I allow myself to move this thread to "No Limit / Low Stakes".

GTO  EV is 0

lol :)

Your value is in getting called with your value hands and getting folds with your bluffs.

That is NOT EV 0!

And with his calling frequency he is not making himself indifferent, he is making you indifferent between bluffing and checking with your bluffcatcher(s).

errr....game theory :) i kinda am  not sure if thats ...like that???

tho my mind goes in a swirly im not sure ever mode when it comes to GT..but that wasnt my understanding of it

GTO sumz EV total 0

thereis problem with tread i dont see now what ppl are saying , but i see

I read posts in news, seems like replies are invisible to script error~

Im afraid to disagree with someone named Game theory but none  the less gotta disagree cause i might didnt understand GT well

My understanding of GTO is that its constructing ranges, bet,  check fold  etc frequencies in between players so its absolutely unexplotable and it always in long run sums EV zero, like 2 perfect bots playing against each other and always pick perfect line~ and my understanding is that OP question was in place cause EV of such play for which he gave example is EV = 0

Like picking strategies in game RPS, GTO solve problem is picking 1/3 of a time each goes to absolutely unbeatable strategy, but that equals EV zero because both opponents are playing perfect game

Making GTO for poker is, of my understanding creating same EV zero sum as final product in theory ( as in example made by OP )

Why ppl play GTO then and analyse it, study it, advise it etc?

 MY understanding of matter is that its cause most players dont play GTO balanced strategies, by either calling too much ( we value bet 2 bluff 1 , and for example they call 3, making us 1 value bet always a profit ) or folding too much  and in such way our perfectly balanced GTO play that against perfect opponent that makes EV sum zero, in reality is significant EV + 

 EV + comes from NOT  as a result of a GTO , but as a result of opponent not playing GTO

GTO result in perfect conditions remains zero

So i think OP has valid question, and sum of bets he gave example for is EV = zero, but in reality due to imperfection of players playing NOT  GTO makes you EV + by fact that players arent responding in GTO correct frequencies usually, unless of course you run into GTO genius at tables

The EV (= expected value) is the weighted outcome of all possible situations that can occur.

Each possible outcome is tagged with the profit or loss - and then weighted by it´s probability.

Like, if we´re on the river and have a potsized bet left and shove - there are three possible scenarios:

1) Villain folds, we win the pot.

2) Villain calls, we win the pot + his call.

3) Villain calls, we lose our bet.

OK so far?

Now, we have to weight the outcomes. So, we´ll take your example. We have one bluff for every two valuecombos and Villain calls 100%:

1) Villain folds = 0%

2) Villain calls, we win the pot + his call = 66% (2/3)

3) Villain calls, we lose our bet = 33% (1/3)

Still with me?

Now, let´s put this together. p is the size of the pot, we have exactly one potsized bet left, so our bet is exactly p. Our EV is the weighted sum of all possible outcomes (that add up to 100%):

EV (bet) = (0 * p) + (2/3 * 2p) + (1/3 * -p)

EV = 0 + 4/3p - 1/3p

EV = p

So, our EV when we bluff with 2:1 ratio is the size of the pot.

Now, what´s the GTO-stuff about this? Here´s the deal - let´s compare Villain´s EV:

EV (call) = (1/3 * 2p) + (2/3 * -p)

EV (call) = 2/3p - 2/3p = 0

That said, Villain is break-even when he calls. The same happens when he folds (his EV for folding is 0 as well). And it happens for anything in between, if he calls 20%, 45% or 74.23%.

BUT - that only holds true as long as Hero bluffs optimally. If Hero bluffs too much - Villain makes money by calling, hence he should call 100% and win money (and Hero loses money). If Hero bluffs too little - Villain just folds 100% - and Hero loses money again.

Wait, what? Why does Hero lose money if he bluffs too rarely? That´s simple - and the last part of this small GTO-lecture. :)

Say, Hero has 10 combos by the river, split into 2 valuecombos and 8 air-combos. Now, we know that if Hero maintains a 2:1 value-bluff-ratio that his EV is exactly pot for every time he bets. He bets 2x for value and 1x as bluff, hence he´s betting 3 times. So in 3 of 10 times he win the pot (no matter what Villain does), in 7/10 times he gives up and loses (with his air). So, his overall EV is 3/10*p = 0.3p.

Now, if Hero bluffs too rarely - say he never bluffs - he only wins the pot in
2/10 times and loses in 8/10 - which reduces Hero´s EV to 0.2p.

Got it?

back to more general terms of GTO...

isn't playing GTO guaranteed to be +EV to 0EV?  That is, if villain doesn't play GTO, then Hero is +EV.  Te best the villain can ever do is play GTO himself and get to 0EV for both players..  

Max EV occurs when villain is on either side of GTO and hero 1.) correctly determines which side of GTO villain is on and 2.) plays max exploitatively ( is that a word??).  ie, if villain calls more than GTO - hero's max EV play is to never bluff -> until villain changes his strategy.

So, GTO is always + to 0 EV vs an unknown villain/range/tendencies, but is not max EV.  Max EV  occurs when hero adjusts to villain by the 2 points above.

Is this correct?

Im afraid to disagree with someone named Game theory but none  the less gotta disagree cause i might didnt understand GT wellMy understanding of GTO is that its constructing ranges, bet,  check fold  etc frequencies in between players so its absolutely unexplotable and it always in long run sums EV zero

If you are playing GTO against a GTO opponent in a symmetrical game, then your EV will be zero. For instance playing one orbit of HU NL (2 hands) is symmetrical if stack sizes stay the same. But one hand of poker is not symmetrical, in general the player on the button has a fundamental advantage, and he should be +EV.

Moreover, if your opponent does not play GTO, then GTO is guaranteed to not lose (EV >=0). But in almost any form of poker you will have strict positive EV.

For instance if you bet on the river given a board of JsJhQd6s3h, you might make KQ indifferent between calling and folding, while calling with 77 is a losing play.

If your opponent makes fundamental mistakes such as calling 77 or folding AQ (assuming calling AQ has positive EV) you are always +EV.

since my value range beats KQ and my bluffing range loses to 77 isn't 77 going to be indifferent aswell if i play gto value/bluff ranges at river?

@juancopani: "Where is the zero EV if im winning 1p, and villain is EV0 ??"

Nobody said that "GTO = 0EV". ;) That´s what GT and me tried to get clear ... 

GTO is about maximizing (!) your EV against an opponent who does the same at the same time. In my example, Hero wins p when he bets. But remember - he wins, WHEN he bets, when he doesn´t bet, he loses the hand. So, from 10 times he bets 3 times, meaning his EV per hand is 0.3p, the EV of Villain is 0.7p per hand (because he wins the pot 7/10 times). So, both players are playing GTO, and both win overall. No zero-EV. Okay?

Only WHEN we bet, then we win the pot and Villain is 0EV. That´s because we keep him indifferent between calling and folding - and folding always has 0EV, so his EV has to be 0EV by definition, otherwise he could adjust, which means, we made a suboptimal play.

If you take the entire game, every position, every possible situation etc.pp. then you come to 0EV if two players maintain GTO-play against each other.