if there is nash equilibrium in NLH, does it make NLH the same game as rock paper scissor(i know its million times more complicate) ?

for example, in the game of rock paper scissor,let's say you earn 1 point when you win, you lose 1 point when you lose, and when you tie, you earn 0 point. in this case, if you do rock 1/3 the time, paper 1/3 the time, scissor 1/3 the time, you are playing pure GTO, no matter what your opponent do, you will always get 0 point in the long run. however, if your opponent doesn't use the same strategy as you do(pure GTO), you can change your strategy to exploit him, but at the same time, you are no longer playing pure GTO, which you are not at nash equilibrium anymore.

in conclusion, if you use pure gto, no matter what your opponent do, your EV should be 0 in the long run?

Is this the correct understanding of GTO and Nash Equilibrium? please leave your common

update:

I talked to someone in a group chat and found out that, unlike rock paper scissor, there are dominated strategies in NLH.(it basically means the strategies worse than the others). for example: all in with 27o all the time and fold any other hands. you will lose against GTO strategy.

dominted strategy don't exist in the game of rock paper scissor. no matter what strategies villain use, both of you will have 0EV as long as you play GTO strategy.

my guess is that NLH and RPS have different type of nash equilibrium

I just had another thought on GTO.

any imbalance, or dominated strategies, are based on the deviation from nash equilibrium, which is GTO strategy.

In another word, when you try to exploit villain, what you do is find his leak, which is where his strategies deviate from GTO strategy. and change your strategy to exploit him. but everything is based on the understanding of GTO

is this correct? if so, does it make GTO the only strategy that work? (if everyone is smart enough like super computer)

This has been discussed a few dozen times here.

Short answer: Unlike rock/paper/scissors, most deviations from GTO will actually result in a loss of EV against GTO in poker.

This has nothing to do with the existence of dominated strategies though, you don't have to play a dominated strategy to lose against GTO. In a game theoretic sense there are few actions that are actually dominated in poker. An action is (strictly) dominated if there exists another action that always has a higher EV, no matter what the opponent's strategy is.

For instance if you are in the BB and SB open shoves for 100bb. Calling with a hand like 72o is NOT a dominated action by that definition. Clearly there are some strategies that SB could play where calling with 72o would be better than folding, e.g. if he is only open shoving with 62o.

Adding to what plexiq said, the way you'd lose money vs a GTO villain is by making plays they'd never make. Any play they'd never make is one with a higher-EV alternative.

If you deviated from GTO while avoiding all those strictly bad plays, you'd break even against GTO because your deviations would be limited to those where where you're taking equal-EV lines at imbalanced frequencies. However, you'd be exploitable by someone who capitalized on your imbalances.

(If plexiq disputes anything I just said, take his word over mine.)

I think this is why the current popular strategy of betting small with your whole range on the flop as preflop raiser in heads up pots is founded in the false belief that it's not exploitable. i think it's very exploitable, but solvers don't recognize this as being exploitable because of how the comaximally exploitive strategy pairs are formed.

What do you mean?

ive posted before in a thread about cbetting your whole range for a smaller sizing than optimal and i responded that i thought it was exploited by more frequent flop raises and more frequent flop continuation in general as the big blind. they said something like "the solver says its only exploitable at negligible rates" or something to that effect.

my position now is that the machine isn't going to find the maximally exploitive strategy vs (insert deviation here). its finding the comaximally exploitive strategies.

as a test, you could have the big blind lock all of the hands in range that use mixed strategy on the flop as either (call or raise vs the cbet). then see how exploitable the solver thinks the big blind is from the flop on.

if theres not a huge margin for exploitive profit given these conditions, then I think it would stand that the solvers don't know the profitability of the maximally exploitive strategy.

If you lock the solve in one strat for player A, then player B will adopt the maximally exploitative strategy. I'm still not sure what you mean but when the solver says exploitable for x then x is the maximun ev you can extract indeed

the maximally exploitive response vs deviation is not the same strategy as the nemesis strategy vs deviation.

if you're right,, solvers must be capable of both finding maximally exploitive strategy in addition to finding the nemesis strategy vs any deviation.

can you look up both strategy results? if not i'm still skeptical, but have been terribly wrong before and will be again.

OP - to answer your question:

GTO will profit against suboptimal play. However, you can make more profit by making exploitative adjustments to take advantage of your opponent's mistakes. Keep in mind, however, that this opens you up to counter-exploitation.

Your logic goes like this: The GTO strategy for rock-paper-scissors gains nothing against any counter, therefore this must apply to everything else. But look at any strategy game, chess for example has a GTO solution that can be approxmiated by software. Clearly a GTO chess strategy will destroy a suboptimal strategy (try playing a computer if you don't believe me).

Here's a helpful article: Does GTO play make money against bad players?

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Can you explain the difference? I thought the nemesis strategy is the same as the maximally exploitative response?

Solvers always solve for the highest EV play. This means if you lock one player's strategy such that they can't adjust (on one or several nodes), then the solver will always play the maximally exploitative strategy against it.

If both players are unlocked, then they go back and forth trying to exploit each other until something near Nash Equilibrium has been achieved.

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Regarding the small flop range bet, I think it's efficient (in certain situations) because it gives away the least amount of information about your range. IMO this play is only really useful when your opponent will struggle to defend often enough. It's a highly exploitable play in some situations.

the nemesis strategy is one vs which the deviated strategy may not increase ev by changing its strategy with future actions.

the maximally exploitive strategy is the one vs which the deviated strategy has counter exploitive options that may increase ev if deviated strategy changes its strategy with future actions.

sorry the wording is so cumbersome. just waking up.

this video analyzes the difference:

https://www.youtube.com/watch?v=xfMmaWO42o8

Are you referring to minimally exploitative play vs maximally exploitative play as discussed in that video? (It seems with nemesis strategy you mean his definition of minimally exploitative. If he introduces a different definition for nemesis then please provide a rough timestamp.)

What Lezaleas was referring to is actually the "minimally exploitative strategy" as defined in the video. You lock in some range or ranges of a player and then calculate a Nash equilibrium for all the unlocked ranges. This is the typical usage scenario in solvers. The player with the deviated strategy can not increase his EV by changing actions other than the locked/deviated ones specified earlier.

The "maximally exploitative strategy", as defined in the video, would lock in the entire strategy of one player (including any deviations from GTO) and then calculate the best response for the other player. So one player would remain completely static with their strategy and the other just extracts the maximum EV possible. This would be a much less common thing to do and may not be possible with all solvers / or would involve a lot of manual locking.

yes. any nemesis strategy by definition guarantees minimum ev of zero.

right. so when solvers report +x ev exploitability, is this a measurement of maximal exploitation or minimal exploitation?

If they display +x EV exploitability for a solution as a measurement of the NE solution quality, ie the Nash distance, that should refer to the maximum EV any player can extract by unilateral changes if all other players stay static. That would correspond to the "maximally exploitative strategy" definition of the video.

(There's a few caveats here you need to be careful with: Typically you calculate the exploitability within the game/betting abstraction, not for the full game. If you only allow a certain cbet size in the calculation, and no alternatives, then a typical exploitability calculation will not consider any EV that may be gained by using a different bet size.)

Ok I stand corrected. Thanks guys.