Would a Solver Beat 25NL? 

We need to find a dude who tested his RTA vs NL25 pool. He knows the answer.

I play 25NL recreationally. I also study every day. I am not incredibly intelligent so I struggle to understand the underlying principles of GTO solves sometimes. But I do my best. However, when playing I rarely emulate the solver. Instead, I try to kind of have a sense of what is correct then adapt/adjust that strategy to reality, using GTO more as a guardrail to my strategy. BTW, fish do fold. Fish do bluff. For me the key is recognizing the proper spots. Hand Reading, I think, is just as important, if not more important.

I am presently taking my time, digesting this content, contemplating my thoughts and understanding my motivations for commenting. This will take some time. I will be back later.

I coach a student (more of a friend) who's primarily a live midstakes pro on how to better incorporate GTO type concepts and theorem into their game. I like to explain to them that you have a game vs recreationals and a game vs other regs. - Vs recreationals you can do whatever you think is highest EV. Your objective here is to make money and not be balanced unless it's higher EV (rare). The decision points are specific player reads vs overall population reads of recreationals. I like to think that you can observe even bad regs and potentially learn good value lines to use vs recs. - VS regs : here you want to implement more of your solver theorem. Overall population reads of what most regs/player pool is doing in spots vs what a solver is doing. Where the difference is and how to correctly adjust and implement. A lot of this is what I call 'taking villains down the unknown parts of the game tree'. Specifically when people are mindlessly mashing range bet, where can you find raises with what parts of range and further, if you wanted to where could you deviate further if it forced many errors. etc. I recommend a lot of your videos as you have a systematic way of explaining concepts that I know but don't have concrete names for, so thankyou. PS In short you could teach a solver to crush the pool if you allow it to do machine learning against non-optimal villains. I massively advocate for actually overbluffing in many spots at low stakes as the average reg is both weak and greedy so they have massive gaps in their ranges.

Great work Pete! Carrot Corner continues as the best RU-vid channel

Learning what exactly better poker in terms of what the solver would do and why can help a lot of people get better by: bluffing more when they previously didnt, calling c-bets more when they didn't, checking more marginal hands and being less worried about getting outdrawn and making bigger value bets and bluffs. Then you can better understand how people often make huge mistakes.

Hey Pete! I’m probably not really your target audience but I enjoy watching your videos and this is a very interesting topic that I think even a lot of high stakes professionals miss understand. I play poker professionally on mid to high stakes and been around the community for nearly two decades now. So I feel pretty confident that I’m qualified to comment on this subject. However, I’ve never ever commented on a RU-vid video before, but let’s give it a try 😂 The first thing I will say is that I think it’s very close but I’m quite confident the win rate would be small if any att all. I could write a book on this but I will try to keep it as short as possible. The strongest argument for this is that although a solver output look extremely complex with a bunch of mixing everywhere etc. it’s actually not an argument for its performance in a non clairvoyant environment that playing vs humans would be. The only time the solver actually gains EV vs the NL25 player pool is when someone makes a play that has absolutely 0% frequency (lower EV then any of the valid lines). Actually there are tools like GTO wizard where you can upload your hands from a session and get an EVBB loss rate vs equilibrium. I’ve tried this and it seems like it’s only around 2-3bb/100 and part of that is even conscious exploits like folding river vs a nit or overbluffing a spot. As you mentioned, 6 max is mainly just automatic folds preflop over 100 avg hands. So to make up for the 8-10bb/100 rake will be hard even with plenty of fish punting it off and bad regs. Even the hands that we vpip are mainly SRPs where no EV loss from either player happens. And even if someone pure folds a pure call on the flop in a SRP vs a cbet the EV loss will probably not outweigh the 5% rake. Before I end this long post, I will give the solver some deserved credit as well. The outputs we are looking at is an extremely complex equilibrium game state that’s reached by clairvoyant counter exploitation back and fourth until no exploits are left. The equilibrium is extremely sensitive, meaning that as soon as the solver would know even a small deviation from it’s opponents, it would be able to max exploit that and drastically change it’s strategy. You can try this by for example remove 1 bluff combo of player A in a river spot and see what happens to player B strategy. IF the solver somehow was clairvoyant to player pool (or even more extreme, to every individual player) you can be damn sure it would destroy it! However a static non clairvoyant equilibrium output wouldn’t perform particularly well in a micro stake high rake environment. Hope it wasn’t too long to bother reading. I know you know all of this and mentioned some of it in the video. Just wanted to give my 2 cents on a topic I think is very misunderstood. It’s also a quite uplifting thing in today’s online environment to know because there’s so much talk on cheating and real time assistance.

One thing I’m struggling with is that you can include rake in your sims. Wouldn’t that make it more likely for the solver to beat low stakes? For the record, I agree that IF a solver could beat micro stakes it wouldn’t be for much because of the issues discussed in the video.

Ah, a deductive argument! Would still be cool if you gave the syllogistic form (premises and conclusion) If the premises do in fact support the conclusion in this way, the argument is said to be strong. Thus, a strong inductive argument is an inductive argument such that it is improbable that the premises be true and the conclusion false.

I think one important concept was missed: the solver can use totally whack sizes without losing precision (and many of them), which the pool will have no idea how to respond to. What if you add a random 2x overbet or 10x overbet size on the turn? How about a 10x jam on the river? You really think the 25NL pool can avoid making 10bb/100 mistakes against stuff like that? I doubt it. The solver can also execute ridiculous thin value 10% pot bets with random shit that humans can't really replicate. I think if you locked the solver at something like 33% pot, 66% turn, 2 sizes river, then MAYBE I could get behind this, because that's what everyone practices against, but as long as you let it really cook, I expect the pool will be blundering against it left and right.

the part that I don't understand fully (so therefore I could be miles off base is this: the solver is basically set up to play a perfect, unexploitable strategy . . . against itself. Or another player who is playing a perfect unexploitable strategy. All of its decisions to bet, check, call, raise and all of its sizing decisions are dictated by its "perception" (if you will) that its opponent is also playing perfectly. I am not sure exactly how this effects the solver when it is playing a 25nl reg or 25nl fish. but these players are NOT playing the "perfect" ranges and strategies that the solver would be assuming. I am not trying to say that the solver can't beat bad players. I'm sure it can because their leaks are so huge. But it is "optimized" to ply an "optimal" opponent. So, it would likely do better (make fewer blunders) against a 2kNL crusher than it would a 10nl fish. the crusher will never show up on the river w/ T2s and make a flush that the fish would chase. I see this over & over again watching streamers trying to "play GTO" against the microstakes. They frequently make assumptions that are great agains the solver, but horrendous against fish. hand reading is (still) a huge part of poker. and assigning "perfect ranges" on every street to bad players is not going to go well. I think this would be very detrimental to their chances of beating 25nl when rake is considered. now, if the solver could "learn" (not sure why the streamers can't, lol) and exploit, it would destroy these stakes. but, by definition, it cannot exploit. so, it had better get a (really good) rakeback deal.

GTO play isn't trying to exploit anyone, it's trying to be unexploitable itself. Big difference. My understanding is optimal play encompasses an understanding of GTO, recognises where opponents are deviating from that, and uses that to exploit them. A solver acting without any knowledge of the pool's tendencies shouldn't theoretically have any advantage whatsoever (imo).

Love the content, would you do video how to play small pocket pairs just like you did with AK.

Sorry but the question really is obvious. It is not obvious how a solver performs compared to a reg but the question is pure clickbait. Its just simple math: For anyone who used solvers or training sizes with solver solutions knows that even the best players make around 5-10BB/100 mistakes. Recreational players will make way way more. So the average player will make well over 30BB/100 mistakes in 25 NL... What does this number mean? Everyone who plays GTO against them will earn an equal share of these Mistakes minus the rake. Is the rake over 30BB/100? Very surely not. You may dispute the 30BB/100 number but I it is actually on the low end. The solver will never punt and just one punt can easily cost 10-20 BBs.

Hi Pete. You said that good regs win 3-4 bb/100. What stakes is this assuming? Is this same for 25nl or 50nl?

Wrong question. The solver works with the parameters you provided. GTO play and a solver (which is just a program like the calculator) are two different things. For example in the case of the pot vs the fish who snap calls the turn and you think you have almost zero fold equity on the river -> you need to node lock the river call range of the fish. If you think he calls with every pair+ (because he snap called so he must be tilted or sthing) then the solver will say you shouldn't bluff at all and that's it. The correct question would be can we beat 25NL playing perfect GTO without any deviations? And on that front I agree, probably we wouldn't be able to beat it but it's not hard to imagine why... because humans don't play perfect GTO, we all have different ranges in every branch of the decision tree. If someone would come up with an AI algorithm which can evaluate the opponent based on his/her stats (or if there is none then use pool tendencies) and based on these data recalculate the decisions in real time it would crush. And that would be the end of online poker. :D

Remember guys, poker solvers are infinitely easier to sell to people and you don't even have to offer up your own time as a coach, you just say study. These players are ultimately going to be easy to beat because at the end of the day, trying to play like a solver poorly will lose them a ton of money, mostly on the turn and river. The deeper the better.

Carrot poker is very quality tempted to check out the paid content soon

Your arguments remind me of the explanations in the 1980s as to why chess computers were not going to be able to regularly beat grandmasters. It turned out that humans just didn't understand that increasing computing power by a billion rendered the defects in the computers' game completely irrelevant. In 2019 the bot Pluribus played 6-max against a roster of five human pros and smoked them winning 5 BBs/100. I'm not sure if Pluribus was GTO or a trained AI but I don't think it matters much. The human team included Linus, Nick Petrangelo, Seth Davies etc so pretty strong.

MDA + Population tendencies is superior to GTO at low to mid stakes. Especially superior for live play.

Awesome video pete!

I remember when solvers came out and I was trying to hypothesize this exact point and got absolutely annihilated on 2p2.

fish actually overfold so your average reg will play worse against them

I do think that ‘Game theory optimal’ alone as a term applied to solvers needs to be clarified as ‘engine GTO’ with solver vs solver and ‘exploit GTO’ where as per node locking it gives the optimal response against human mistakes. It’s simply that we aren’t providing the full information to the solver and therefore by not giving this distinction we are suggesting the solver is inferior to humans when I’m sure bots adjusting to the above and calculating true EV would wipe the floor with humans. Especially when you could give AI mass data and it can categorise and exploit with more sophistication than humans. Yes there are timing tells and other things but we will lose the arms race eventually and I wonder almost if this anti GTO is just marketing to encourage the ‘feel’ players to keep playing. Wait a minute we need the fish - yeah screw GTO!

8:30 thats not true, it is possible solver to lose 6max. In 6max game you can have someone who is a rat who hurts you, hurts themselves but someone else makes a profit on it.

100% a solver would beat 25nl omg rake im so stupid. still probably but I definitely got owned

If you were playing rock paper scissors and throwing 33% of every option, and paying rake, you lose vs every strategy. But poker is not rock paper scissors. The question should be framed as how many big blinds is passive exploitation worth, and is that greater than the rake hurdle. The fish will overbet bluff when he doesn't need to to get the job done, he will let the bot realize too much equity by screwing up his frequencies, and he will use the hands with the wrong blocker effects to put in his ranges. But the bot will never take advantage of him, say, being a station. The fish can literally x/c down all of his bluff catchers (as long as he can actually beat bluffs) and they will all be zero ev calls, he can never make a losing call vs the solver because solver is always bluffing exactly 33% of the time for pot on river. So the fish can make any error he wants in terms of being face up, the only error that actually makes the bot money is just playing too many hands. The bad hands have to go somewhere and his range simply won't have enough equity at showdown to break even no matter what he does with it. The fish can also bet on boards that are range checks, basically just deposit money into parts of the game tree that are dead, where the bot would fold air if he had it, but that turn or whatever basically lets the bot get there with so much of his range that the fish is just jamming into the nuts a lot. So whether that ends up exceeding the rake depends on the rake and depends on how big of a fish he is. If he is the open-jam any 2 type of fish, the bot will fold everything but aces, but 1 in 200 hands he gets the fish's stack and 160 of those 200 hands would have been folds pre anyway. It is definitely possible to make a 50bb or an 80bb blunder in exploit-land, like when a Russian nit reg overbets the river in a 4-bet pot and his 4-bet stat is 3 so ak is not even in his range. Or you can try to move people off of rivered flushes by claiming that you boated up on the turn. There's another Scotsman weazel1991 who tries to do this GTO shit in low stakes and always checks his sessions to make sure he doesn't blunder in wizard, maybe you're talking about him. and he has a modest win rate in 12nl, mostly blue line, which is what I would expect, but when he moves to 60nl acr (the game I can't beat) then he starts making equilibrium calls of shoves versus a pool which is mostly nits and some GTO regs. Against that pool, when he's wrong he loses 120bb, some of which he does get back 4-bet bluffing these nits, and when he's right they're break even calls, but either way he pays like 10bb every one of those pots he wins. That's why there's as far as I know a tiny minority of profitable players in that game, but a significantly larger number of nominally losing players who break even between rakeback and the weekly payouts for the progressive rake race, which just acts as a tax on occasional players paid to full time grinders. Pretty sure weazel is a pretty good example of what you're talking about. I keep telling him don't pay off that shove you idiot and hes like "but they are sniping my stream so I have to play GTO" and maybe he's right. But he's getting "content equity" and I'm not.

Not necessarily disagreeing with you as a whole, but i'm not sure about the idea that the solver would lose out on EV because it didn't bluff when people were over-folding and bluff when people were under-folding etc. If you're saying that the solver is blundering by not exploiting, you're effectively saying that the solver is being exploited. We know that's not possible because it's pure GTO / a Nash equilibrium. That's what worries me about your argument. How to express this based on individual examples, maybe if you think of a player pool as a bunch of frequencies, like a solver output. The money lost by bluffing a calling station would be balanced by the times when you're bluffing a nit. I guess the frequencies of the player pool cannot deviate to a point where it would exploit a solver's strategy, because a solver's strategy is by definition unexploitable. But then even if you consider one player who's a calling station, bluffing them might be balanced by other nodes of the game tree. Like the calling station calls when the solver has value more often than is optimal, so it gains EV that way. I've kind of always considered it as a balance, when someone deviates from GTO, they are exploiting, even accidentally, but are also opening themselves up to exploitation. The solver naturally exploits these deviations. And another thing is that I've always considered Nash equilibriums as unstable equilibriums. So like if some is even slightly over-folding versus equilibrium, the correct play is to always bluff them. There's no difference in EV between bluffing them 60% or 80% or 100%, they all have the same EV. But I guess where this is iffy for me is that this maybe applies to only certain hands. I don't think I'm arguing that you should bluff them with any two cards, but maybe. I'm unsure of my understanding here. Either way, it's a fascinating thought experiment / discussion. I'm from a maths background, so I've always found game theory really interesting.

Hi Pete, I really loved this discussion! I think you're absolutely spot on as to of why some people ardently defend the importance of studying GTO strategies. For years there were discussions about how to implement different strategies or ways to play specific spots vs. specific player types, with many conflicting opinions, but no one really knew the 'correct' answer until solvers came along. Now solvers provide a great anchor point to aim for theoretically and that's a great source of psychological comfort that we can use to prop ourselves up emotionally, especially after horrendous sessions. Regarding whether solvers would have a big enough win rate to beat 25NL. I think you're absolutely right that it's probably very close but perhaps something I'd like to add is that, while solvers aren't capitalizing against huge fish with big leaks, a big advantage they have is that they don't make a lot of costly errors that humans are prone to do. Through tilt or even mis-identifying game flow dynamics that causes them to vear off massively from their standard strategies. Playing a very consistent solid style which I think many recs, myself included, struggle to do. Though, I guess strong Regs don't fall into this trap as often either! Thanks for the content.

I think a solver comfortably beats 25NL. I understand much of what you’re saying, but when I’m considering the EV of a solver, what actually should be considered is the play of humans rather than the play of the solver itself. The question is therefore, can the 25NL pool play 100 hands on average without making 8-10BB of theoretical mistake whilst playing an intentionally imperfect strategy from a theoretical perspective.

A couple quick notes: The EV loss figure generated by GTOWizard is going to be an underestimate because it cuts off once you make the first mistake in a hand. If you make a mistake on the flop, the EV loss is generated by assuming you have an optimal strategy for all future decisions. In reality you can and will make further mistakes in the hand, which will also be more costly since the pot is bigger. One ballpark way of estimating this might be to look at the average EV loss on each street and adding this to the EV loss of each hand with a mistake earlier in the tree. Obviously imperfect but better than nothing. I think this is important conceptually too--some hands players will be losing quite a lot of money on by just really misplaying a spot or board texture, and they'll do it across multiple streets. Those are the spots where I think the solver is really going to crush. 3 bet pots are the first obvious example that comes to mind. Humans at these stakes play these pretty badly at every street including preflop. I think the solver will make a lot of EV here by playing more accurately pre (flatting fewer 3b especially OOP) and then running over everyone, including the regs, on every street, by a lot. Next: I think this is a really interesting question to put in the context of an anonymous zoom pool. That takes away a lot (but not all) of the player specific reads and mostly forces you to play only against the population.

I think your appeal to authority at the end is not fallacious since they are experts in the field and you don't suggest that therefore your conclusion is necessarily true. Be careful not to confuse "deferring to an authority on the issue" with the appeal to authority fallacy. Remember, a fallacy is an error in reasoning. Dismissing the council of legitimate experts and authorities turns good skepticism into denialism.

The poor leaf 🍃

What you said at the start is correct. The exploitative bot that learns would make a much better player. If a solver is always playing with incorrect range assumptions then obviously it’s not going to have outputs that are not exploitable. We are constantly assuming ranges of our opponents, it doesn’t even seem like this should be a debate, go to any casino and find the 75 year old guy that has his ton of soup in the morning and call him down in a 4bet pot and see what happens 🤷‍♂️

solvers can easily account for rake structures as I am sure you know. Also, you must recognize that it seems to me that by definition GTO is unexploitable by any given strategy (that follows a few parameters. And I would assume that these solvers by now have approximations such that no human has deep enough ideas to exploit the inconsistencies the solver has with GTO itself ), hence, any union of these strategies also cannot exploit GTO play. Having said that, of course we know that solvers would be defending turns way too wide calling obvious value sizings vs the 25NL population, just as one example, but the previous point still stands.

I don't know too much about the technology behind solvers in a detailed technical sense, but my modest understanding is that they (either related to their primary functionality or just by having the capacity) run millions of iterations to determine a model for the most profitable decisions. I would imagine that it wouldn't be beyond the solver's capability at all to stratify in some meaningful way the changes in gameplay at various limits, perhaps by the limits themselves or changes in the frequencies of routes at said level, and then produce different optimisation decisions for the varying strata. In short, it could have different 'modes', such as 25NL mode vs. 1000NL vs. pure GTO mode which are tuned to maximise profits in the different environments. This would be reflective of a human's decision to 'never bluff fish' and 'play tight', but with a basis far more entrenched in powerful statistics--one that comes to mind for me is how often micro recs (and maybe regs...) will merge horrendously and barrel with a marginal value hand like 99 or JJ, then jam it in a panic when their opponent doesn't fold top pair. If the solver itself couldn't do that, I don't think it would be beyond the scope of some specific programming or additional software. Just thinking out loud and wondering what you think?

"This guy is pondering how he got here from outer space..." lol

Although I knew it was clickbait I still decided to watch half an hour of this rang and you really managed to convince me. I like your channel and you analysis, although I sometimes disagree. In this video you made so many wild claims falling into the same logic traps you criticise. You said it yourself "you don't know where the EV is coming from" but thats just it. you are ignorant and dont want to know. Thats where the video should have ended instead of keeping on rambling about complete nonsense. Your comparison are right, but what about all the hands against other regs? Thats where the EV is coming from. People wildly underestimate how many mistakes regs make

Hey, Pete. In your opinion, what winrate is possible on 25NL nowadays after rake in bb/100 ? I wasn´t able to find any 500K+ hand graphs on the web, so I just really have no idea. Everybody just share their 50K hands winning graphs (which means nothing) and that´s all 😅 Even eastyyy22 didn´t make anything spectacular playing online in 2022. I am kind of stuck at 25NL and I honestly don´t know what to think anymore. Thanks