GTO vs Exploitative

Recently at pokervip.com we have had articles on how we can construct ranges as both the aggressor and the defender using GTO principles. But what exactly is GTO? Should we make use of it? Is it true that GTO strategy is simply a way of playing break-even poker?

When we hear poker players talk about “GTO” they are using an acronym for “Game Theory Optimal”. Game theory is a branch of mathematics which deals with analysis of strategies in various situations. The dictionary definition might be the most useful so we are completely clear.

“The branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant's choice of action depends critically on the actions of other participants. Game theory has been applied to contexts in war, business, and biology”

Game theory is currently being applied to poker in a variety of different ways. The idea is that there is likely an “optimal” solution for playing the game of poker. In fact it has been claimed recently that the game of HU LHE has been solved by the University of Alberta's Computer Poker Research Group (CPRG).

As yet HU NLHE is not even close to being solved. It's 6max and FR counterparts are even more complex and will take far longer to solve. However we can still use our knowledge of game theory to make approximations regarding correct strategy without completely solving the game.

In many cases the answer to this question will be “no”. A strong understanding of GTO concepts is only really necessary when playing against very tough opponents. 

Having said that, GTO is still worth consideration by all players for the following reasons.

In most cases we can think of GTO as a defensive strategy and the opposite strategy, exploitative strategy, as an aggressive strategy.

Following GTO is a little bit like hiding in a bunker during a war. We are far less likely to get shot, but we also are not going to be doing that much damage to the other side. If we come out of that bunker we can be much more effective, but we also open ourself up to danger.

So essentially the way we make the most money in poker is to actively try and exploit our opponents' leaks. But in doing so we potentially open ourself up to counter-exploitation.

For example imagine our opponent folds way too much to 3barrels. We should likely be firing that river a ton. We will make a lot of money doing this. However, we are now in a situation where we are technically bluffing the river way too frequently which is exploitable. If our opponent realises this he could potentially start calling down more frequently and exploit the fact that we are bluff heavy. We now lose significantly more money than we would have if we'd played a balanced GTO strategy.

However if stick to our GTO strategy regardless of what our opponent does, we will never get to exploit the fact that he folds too much to river bluffs. We wouldn't be maximising our profits in this case, but at least our opponent won't be able to exploit us either.Seeing as our opponents are generally highly exploitable and also unaware of their leaks, we should place most of our emphasis on playing as exploitatively as possible. In most cases even if they feel like they are being exploited they won't necessarily understand how to make the relevant adjustment.

It's easy to see how huge confusion arises. This has been the topic of intense discussion for years among players first being introduced to the topic. 

If we check out the article written here on GTO aggression we can see a simple example where we fire the river with a balanced range. We stated there that our opponent's EV does not change regardless of what he does. If he folds all of his bluffcatchers his EV is 0, if he calls all of his bluffcatchers his EV is 0. How exactly are we making money?

There are at least 2 lines of thought that can help us answer this question.

Firstly does 0EV really mean our opponent is breaking even here? Imagine that we are routinely cold-calling preflop, calling the flop and turn, and then open-folding the river. (Remember that our overall EV is 0, so even if we call with all of our bluffcatchers, it is essentially the same as open-folding the river). Is our overall winrate going up or down? Quite clearly our winrate is going down overall, despite the fact that our opponent's river EV doesn't change. His EV for the entire hand will be positive. 

So the first point of confusion arises when we analyse individual streets without considering the action which leads up to that street. We must also remember that in many of the examples used we are playing against an optimal opponent who reaches the river with a balanced range. We also make other sweeping assumptions such as: we are perfectly polarized and all of our opponent's bluffcatchers lose to our value hands but beat our bluffs. This is naturally a drastic oversimplification.

There is a chance our opponent makes mistakes on earlier streets and defends non-optimal ranges. Also imagine the situations are reversed and our opponent simply does not bet the river as frequently as he should be. Perhaps he always gives us a free showdown and never takes advantage of the fact that he can “win” by making our range 0EV when he fires a balanced range. It should be really simple to see how our EV is higher in such a situation where we get to fully realise our equity as opposed to none of it.

Essentially, GTO poker strategy does not guarantee a positive winrate. However what it does do is guarantee a minimum winrate.

Imagine a HU game where we always played OOP. GTO would not be able to guarantee a positive winrate in this situation. However it would guarantee that there is a maximum threshold on our losses. Assuming the same HU game but we were always IP, then GTO can guarantee us a minimum positive winrate.

If we play a perfect game then nothing our opponent can do will take us below these minimum thresholds. However, we can increase on these minimum thresholds if our opponents makes mistakes. 

Usually simple thought experiments can confirm this kind of assumption. For example take an extreme situation where we play a GTO strategy except our opponent open-folds every river. Are we making more than our minimum profit thresholds in such an example? Obviously we are absolutely crushing here. We should be able to see that the expectation of a GTO strategy is not limited to our minimum threshold only. It can increases as a result of our opponent's mistakes.Now obviously we would wonder who exactly ever open-folds the river. It doesn't really happen in practice, but we used an extreme example to help us understand how our opponent's mistakes can have an impact on our winrate. It won't take such a drastic form as river open-folds. It will appear in situations where opponents fold hands which are way too strong to be folding. Or they will miss obvious bluffs in the best situations and not fire with the correct frequency. We may end up being able to realise a significant amount of additional equity compared to how much equity our opponent realises when we are the aggressor. 

Again let's start with the dictionary definition of Nash Equilibrium.

“In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.”

The concept was named after mathematician John Forbes Nash, although he was not the first to begin work on similar theories. If you are interested in John Nash, the film A Beautiful Mind with Russel Crowe is based around his life.

As described above, Nash equilibrium is reached when all players are using a game-theory-optimal strategy. In a heads up situation where two optimal opponents are involved, no-one makes any money. If it's a raked game then both players will trade stacks back and forth and slowly lose money to the rake. This is essentially where the idea that GTO makes no money originates. If both players are optimal this is actually the case.

As the definition explains, no player has anything to gain by deviating from the optimal strategy. If one player tried to make a deviation from the optimal strategy, this would be considered a “mistake”, and his opponent would gain in EV. However not all “mistakes” will cause a loss of EV. This is another reason why the subject of GTO confuses many.

We don't always make money when our opponents deviate from an optimal strategy. At least, not if we continue to play a GTO strategy ourselves.

So to return to the river situation we described earlier. Imagine we face a pot-sized bet on the river. All the standard game-theory traditional assumptions are in place. We have a range consisting entirely of bluffcatchers and our opponent is perfectly polarized and balanced, etc etc.

We mentioned that our EV does not change whether we fold all our bluffcatchers, call all our bluffcatchers, or fold a selection and call a selection. But are all options correct from a GTO point of view? Not at all. We should be defending in such a way that our opponent is not incentivised to increase or decrease his bluffing frequency.

So if we know our opponent is betting 1PSB, he would need to succeed about 50% of the time if he were bluffing in order to break even. GTO strategy involves insuring that he doesn't succeed more or less than this threshold. So we should call 50% of the time with our best bluffcatchers and fold the remaining 50% of the time with our worst bluff-catchers.

But what happens if we fold 100% of the time. Our EV does not change, neither does the EV of our opponent. So how exactly does our opponent profit from our mistake. If he continues to play a GTO strategy he doesn't actually profit from our mistake. Seeing as this is one of the commonly cited examples helping us to understand river play, it's easy to see why players get confused and wonder where our profit comes from. Even if we deviate from optimal play and fold all of our bluffcatchers in this situation our opponent doesn't directly profit.

This does not mean in the above situation that our opponent cannot profit from our mistake of folding with 100% frequency on the river. Just as it sounds, if we are folding with a 100% frequency in any situation this is highly exploitable.

But in order to exploit this our opponent has to make an active change to his strategy. We are no longer in a Nash equilibrium because we can improve the profitability of our strategy by making adjustments.We would start by bluffing more frequently than we should in this river situation to exploit our opponent. In doing so we'd be creating an imbalance in our own game where the correct adjustment would be for our opponent to start calling 100% of his bluffcatchers as an exploitative response. If this situation arose we'd lose more money than if we'd stuck to a GTO strategy. But so long as our opponent does not make the correct adjustment, we make considerably more money playing an exploitative strategy as opposed to a balanced one.