

10% value hands which fire turn and river
5% bluffs which go on to fire the river
7.5% bluffs which will check/fold the river

So if we calculate our real buff:value ratio on the turn we have 12.5 bluffs for every 10 value hands. This gives us a bluff:value ratio of 1.25:1

GTO: Flop Buff:Value Ratio

Feeling brave? GTO poker

All the required information is here for calculating our flop bluff:value ratio. We simply follow the same method we used from turn to river. The calculation will be listed below, but feel free to take a shot at the answer by yourself.

Ok so we are firing 22.5% of our total flop range on the turn. We should balance these with an additional 11.25% of hands which will fire the flop and give up on the turn.

To break down our range again:

10% value hands which go on to fire the turn and river.
5% bluffs which go on to fire the turn and the river
7.5% bluffs which will fire the turn and check/fold the river
11.25% of hands which fire the flop and give up on the turn
33.75% of hands we reach the flop with are betting
23.25% of these hands are bluffs
10% are value hands

We can calculate that our bluff:value ratio in this case is about 2:1

So what can we learn?

It's an interesting mathematical exercise but for many of us it may feel somewhat abstract at this stage. Of what use of this to us in our games.

The larger we bet, the more bluffs we can have in our range
The earlier the street and the deeper the stacks, the more we can get away with bluffing

So typically, if we find ourselves in a river situation where we frequently have a lot of air in our range and relatively few combos of value-hands, overbetting may often be correct.

In the reverse situation, where we don't have many conceivable bluffs and our value-range is very strong, we should be using a very small sizing.

Finally we should avoid bluffing as frequently vs short stacks in a postflop situation, whereas in a deep-stack situation we can use the additional stack sizes to place a huge amount of pressure on our opponents and bluff more frequently.

in a deep-stack situation we can use the additional stack sizes to place a huge amount of pressure on our opponents and bluff more frequently

GTO: Why don't the results seem logical?

While the methodology is correct we may be left wondering why are calculations indicate a 35% cbetting frequency and feel that it should be slightly higher. This is likely due to the huge simplifications we have made to produce this model.

We've assumed that all of our value hands will be used as part of a 3 street hand and not a 2 street plan. Adding more value hands will increase the frequency with which we fire the flop.
We haven't discussed our check/call or check/raise ranges. We've simply assumed that if we check we are always giving up, which is illogical.
We haven't factored in the equity of our bluffs and our value hands. We've simply counted combos which will result in noticeable inaccuracies
We've assumed we are perfectly polarized on the river, and we might not be

These are just some of the issues with the model. To create a perfect GTO solution our model would need to take in to account all of these issues and more. Hopefully we can quickly begin to see that having an accurate calculation for any situation is a highly complicated procedure and at this stage really still involves much guesswork.

Author

w34z3l

I am of British nationality and go by the online alias w34z3l. I am considered one of the top consultants in the field for technical analysis (i.e. database work) and application of game theory concepts to various card games. I make a ... Read More