For me, the nash equilibrium has been a very confusing concept, mostly due to conflicting information found on the internet. However, I found one source that seemed to clear things up a bit but before I take this understanding as gospel, I want to run it by the forums to make sure I'm understanding how to apply these concepts to real world poker.

According to this article:

1.) nash should only be used as a starting point, a baseline strategy. This is especially true with higher than 10BB's between the 2 players. If the BB's is 10 or below, then you should hold more firmly to nash but still deviate when an opponent is overly loose or tight. So in reality, nash is only optimal when an opponent is also using the nash chart. If the opponent starts deviating from it, then I also need deviate and try to exploit my opponents weaknesses (as exploitable strategies are still the most optimal strategies in poker). But if my opponent goes back to using nash, then I must also in order to avoid being exploitable.

and

2.) while nash might not always be optimal, it will always still be unexploitable when used, meaning you can't be -EV when it's used.

Now number 2 is one I'm definitely more unsure about but again if anyone can help my understanding be confirming or denying anything about my 2 points it would be much appreciated.

1: 100% correct
2: 66% correct.

Last part (cant be -EV) is not true. For instance if your opponent calls too wide. A nash shove might actually be worse then a fold, and is therefor considered to be -EV. (This is especially true on bubble spots vs calling station)

Re point 2, the biggest issue the concept of -ev.
-ev is a fine term, but lets be clear what it means, that is to say more correctly not -ev but in fact -ev compared to what?

Shoving nash will always be inexploitable.
So long as you shove the whole nash range.
That does not mean that it's the most +ev thing to do.
If there's a spot where nash btn shove range is say 35%, but actually you 2x or limp AA-TT and AK, but still shove K9o and all the other worst hands in the range then those shoves are no longer inexploitable as the blinds will now be correct to call wider than nash as your range is weaker, and by doing this they are exploiting you, the bottom of your range will become -ev compared to folding as the 1st responder correctly points out.

All in all, I'd honestly advise you to look at nash as a starting point, then work really hard on developing an understanding where you can make more $$$ by deviating from nash - this is where all the edge is. You aren't going to make any money by using nash all day because you won't exploit people hard enough to beat the rake then still make a profit, it'll be sub optimal in almost all cases. GL

1. You don't need to adjust from equlibrium to beat your opponent, you would still easily beat whatever adjustment they make, assuming you're playing an equlibrium strategy. But yes, if someone is deviating from equlibrium and you have a good idea in what way they're deviating from it, it makes sense to make a small adjustment.
Also, nash charts (by this I'm guessing you're refering to push fold charts) are only equlibrium strategies if the only option is push all in or fold.

2. Yes, but if you're refeering to push fold charts they aren't equlibrium for any spot where either a limp, min raise or any other size is included in a NE strategy(This is probably the case for anything over 9-10bbs ring, and about 6.5bbs HU).

"You don't need to adjust from equlibrium to beat your opponent, you would still easily beat whatever adjustment they make, assuming you're playing an equlibrium strategy"

This would be true in a rake free cash game, but wouldn't be true in any non winner takes all SNG format.

GTO is never -EV (not including rake). That is why its called GTO. Sure there are better ways to exploit players that are very poor at poker but GTO is never negative EV.

Not only does this not add anything to help OP as almost nobody spends any real time playing rake free sng's, it's also a demonstration of how badly us sng players understand GTO, and what it means in most practical scenarios.

There are TONS of SNG spots where huge chunks of a nash pushing range will become wildy -ev if the BB is psychotic and calls way too wide.

This is a common misperception and can easily be shown with an example why it is:

You are facing an openjam of your opponent with 10bb eff. He, for whatever reason and however unrealistic that is, decided to only jam AA. Calling any other hand than AA is now obv a worse response than folding it (we do define -ev as "worse ev than folding" here, right?), altho a lot of these hands are better called than folded against a nash equilibrium jamming range.

What is true tho, that if you play every hand according to your push/fold nash equilibrium chart (and your opponent lets you do this by never limping, 2x/3x,... ; so this is kind of a toy game), you are guaranteed to overall not be losing in ev to your opponent. That is not the same as all individual decisions being "+ev".

GTO doesn't refer to a single hand against a wildly unbalanced player, I agree that you would have way more +EV in this single hand by exploiting your opponent by always folding to their shoves. GTO Nash tables are a balanced call and shove range that cannot be exploited by the opponent over a series of hands and will have greater +EV over the course of a hyper sit and go than the player who only shoves AA (which he only gets 4.5% of the time). Both GTO and Exploitative game play will crush this player. Exploitative play (folding to the rare shove) will crush this player much quicker tho.

You don't need to explain to me what GTO means
Thing is: Ppl commonly make the mistake explained above.

And no, depending on the games u play gto ranges are not going to "crush" your opponents but maybe largely "wrong". Imagine a realistic scenario where u are on the bubble with recreational players. Anytime u jam your gto range into the dude who calls too much or call your gto range against the guy that jams not enough, u are spewing ev to the players not involved. That your opponents making the "wrong" jams/calls suffers does not necessarily mean u are gaining from it unless we're talking HU.

I don’t know if I’ve seen this concept before explained quite like this but here goes.

Think of 2 forms of EV—Hand or situation EV and Game EV. The former is for a defined hand or set of hands while the latter is for the total game, all hands. GTO is designed to yield a zero Game EV if both players employ it in a heads up game, assuming no rake. It does so by maximizing Hand EV. Clearly there are some hand situations that are negative EV for the GTO player (villain has a royal flush, quad aces, etc.). So, while individual hands may have negative EV, GTO still guarantees that Game EV will never be negative.

This thread is a festival of fails:

-talking about "GTO" without specifying that he thinks about the "push/fold subgame"
-"GTO is never -EV"
-that example when GTO is -EV when he only pushes AA and you call
-almost nobody spends any real time playing rake free sng's

They rake hands in SNGs now? Do they take out your tournament chips every hand?

Ofc you have to consider rake in SNGs, just because its a bit more abstract...

I feel I learned a lot now you quoted a few things you don't agree with - without explaining why or in ANY WAY DISCREDITING them.
It's literally like people only come here to **attempt** to prove others wrong.
I remember, and this was a while ago mind you, when people posted here to dicuss strategy and learn. Now it's standard to just flame people with nothing of ANY VALUE added to the conversation whatsoever.

I might as well tell you I've fixed the worlds problems by listing environmental issues and population control, it's easy as p**s to do and adds F**k all.
Whilst trying to contribute to this thread the only thing I learned is that on balance the most ignorant people are also forthright.
Anyone genuinely trying to teach or learn is generally open and non combative.
Not sure what the other are up to...

This is a pretty good basic summary of GTO, and the foundation of what knowledgable players are working from in this dicussion.
But it is TOO basic in that if we have ANY relible info of how our opponent deviates from GTO, then we will both:
a) make much more money trying to exploit them than by playing GTO
and
b) some (potentially large) portions of our range could become fairly -ev

If anyone doesn't understand why this is then rather than explain it, I'd ask that you get the nash range SB push range for a given spot, pick the bottom 25% hands of that push range ( which is +ev in GTO obv) then make villain call say 25% wider than NAsh, and see how those same hands perform against the NON nash caller.

GTO is great when you are readless, when used in combination with population tendencies.

An exploitative read based strategy will reap more rewards however unless you're playing near perfect GTO players, always. So while Nash is a useful starting point, it should be just that... A starting point.