River spot in 3! pot

Hi dayman,

You may post hands for analysis here, but only ones played on Replay. I apologise for the delay in replying to your question.


Why is easier than how. Why is due to the fact that as your opponents get better, you cannot play face-up and hope to do well. Fortunately, the game is a continuum so we can learn as we progress. We don’t need to be perfectly balanced since we will never be playing against the top 0.001% of players. Still, to keep an edge over the players we do face, its important to always know just a little more than they do.

I’ll try to look at the question some more over the weekend and address some specific points. @dayman and others can address this as well. In the meanwhile, here is a video from a tournament perspective that will explain how more theory oriented players look at the game. This is still highly exploitative poker but far more balanced than what we see in the average game.



Thank you @grapevine.

On the river, I would check back. The hand does have marginal showdown value and will win occasionally.

I think the river is a spot to bet small. If you hold an ace and bet big, you only expect to get called by worse from aces with lower kickers and maybe some 9s. However, having an ace blocks the worse calling hands, but does not block the folding or better hands. If you opponent is tricky, he will recognize that the ace is better for your range and check back some sets and two pairs. Notice your preflop 3-bet is quite small and your opponent may call with suited gappers, especially considering you 3-bet super light. Therefore, a small bet is more effective as it forces under pocket pairs to call and does not pay off two-pair or better too much.

With a small bet, you don’t need to have very many bluffs. I think you can easily find enough hands that have no pairs like broadways to bluff with. If you decide to use a larger bet size, I think bluffing is ok if the opponent will fold pocket pairs, although I still prefer checking for the showdown value it has.

I think 67s is a great hand to 3bet with. Unless the opponent is only open raising his nutted hands or drastically overcalls vs 3-bets, I would 3-bet 67s everytime BU vs HJ. When it does hit a pair, it is almost never dominated. It’ll often be second pair of worse, but unless there are high cards, it’ll often be best. Even if the opponent has a better pair, you still have 10 outs.

In addition, you are in position which makes draws much more profitable. The opponent will have better flushes, but that does not occur as often as you think with only 2 people. 67s also brings board coverage. When a low board comes, it no longer means you only have overpairs and overcards, making you much harder to play against. I like to include a variety of bluffs, including some that don’t have an ace.

I don’t think bluffs should be -EV. If they are, you are bluffing too much or are playing against a calling station. You should have enough value hands to make it difficult for you opponent to call down light. Sometimes, your opponent will have a hand and you will lose. Other times, your bluffs make it through. Overall, bluffs should be 0 EV or slightly +EV.

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The stakes are important to know. Is it 100NL on Pokerstars or 5/10 on Replay?

At elite stakes on Replay, I think your preflop and flop lines are ok, but your 3-bet size should be 13, to create some fold equity and with the UTG BB being in the pot. Pretty much nobody should be folding to 10.5bbs, and with 76s you should be happy just to get a fold pre.

The flop is tough because you have a few backdoors and a bit of SDV, but not a lot of either. So betting is tough because is it a bluff when you have middle pair? Your size is fine, but because of your small 3-bet, villain can have basically anything.

It may not be optimal, but in this spot I would probably bet the turn (since you’re repping an overpair+) and if called check back the river, just because you get more information from another call or re-raise on the turn than from going for a bluff or thin value on the river.

As played, just check back the river. In my opinion you aren’t effectively repping a lot of value, so you could get called down by 9x+, and since villain can call your small 3-bet wide I would give them more sets/two pair/straights than I’d give you, so you can avoid the slow play. I don’t think villain is heroing you with 66 or worse, but they will call with most hands that beat you (9x+), so you don’t really gain much by bluffing with marginal showdown value. You could definitely have played some monsters this way (86s if you have 76s), but you aren’t telling the most compelling story.

At first it seems like the A on the river is good to bluff, but I think villain is equally likely to get to the river with Ax as you are. They would easily play this way with AJ or A5s, again based on the 3-bet size. Calling 3-bets out of position with less than premium hands is a dicey proposition, but they should have plenty of straight up equity to call 6.5bbs in a 17bb pot. It is +EV for them to call with 28% equity (if my pot math is correct). So, even if they give you QQ+/AK, they could call with all pocket pairs, suited connectors and gappers, and suited Ax. Of course they are OOP and maybe at a slight range disadvantage that creates reverse implied odds and makes it tough to actualize their equity, but if they know you can have suited connectors or other “bluffs” in your 3-bet range then they can comfortably call with almost their entire opening range. Using EV calculations and equity is not an accurate way to determine strategy (as ranges are unknown and equity can not be actualized), but it is a helpful way to determine what ranges make sense and when it can be profitable to bet/bluff.

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I would be very cautious about doing anything 100% of the time. Now, I don’t know what ranges you are assigning to HJ in the games you play but for online 200NL+ games, 7/6s is not a 3! BTN vs HJ. 7/6s falls into the flatting range vs population HJ opening ranges (assuming a 3x open and 5% rake).

If I have the chance later, I’ll post a slightly modified but solved BTN vs HJ 3! range (proofed through Monker Solver).

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I’d be interest to hear more about this. From what little I know, it seems like the game has evolved a lot in the past year. My default would be that you are 3-betting suited connectors and small suited Ax a lot of the time in a relatively high level game (though definitely not 100% for pretty much any action). It seems like the tendencies are moving towards seeing more flops rather than going through as many leveling wars pre-, but that could be totally wrong… If that is the direction, what is the mathematical/logical reason for it? Is it just better players trying to emphasize their postflop edge by not getting pushed off their bluffs pre and having a range that hits more board textures or is there more to it?

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This is actually for a 2.5x open and a 21.6% HJ opening range in a 5% raked game. It is not the actual solved range because this format does not allow me to input frequencies. Therefore I simplified it somewhat but kept the ratios and board overage about the same as it would be for the perfect solution. This range will not sacrifice much EV vs optimal.

I think that the game is evolving rapidly as people become more familiar with solvers and aggregate more actual data. Monker Solver also contributed a lot to preflop ranges.

From my personal experience, when I was introduced to GTO, I fell in love with it. I went down the rabbit hole, kept going until I hit oil and then just kept going. It fascinated me to the point where I didn’t notice how much value I was giving up in actual games. Only after realizing that the theory was not a real-world solution did I stop misapplying it. Now I am using theory to find maximally the exploitative lines available vs populations and players. For example, if theory says to 3! K8s vs a good opponent who will fold better Kx hands but the player I’m facing won’t, then I have to simply fold it. Insisting on making the 3! just because that’s what theory tells me is right is an error - one that I made for quite a while because I was devoted to the theory and lost sight of the actual game.

I say this because I doubt I’m the only one who has gone through this learning process. Computers are spitting out solutions and the inclination is to take them as gospel. Comparing optimal play to how people actually play reveals EV loses unless we adjust to reality. My new favorite thing to play with is the node-lock function on Piosolver - I take optimal solutions and then go back in to edit the trees for how people actually play.

I think its a matter of defining bluffs preflop. Playing certain parts of our range in position vs various opening ranges is a great strategy. I’d rather be pushed off Q9s than 7/6s so I am more inclined to 3! Q9s as a bluff but flat 7/6s. Same reason I’d 3! KQo but flat KQs in position. Its fine to get pushed off hands that play miserably but not ok to get pushed off hands that perform great in position.

It is almost discouraging how close to being solved even a game like NLHE can be, but it is certainly interesting to consider these lines in relation to real world behavior. I guess there is so much data out there that the AI can go beyond a theoretical optimal play and adjust its play to particular opponents or player types. On some level it boggles my mind that a computer could ever be that good because there seem to be many different ways to play well. Some players can take almost any hand and be unreadable while being extremely polarized or taking a more moderate approach. The approach that wins consistently against really good players can be disastrous against fish. It seems like the dataset would have to be tailored to the exact population of interest. And looking at how much the game has changed even in the past few years that data must be shifting all the time.

Just to give an example, you mentioned flatting hands that hit boards well and bluffing hands that don’t, but then a good player could recognize that you have a lot of 2 card flushes when you flat or that you have fewer 2 card flushes when you 3-bet. So doing that is really exploiting opponent weaknesses at recognizing your betting patterns rather than making a sort of unexploitable play. Seems like I need to check out a solver to see what exactly it is doing. Is it just taking EV calculations from identical spots in particular databases? It seems like the assumptions (21.6% HJ, 2.5x open) are very important inputs and the entire decision making process would change for a 2.3x open or a 23% open range, which is all starting to make my head hurt lol.

I work with large datasets outside of poker, and there is definitely a zeitgeist of data being the answer to everything like electricity or radiation might have been in previous centuries. When thinking about statistics I am wary about garbage in creating garbage out, and specifically whether it impairs the human decision making process. For example, you might de-emphasize some very good evidence (timing tells, external tells in live games, sizing tells, even the preceding hands) to try to fit a balanced or particular exploitative approach. I am not disagreeing with you at all (and you seem to be making a similar point about not relying on the theoretical), and there is evidence of AI systems beating very good players. Just need to see what data is out there. I imagine you have to pay for the good stuff?

Not quite - If you look at the BTN vs HJ range I posted above, the number of suited hands I’m flatting with and bluffing with is relatively equal. It would be closer to equal if frequencies were included. Its all about constructing the ranges so that we don’t have too few or too many of any 1 particular hand strength in any category.

The game changes and the data changes all the time. Populations have tendencies and those need to be accounted for when developing a strategy. You also have to be willing to change your assumptions based on new evidence. A good example is what’s happening online now because live venues are closed. Online play is far more technically advanced than live play and so we construct strategies to account for that. If you introduce a whole bunch of new players coming in from live games, you have to adjust back.

You know better than most that the outputs are only as good as the inputs. We all have access to our own hand histories to use. In theory, datasets are not supposed to be bought or sold but in practice they are. We also get data from stables if we happen to be involved with running one. Crunching the data is beyond most of our means. Not everyone can get time on a supercomputer like Michael Acevedo did. Most of us have to run approximations or work with limited information just based on the computing power we have available to us.

I wouldn’t be discouraged at all with how the game is developing. The fact of the matter is that almost everyone who plays this game is pretty bad at it compared to optimal. 99.99% of people who play will never get much past ABC poker. Only people who are making their livings at this game (and the odd ducks like myself) are able to spend the time required to study it to any high level. The sheer amount of information makes it impossible for the vast majority of players to even begin to digest it. So long as bots don’t take over online, I think the game will be fine. Also, even if we don’t have access to all the data and the highest end strategies, if we can bring ourselves to understand some of the theory, we will be far ahead of almost everyone else. If I’ve learned anything in this game its that we make money by being exactly 1 level ahead of our opponents and putting in volume.

Outputs are very sensitive to inputs. That’s why its more important to understand the why than the what. If we understand why, we can adjust the what on the fly.


I really wish that I could speak this language. I can get by in Italian, Turkish, French, Spanish and German. I even speak a little Russian and Portuguese but I have no idea what you just said.

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And this is the crux of it.

And this is where it all starts to fall apart. 21.6% HJ open range? You can’t justify anywhere near that level of precision. In a normal distribution, 95% will be within +/- 2 standard deviations of the mean, but that translates to a huge difference in ranges.

The Ai guys have been trying to apply GT to poker for at least 25 years. Some of the big universities have dedicated teams who have been working non-stop on the problem, and they keep running into the same brick wall… player modeling. People are unpredictable. You may never play that 21.6% guy, he might not exist. Even if he does, he probably won’t be playing a totally static strategy.

I’m not knocking the “GTO” guys. There are some interesting concepts coming out of that school, and some goofy ones too. I would be willing to bet the vast number of them don’t know the first thing about game theory though. For example, how many can manually do a regression analysis using multiple iteration elimination of strictly dominated strategies? How many could do it for a 4 way NLHE hand?

Feed it to fropzirra and take whatever it poops out as gospel. look ma, I’m GTOing!

Warlock, you are the very first person i have seen that is actually starting to get it, bravo!

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Those who have fallen down the GTO rabbit hole would be well served to climb out of it as fast as possible. If you want to stay one step ahead, you have to move beyond GTO,Yes, the theory is important, but it’s only one part of the game.

Truth be told, the game hasn’t changed at all. What HAS changed, however, are the ways people approach the game. What you should be studying is PTO… People Theory Optimal. Mr Warlock hinted at this when he said, “if theory says to 3! K8s vs a good opponent who will fold better Kx hands but the player I’m facing won’t, then I have to simply fold it.”

Does this not imply that the people are more important than the theory? The theory itself is far less important than it’s application., and the application is largely dependent on factors other than pure theory.

Mr Warlock said, “.the outputs are only as good as the inputs.” Yes!!! So why not attack and exploit that at it’s root? If I employ a series of “range distortion” techniques that make it virtually impossible for you to accurately estimate my ranges, how can you possibly determine an “optimal” strategy against me?

Sorry, but the cutting edge of poker is not GTO. That well is about dry. If you really want to stay one step ahead, look at what the AI guys are doing. A good starting point would be Carnegie Mellon University’s “Pluribus.” AI will change the way poker is played just like AlphaZero is changing chess.

For example, “Pluribus placed donk bets far more often than the professionals it defeated.”

And, 'There were several plays that humans simply are not making at all, especially relating to its bet sizing."

This is an advancement in application, not theory.

AI beats professionals in six-player poker

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What seems like it would be most helpful (and maybe this is what solvers are doing?) is presenting data (EV data or frequency data) for how other players have played similar spots. I imagine something similar to a chess database, like: HJ opens of 3.5x at 100NL get 3-bet X% of the time by the BTN, SB, BB, get flatted X%, go multi-way X%, get folds X%. This would be really cool for turn and river situations in particular, but the more streets, the more the tree can branch and the harder it is to make meaningful inferences (e.g., a timing tell could make all other data meaningless).

An EV estimate would also be helpful, like previous opens of 87s have generated a -0.1BB/100 win rate at 100NL over the past year. Tables like that do exist for fixed limit, but don’t really apply to no limit. Instead I use raw equity to get a sense of it, but obviously hands play so differently it isn’t that useful, especially accounting for fold equity or implied odds.

The best thing would just be a regression model that automatically inputs the spot into a relevant database and tells you EV and distribution of opponent actions for your exact hand for different actions and sizing, but that would be hard to implement in real time. It seems like I’m imagining rather than maximum unexploitability (GTO), using data-assisted decision making for maximum exploitation. But then again, if everybody suddenly knew how the majority of players act in a given situation it would just up the thinking by another meta-level.

Anyway, it doesn’t really matter when I’m sitting here on Replay 3-betting JJ and getting two callers OOP who both have suited gappers, going for stacks with both while ahead on the flop and then losing… Exploitative play doesn’t need to be data science.

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This is why datasets are so important. No, I can’t tell you specifically if player X or Y is working off a 21.6% opening range from the HJ. If I have a few million hands as a sample, I can say that the population is doing this and have a high level of confidence. Using the population numbers gives me a baseline to work from. Adjusting to specific players based on observations is easier if you have something to work from. Otherwise its all guesswork.

I don’t let the perfect be the enemy of the good. If I can gain insight through solvers and through AI and through exploitative strategies then I’d be nuts to ignore any of them, even if none of them give me a complete picture. When I was doing my doctoral work, my focus was on explanatory power of equity valuation models. When I came up with a model that had ~50% explanatory power, I was not laughed out of the room because it couldn’t explain everything. In fact, since the best model in use at the time had an r2 of .42, I had people knocking my door down for access to what I had done. 50% isn’t 100% but its a hell of a lot better than 42%.

Thanks. It has been quite a journey and I don’t regret any of it. I have said before that I would be content to study the game whether or not I ever played another hand. I also love playing the game and would continue to play it even if I never saw another solver or database. Fortunately for me, I don’t have to choose 1 or the other and can continue to enjoy both aspects of the game.

Spend some time with Piosolver and I think you will see much of what you are looking for. Its a really cool toy if you geek out about this stuff like I do.

But the data reveals what the most profitable exploits are. The game is so complex that finding the best exploitative strategies vs any population/player is impossible to work out without the use of a solver. This is why the node-lock feature on Pio is so great. No, it probably doesn’t matter for playing against pools that make enormous errors all the time. It starts to matter as edges decrease as the pool gets better.


The perfect is only the enemy of the good when zero facts are in doubt or dispute AND there is unlimited time to consider the objective AND that objective is attainable. Otherwise, it’s a crap shoot. And always will be. But it works pretty well for material supplies (neither too much nor too little) and it sounds wonderful.

PS I learned this from an old gunnery sergeant, lo, decades ago.


I like your thinking, SPG.

GTO is an undiscovered country. No one knows what GTO play is. Anyone who claims to doesn’t know what they’re talking about. I guess it’s a mouthful to say “Game Theory Optimal Hypothetical”, or doesn’t sound enough like a cool car.

What “GTO” players really mean is that they try to play a math-based strategy, in order to ensure that they are not exploitable by players who play a strategy based on psychology, or, well, anyone. While invulnerability is desirable, what ultimately matters is your win rate and bankroll management. The stated goal of GTO strategy is not to lose – it is not designed to maximize profit.

Fundamentally, the decisions involved in how to play your hand need to be rooted in math as well as understanding your opponent’s approach to the game, finding their weaknesses, and exploiting them to maximum advantage.

The toughest players are those who hide the true strength of their hand very well, who are unpredictable, and who keep you guessing, off-balance, and uncertain. But when you can’t figure your opponent out, the answer is to retreat back to playing a mathematically sound game. And when you don’t know your opponent yet, the way to start is from a mathematically sound game. And if you just stayed on a mathematically sound game all the time, you’d certainly do alright, as long as there’s enough people playing imperfect poker that you can beat.

Math is most important at showdown, where hand strengths are compared. Ahead of that, it’s pretty much all psychology. But really, it’s psychology built around math, and if you peel back our skulls and look at the cards face up, it becomes evident that math has been important at every stage building to the (possible) showdown.

If you can close the hand without a showdown, psychology is all you really need.

But you’re going to have to showdown in a certain number of hands, probably a lot of them, and certainly in a tournament at least the last hand you play. And to get to a showdown with a strong chance of winning, it’s necessary that you get there with a hand that has what they call showdown value. You may or may not get the pot, but you want to have a good chance at making the best hand when the river card is dealt. (This isn’t news to anyone, is it?) And it’d be nice if the pot were a size that was worth the chance you took to win it.

To make things ultra simple:

Whether to continue in the hand, you should evaluate:

  • The current strength of your hand.
  • The potential strength of your hand, relative to the theoretical nut hand.
  • The odds of your hand improving by the river.
  • What hands currently beat you.
  • What hands potentially beat you.
  • The odds of your opponent potentially having one of those hands.

The calculations above are mostly straightforward, but time constraints being what they are, I think most people memorize the most important probabilities and use approximation.

How much to bet or call is a lot harder decision to make, but it largely boils down to:

  • How likely you are to have the strongest hand at showdown.
  • How much your opponent will be willing to call with a hand weaker than what you have. (Value betting)
  • If you’re unlikely to have the strongest hand at showdown, how likely a bet size under consideration would get your opponent to fold a stronger hand. (Bluffing)
  • If you’re probably on the strongest hand now, but might be likely to be outdrawn at showdown, how likely a bet size under consideration would get your opponent to fold a weaker hand drawing to a stronger hand. (Protecting)
  • What hole cards you think your opponent believes you would make the considered bet with. (“Level 3+” play)

The “would get your opponent to” part of all of those decisions is psychological, but your opponent’s psychology is going to be influenced to a greater or lesser degree by all the math involved. The closer everyone moves to GTO, the better GTO thinking is at approximating your opponent’s psychology. Of course, whatever anyone happens to think GTO is is an approximation, and it’s a bit like a game of darts – everyone claiming to be a GTO player is at a point some distance and direction from the bullseye – but no one is entirely sure exactly where the bullseye is.

But for everyone else, you want to deviate from GTO in order to exploit mistakes and weaknesses that you observe in your opponent’s game because they are themselves not playing GTO.