Can the solver beat NL25? The answer seems too obvious. Of course it can, right? But I'm not at all convinced. Of course, we are talking about the win rate after paying the rake – it is not so easy to beat this limit with the rake. Yes, there are a lot of weak regs and amateurs at this limit, but the rake is really high.
Let's try to approach the issue logically. We will discuss the rake, the strengths of the solver, and what it is better than all opponents in, then we will talk about situations in which the solver's win rate will be lower than that of the regular players. Let's compare him with weak regulars, then with strong ones, whose win rates at NL25 are known to us. This is a good starting point. Next, I want to talk about why people like to copy the actions of the solver so much and why this is not always correct. I may even be able to convince some of you to stop copying it. If coaches listen to me and force students to play strictly according to the solver, maybe they will wonder why they are doing this: because it is useful for the player or because it is easier? And then we will issue a verdict.
So rake. Rake is the tax we pay when we win pots. It has a percentage of the pot and a max limit. Zoom25 at PokerStars seems to have a max limit of around 8bb and a bet of 5%. That is, when you win a standard pot of 200 blinds, you pay less than 5%, but just a little bit. At higher limits, the max limit of the rake decreases, so the load becomes slightly less. If you calculate the rake at NL25 in bb/100, it will be somewhere between 7.5 and 9 bb. That's a hell of a lot. Probably, some part of it can be returned with rakeback, but let's forget about it for a while. It is very hard to beat the game with such a rake even when you are noticeably outperforming the field. Therefore, the question of whether the solver can beat the rake at this limit seems to me open.
Of course, I'm talking now about 6-max. Heads-up is another matter. Almost all hands are played there. The button folds only 15% of hands, and in the remaining 85% he can use the advantage of position. In 6-max, we enter the pot much less often. If your VPIP is around the optimal 22%, this means that 70 to 80 times out of 100 you will simply fold your cards. There will be J4o in the cutoff, and eights when there is a raise and a 3bet, and so on. Therefore, the win rate will be lower compared to heads-up.
We find ourselves in a tough spot from the very beginning – on the one hand, high rake, on the other, the need to fold many hands before the flop. And although a solver playing a non-exploitable Nash equilibrium strategy will by definition not lose to people without taking into account the rake, there is no guarantee that he will remain in the black after paying the rake.
In what way is a solver superior to a human? First, in balance and non-exploitation. There are no holes in his strategy, all frequencies are perfect. No amount of tweaking will help you increase your expectation against him. Its algorithm is based on balance. (You can, of course, design a bot that plays in an exploitative style, but we're talking specifically about the GTO solver.) Its strength is that even if you know its strategy exactly, no amount of tweaking will help you increase the expectation against it.
How important is this in practice? How valuable is it that the opponent cannot exploit you, even knowing your strategy in all its nuances? Think about it, if you like. In my opinion, it will not bring any benefit. Even if there were vulnerabilities in the solver's strategy, people would still never reveal them.
Secondly, the solver selects the lines with the maximum EV much more accurately. If the GTO considers a c-bet on a particular texture with a particular hand to be an error, the solver will not make that error. If a hand has enough value at showdown to not bluff it on the turn, the solver won't bluff. On the river with a bluff catcher with a bad blocker, he won't pay off his opponent's bet.
It's valuable. But the value of infallibility is not absolute. It is clear that the solver is much better than a fish that has left the table, making bad and expensive mistakes. However, when we compare the solver ideal with the play of regulars, who have learned well to avoid obvious mistakes, who said that the difference will be so huge? I hear your objections: "Come on! What nonsense is this? Of course, Solver will play much stronger!" I want to take on the role of devil's advocate and argue against that statement.
The ideal accuracy of a solver in borderline situations is small strokes on a large canvas of the game. Large strokes are simple and obvious solutions, as well as a brazen exploit!
Hard-hitting moves against certain types of players have a far greater impact on win rate than higher level plays based on blockers and other theoretical niceties. Faced with a tilting fish that has lost the ability to fold, the solver will do something that no regular will do: in response to a turn pot-bet, he will check-raise and shove the river not only with value hands, but also with bluffs. Of course, his value will win back all the EV lost on bluffs, but the point here is that not only a strong, but also a fairly average regular, will play his value in the same way, but he will slow down with bluffs, seeing which opponent he has to deal with. I doubt that the unmistakable play of the solver will win them at least as much against fish as the regular will get with his rough adjustments. This is my main argument.
I would love to always know the ideal theoretical line and EV of each action during the hand, but I don't think that many small edges outweigh some huge edges from sharp adjustments to fish. At NL25, the money comes from weak players. That is why the game selection plays a key role at this limit. That's why Garrett Adelstein performed so well on Hustler's cash game streams – because he ended up at a table full of recreational players. It's no coincidence that good regs are so obsessed with table selection. As calculations in my discord group showed, a losing player adds 5-8 bb/100 to the win rates of the rest. This is more than any edge a top reg can get over a weak reg. If the ability to better interpret complex and close situations were so valuable.
The solver will play more accurately than the regulars, but he will never deviate from the Nash Equilibrium. A regular, playing against a fish, will make much more plus deviations than minus ones. When I sit at a zoom 200 or zoom 500 table with four regs and one fish, I make very hard adjustments against the fish that are highly likely to be profitable. I can't calculate, but intuitively it seems to me that these adjustments will affect the win rate more than solver accuracy.
I know from coaching practice that a weak reg plays with a win rate of -2... -3bb/100, sometimes even -5bb/100. The strongest regulars in the limit beat him with a win rate of 3-4bb/100 – higher win rates at NL25 are very difficult to get without insane selection and a very good understanding of weak opponents, although this is also possible. Thus, the difference between weak and strong regulars is not that big – 6-7bb/100 maximum.
At the same time, even a weak regular will obviously play a lot of big pots against unbalanced fish more efficiently than a solver.
When I discussed this issue on Twitter, the following counter-argument often came up: the solver will crush opponents because it will bluff much more often and harder, forcing people to make expensive mistakes. I partially agree, but we all know that there are situations in which fold equity is close to zero – and in the solver world, there are none, and the machine will bang its head against the wall and hopelessly bluff into the strongest lines. On the other hand, there are small pots where amateurs often overfold too much – and regulars exploit this weakness much more often than the solver. So another question is who will win more without a showdown – a solver or a good regular!
Maybe you don't think my arguments are convincing enough and still believe that the solver will destroy NL25. Maybe you hesitated and think that there is something to it. I can't ask for more.
But why are people so worried about the hypothetical success of the solver? Why is it so hard for them to accept the possibility that the machine won't beat the rake? In the comments, many have entered the stage of total denial without any serious arguments. I don't want to offend anyone, but I just don't see where the extra EV will come from to make up for the lack of a hard exploit.
Probably, the point is that people find it very attractive to come to a winning game by simply copying the lines of the solver. However, this is a harmful and misguided concept that I urge you to get rid of as soon as possible. People tend to look for reliable support, to protect themselves from chaos. Uncertainty is scary. We need order, and we are looking for protection from the solver. However, think for yourself: can what the robot does against a strategy that no one ever uses against us bring maximum expectation? If you say yes, I simply do not understand your logic. It seems to be just a matter of faith.
Do not misunderstand me. I don't neglect theory. I think that theory is amazing, how cool! I've spent years learning from a solver how poker works. But playing at a real table is chaos, and it must be accepted as it is. Every hand, we play against an opponent with a specific strategy, not against the machine we practiced with last night. And our task is to quickly understand their differences.
Finally, let's discuss the empirical data. No, I didn't play 100,000 hands with a GTO hint, that would be unethical. However, I have training data in the GTO Wizard where player responses can be compared to solver lines – the program calculates the difference in EV between you. Believe it or not, I know people who can't beat NL5, but are fanatical about GTOs and are very close to solver lines – their decisions are only 2-3bb/100 worse than soft ones! It looks like being close to the GTO has little effect on your practical win rate.
We also experimented with a pair of solid 500 zoom regulars. Their results in the GTO Wizard were almost indistinguishable from the solver ones. Thus, being in their place, the solver would play only microscopically better, and this is even before adjusting to opponents. Most likely, the 500 zoom solver will not beat it.
Will he beat a much weaker limit (though with a higher rake)? Tough question. If you force me to answer, I would say, rather, no. 70/30, it would not.
