Validity Of Solves Which Are Based On The Wrong Ranges
I watched a training video that covered 3bet-pots as the aggressor in position. The main discussion was how to decide on frequencies and sizings. The decision criteria were equity advantage, nut advantage, and nut advantage over time (whereas equity advantage apparently almost always lies with the 3bettor IP).
One board that was covered was something like Qh 5h 2h. The instructor mentioned that this was a board where Hero has the immediate nut advantage and keeps it on future streets. As a reason for having the nut advantage over time, he quoted that Villain has less offsuit broadways, like for instance Ah Qc (which he apparently "never has") and therefore less flushes if a heart falls OTT. The resulting strategy was betting with a high frequency and small sizing.
This leads me to my question. People usually mention that to exploit, you first need to know what the GTO strategy looks like. And that without such a baseline, you're basically just guessing if Villain is doing an action too often or too little (except for the obvious cases). This sounds very reasonable. However, what would a baseline, like the one being taught in the above example worth, if the assumed ranges are not appropriate. I could imagine that the strategy wouldn't change too much in the above example if Villain had a similar amount of offsuit broadways. But aren't there likely other scenarios, where assuming "wrong ranges" would make a big difference aka make my assumed baseline just wrong?
Do such gto strategies fall apart / lose their relevance once Villain plays a different range as the one the solve is based on?
20 Replies
Yes, which it's why it's always more important to know how strategies change as ranges get wider/tighter, as opposed to memorizing the strategy for a specific range.
If you add random crap then GTO should (in theory) reconfigure to exploit the crippled range. But in reality adding random crap to exploit a GTO player would only work out well if you knew the adapted GTO better than your opponent and could thus exploit their now imbalanced reaction.
Not impossible, and I guess that's where high stakes regs/crushers end up searching for EV. But if you're that good you're already using counter-exploit GTO to milk everyone who hasn't mastered GTO yet. Which is everyone. So why bother?
Yes, which it's why it's always more important to know how strategies change as ranges get wider/tighter, as opposed to memorizing the strategy for a specific range.
If you add random crap then GTO should (in theory) reconfigure to exploit the crippled range. But in reality adding random crap to exploit a GTO player would only work out well if you knew the adapted GTO better than your opponent and could thus exploit their now imbalanced reaction.
Not impossible, and I guess that's where high stakes regs/crushers end up searching for EV. But if you're that good you're already using counter-exploit GTO to milk everyone who hasn't mastered GTO yet. Which is ever
Keuwai's statement is accurate and eloquently simple.
@dude45, no. "GTO" cannot be exploited by definition.* It's possible GTO strategy could have less EV vs. a random strategy *in a specific node* such as this one when compared to the equilbrium strategy, however, it would then lose EV in other nodes such that the total EV difference is equal to or greater than zero.
@Ceres, "GTO" does not "reconfigure" or "exploit" it is a strategy that does not change based on the opponent--period.
*Only in collusion/cheating type instances.
Just coming back to this to help try to illustrate the point and more clearly answer the OP.
If you can imagine a situation where OOP preflop here only ever called with AA and folded everything else and was playing against the "gto" equilibrium strategy (which is NOT deviating in anyway against the opponent only calling AA), then the GTO player continuing to play the equilibrium strategy in all postflop nodes against the opponent that only has AA is obviously going to perform relatively poorly postflop. However, he will gain a lot of EV preflop due to the fact our opponent is almost always folding and never 4-betting.
Back to the OP: As keuwai stated it is important to understand how your strategy might change vs. different ranges compared to what you're typically studying (i.e. wider or tighter). In the situation you're describing where our opponent maybe is deviating preflop such that his range is wider/tighter, then you would want to also deviate a bit preflop either widening or tightening your 3b range, possibly adjusting your 3b sizing, or simply just deviating in the other nodes: facing 4b, or the postflop nodes as a function of flop texture.
While the ranges are incredibly important for solving for the nash equilibrium, if they are only a bit off set (slightly tighter or slightly wider), then the postflop statistics (which are a function of the ranges but easier to digest) are going to be more useful in determining how you deviate.
In your example, maybe your opponent is either a bit wider or tighter than equilbrium and in equilibrium vs. a small bet oop is supposed to fold some arbitrary value X at equilibrium. This X value being whatever is in the nash equilibrium solve the coach is reviewing. If your opponent is folding << X or >> X that is going to be more useful in starting to construct how you should be playing postflop rather than guestimating his range and how it interacts with the board... at least to a certain extent.
My GTO posting theory is to reel off a load of bollocks in the hope someone better than me chimes in with a superior answer!
Brokenstars is right on the money. GTO strategy is a constant strategy; it does not change no matter what strategy your opponent uses. What GTO is is a strategy that an opponent cannot devise a counterstrategy to that would increase his EV, and by implication reduce yours. The term “optimal” in it is misleading. GTO is most certainly not the optimal strategy in all situations, and it may not even be optimal in most. There is usually one or more strategies that will outperform GTO against a given opponent.
To get a better idea of what GTO is and is not, consider a hypothetical heads up game. You are playing an opponent who tells you his strategy - “I’m going all in PF with AA and folding everything else.” Obviously GTO is not optimal, and the optimal strategy is far from GTO. You should minraise ATC preflop and fold to a shove (unless you also have AA). There are 4 outcomes - 220/442 you are sb and opponent folds, win 1BB. 220/442 you are bb and sb folds; you win 0.5bb. 1/442 you are sb and bb shoves; you lose 2. 1/442 you are bb and sb shoves; you lose 1. Your EV is 327/440 bb = 0.74bb for a win rate of 74bb/100 - pretty good and much better than GTO
Now suppose your opponent is not stupid and sees the error of his strategy and starts adding non-AA hands to his range. He has reduced your EV if you keep playing the optimal strategy from before - he has exploited your strategy. You might come up with a new optimal strategy for his new one. He can then modify his strategy and you can further modify yours. Seemingly we are in an endless game of cat and mouse where we both can continue to adjust and counter adjust to exploit each other. Mathematics tells us otherwise though. We reach a point where we begin to have less and less improvement in our EV when we adjust. Eventually we reach a point where any further adjustment has zero effect on our EV. This is the Nash Equilibrium strategy (a much better name IMO), and is the one we normally call GTO.
Well, to know how to play flop vs someone with AQo in their range you would have to understand how strategies are built based on ranges which past a certain extent you can only do by having looked at a solver a lot.
One of the most important skills you're supposed to build when looking at a solver is strategy construction based on ranges, memorising specific strategies helps with speed but it's not as important of a goal and that also comes naturally with time
So what is it now?
@keuwai agreed that such strategy would fall apart once the assumed ranges do not match reality.
From @Brokenstars answers I take that a baseline strategy based on gto preflop ranges and gto postflop responses can still be used against a random live maniac without turning into a losing strategy as ev losses in some parts of the game tree of said strategy will be made up for through ev gains in other parts.
So what is it now?
@keuwai agreed that such strategy would fall apart once the assumed ranges do not match reality.
From @Brokenstars answers I take that a baseline strategy based on gto preflop ranges and gto postflop responses can still be used against a random live maniac without turning into a losing strategy as ev losses in some parts of the game tree of said strategy will be made up for through ev gains in other parts.
Your goal is to maximize EV... if your opponent is deviating, then you want to also deviate in such a way to maximize that EV.
But, yes what I said above is a correct statement... keep in mind a true GTO strategy encapsulates all possible sizes. Doing preflop solves are done via stating a lot of constraints... limiting bet sizes/raise sizes/stack depths and bucketing hand classes postflop in order to arrive at a pseudo-gto preflop range with the given constraints. These are all approximations.
Literally the definition of the GTO strategy is one that no matter what your opponent does he cannot increase his EV vs. that strategy.
If your opponent deviates from this strategy, then it will be possible to also deviate from said gto strategy such that your EV either remains the same or increases.
So what is it now?
@keuwai agreed that such strategy would fall apart once the assumed ranges do not match reality.
From @Brokenstars answers I take that a baseline strategy based on gto preflop ranges and gto postflop responses can still be used against a random live maniac without turning into a losing strategy as ev losses in some parts of the game tree of said strategy will be made up for through ev gains in other parts.
It would be a winning strategy, but a very lazy one. Not highest EV and very easy to improve upon
So what is it now?
@keuwai agreed that such strategy would fall apart once the assumed ranges do not match reality.
From @Brokenstars answers I take that a baseline strategy based on gto preflop ranges and gto postflop responses can still be used against a random live maniac without turning into a losing strategy as ev losses in some parts of the game tree of said strategy will be made up for through ev gains in other parts.
Yes and I agree with that. It really depends on what your starting point is - eg if the GTO strategy is to cbet entire range for a certain formation/board, but your opponent is deviating preflop by calling only AA, then any flop bluff would obviously be very -EV.
But what Brokenstars and aner0 are saying is that you would gain all of this EV back from your opponent's preflop overfold.
Agree with all your points. Just want to point out that the reason GTO is used instead of 'Nash Equilibrium strategy' is because true Nash has not been figured out yet, so solver software solutions are approximations. Calling solver GTO 'Nash' would be misleading. Calculating actual Nash Equilibrium for NL hold'em is quite
daunting and beyond the capability of current computers. Also, there maybe more than one strategies at Nash Equilibrium so referring it as a singular maybe incorrect.
Are you a football fan? If so, suppose you have a very consistent running back who averages 4 yards per carry no matter what the defense does. Alternately you can throw deep and score an 80 yard TD if successful but get sacked if the WR is covered and lose 10 yards.
If you run the ball your expected gain is always 4 yards. Suppose a prevent defense makes it 95% sack, 5% TD. A blitz makes it 50-50. If they play prevent your expected result is -5.5 yards. If they blitz itÂ’s +35 yards. You need to decide what strategy to play. If the defense is always blitzing you obviously throw deep. Throwing deep is optimal. Running doesnÂ’t lose its value if they blitz, but throwing is optimal.
Hopefully the analogy is clear. Running is our GTO strategy. No matter how your opponent plays, you get a constant EV from it. If you know that your opponent is playing a non-GTO strategy though (just like always blitzing in the analogy) you can find a better non-GTO strategy, like throwing deep in my analogy. The risk is that we are wrong about our opponentÂ’s strategy. If he really isnÂ’t playing the strategy we think he is, he can turn around and exploit us. If we arenÂ’t careful when exploiting we might not realize the change and wind up plying suboptimally ourselves. That is not a concern if playing the true GTO strategy.
Agree with all your points. Just want to point out that the reason GTO is used instead of 'Nash Equilibrium strategy' is because true Nash has not been figured out yet, so solver software solutions are approximations. Calling solver GTO 'Nash' would be misleading. Calculating actual Nash Equilibrium for NL hold'em is quite
daunting and beyond the capability of current computers.
Meh, I don't fully agree with this. "Full Nash" would involve letting solvers use every possible bet size, and right now that's too hard so we limit the available sizes. But you can run arbitrarily complex trees. It turns out that the marginal utility of adding more complexity to your strategy drops off extremely quickly. The gain between having say 5 available bet sizes and 20 available bet sizes is negligible.
Also, there maybe more than one strategies at Nash Equilibrium so referring it as a singular maybe incorrect
Yeah that part I agree with. It doesn't really matter for HU Chip EV spots since all NE would have the same payoffs. But multiway spots and non zero-sum spots like ICM/Raked pots create weird situations where there are multiple equilibria and some are worse for you than others.
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Do such gto strategies fall apart / lose their relevance once Villain plays a different range as the one the solve is based on?
No. The game starts preflop, not postflop.
You can't gain EV against GTO by changing your starting range. Any increase you'd make postflop would be offset by losses preflop.
If you plug in a non-gto starting range then you are effectively solving an exploit against that player.
Keuwai's statement is accurate and eloquently simple.
@dude45, no. "GTO" cannot be exploited by definition.* It's possible GTO strategy could have less EV vs. a random strategy *in a specific node* such as this one when compared to the equilbrium strategy, however, it would then lose EV in other nodes such that the total EV difference is equal to or greater than zero.
@Ceres, "GTO" does not "reconfigure" or "exploit" it is a strategy that does not change based on the opponent--period.
*Only in col
Thats my understanding GTO is unexploitable but i thought Keuwai was saying the GTO strategy would fall apart.
No. The game starts preflop, not postflop.
You can't gain EV against GTO by changing your starting range. Any increase you'd make postflop would be offset by losses preflop.
If you plug in a non-gto starting range then you are effectively solving an exploit against that player.
So if you were to replicate an exact solver strategy against a villain who utilizes ranges that do not fit the ones your solves assume, your strategy would still yield at least the same ev as if he were to play the gto ranges? Or it would likely yield even more, be because villain deviated from optimal pre-flop play?
It's hard to wrap my head around that, because all the significant bets are done on later streets. And on these streets the solver strategy chooses actions based on the composition of villains range and the respective actions villain takes with certain combos.
It’s like:
GTO-Doc: “My reasoning to call here is because we unblock hands xyz which are part of villains bluff-range ott.”
Rec: “But these hands aren’t even in my river-range.”
GTO-Doc: “Nevermind, it’s still a winning play.”
So if you were to replicate an exact solver strategy against a villain who utilizes ranges that do not fit the ones your solves assume, your strategy would still yield at least the same ev as if he were to play the gto ranges? Or it would likely yield even more, be because villain deviated from optimal pre-flop play?
It's hard to wrap my head around that, because all the significant bets are done on later streets. And on these streets the solver strategy chooses actions based on the composition o
The mistake the player needs to make to get there with a range that "throws GTO off" is equal or bigger than the problems the GTO strat encounters later. This is true by definition.
You can have the intuition that there's no way a preflop error could compare to a postflop error, but it's wrong.
Having said that, the whole discusdion is theoretical. Whether GTO was infallible or not you should try your best to play to beat your opponents by a landslide.
A street fighter AI bot could probably block and dodge absolutely every attack, but a world class human would get punched eventually. You need to throw punches yourself or you'll get overwhelmed
