Gto Poker Concepts

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.

GTO (Game-Theory Optimal): This playing style is where you essentially attempt to play perfect poker yourself, which in turn only allows for your opponents to make mistakes against you (which is where almost all of your profit will be derived from). Of poker arises from inferring probabilities through the many rounds of betting and making decisions that consider events in the future. To understand the mathematics behind playing optimally, we dissect the game into constrained sub-problems, but the concepts derived through these examples are relevant in real play. Pot Odds De nition 2.1.

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) =

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 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? 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?

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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.
Gto

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.

There’s a buzz word in the poker world these days that you may have heard, but many new players aren’t yet familiar with it. That buzz is GTO.

GTO stands for Game Theory Optimal. What it means is using an unexploitable strategy, which cannot be countered by your opponent. In this article I’m going to explain what it is, tell you why you should learn about it, and then explain why you shouldn’t be focusing on it in games.

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So for starters, what does that mean, an unexploitable strategy? You will also hear the word balanced or balancing used in these discussions. I think the easiest way to explain this is with a basic example:

Let’s say there is $100 in the pot, and you bet $100 on the river. Your opponent, who has a medium strength hand (a bluff catcher, something like JT on a board of QJ963), has to now decide whether or not to call this final river bet. They have to call $100 to win the $200 now in the pot. Therefore the call must be right 1/3rd of the time. If it is right exactly this often, the call breaks even over the long run (losing $100 each of the two times it’s wrong, and winning $200 the one time it’s right). And they have a hand strength that will lose to everything you are betting for value, and beat everything you’re bluffing with. Now, if they had a read that you were a conservative player that never bluffs the river, then they can easily fold to this bet. Conversely, if you were a known wild bluffer, they can easily call knowing they’ll catch you well more than 1/3rd of the time with a bluff. Let’s say, however, that you bet your range of hands on the river such that you are value betting 2/3rds of the time and bluffing 1/3rd. This is the unexploitable strategy… your opponent is now indifferent to calling or folding. If they call all the time, they will break even by catching you bluffing at the precise frequency that the pot odds are offering them, netting them zero won/lost over the long term (and if they fold all the time by definition they win/lose zero on the river over the long term). So you are bluffing at a GTO frequency, making this river bet unexploitable… it doesn’t matter if they call or fold.

Why should you learn about GTO strategies? I think you may start to see from the example, that learning about GTO strategies involves topics like basic math, odds, ranges, and frequencies. As you study these things, you’ll develop a much stronger sense of constructing solid ranges, so when you get to the river in a hand you have a more balanced range… in the case of the example above, picking the appropriate number of value bets vs. bluffs. And learning what types of hands are better to bluff with given the board texture, situation, and bet sizing. A firm grasp of these concepts will help you to make much better decisions, understand situations and ranges better, and help control your opponents through keeping proper frequencies, and exploiting their frequencies (like in the example above, if you were a known bluffer or a known non-bluffer, those are lopsided frequencies that can be exploited by calling down frequently, or not calling down with any marginal made hands at all. These are all concepts that fall under the umbrella of GTO play. Learning this will not only strengthen your understanding of the game a great deal, but also prepare you to play against other very strong players who also understand these concepts. If you are in a tournament heads up against Fedor Holz, playing a GTO strategy will prevent Fedor (or any expert) from being able to exploit you.

Now that we’ve talked about what GTO means, and why it’s a good thing to learn more about, let’s talk about why you should not be focusing on doing this in your games. This comment may surprise you. This GTO business sounds pretty nice. I should work on it away from the tables to strengthen my game. But now in the heat of battle, not use it? That’s right. The reason is, for most readers, you will be playing against opponents who make many frequent mistakes. And thus, although a GTO strategy will be profitable against them, an exploitative strategy will do even better. For instance, in our example above, we know that when we bet $100 into $100, the GTO bluffing frequency is 33% to make our opponent indifferent to calling or folding. If our opponent is a world class player who excels at reading their opponents, this forced indifference is a good thing… by default they cannot get the best of us. Most of your opponents, however, will not be Fedor Holz or Phil Ivey. Especially in the micro and small stakes games, they will be making many frequency mistakes.

So for instance, if your opponent were a tight/conservative player who never calls big river bets without a monster hand, then we will make quite a bit more money over time by bluffing at a higher frequency than 33%. In fact against this player a much better strategy might be to value bet much tighter/stronger hands, and add in more bluffs from our range so that we may be betting with 20% value bets (our strongest hands only) and 80% bluffs. This is a frequency that is well out of balance, and our opponent could easily exploit us by calling down much lighter (a common adjustment to someone who bluffs too much). But unlike the world class player, they won’t recognize this and exploit us, they’ll just keep folding too much. Or on the other side of that coin, if our opponent is a calling station that calls down with any pair or even ace highs, then we can exploit that by betting much wider for value (2nd pair may be an easy value bet vs. this type of calling station), and not bluffing much if at all. Again, a strong player can easily exploit us if our river bets are always value bets and never bluffs by simply folding all medium strength bluff catchers to our bet. But our calling station friend won’t, they’ll just call, providing us much more value long term than the GTO value bet/bluff frequency would.

The study of GTO strategies isn’t for the beginning player. But once you have the basics down and as you advance your game, it becomes an integral part of a more advanced poker strategy.

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