i assume you don't bother wasting your time betting the nuts when checked to on the river given that it's a 0EV play

How about another example: Two players are playing HUNLHE using standard blinds. Player-1 is playing GTO, Player-2 folds every hand preflop. Is Player-1's EV zero?

I gotta say it - this thread is geek p0rn

GTO is playing in a way that cannot be exploited. If player 1 plays in a way that is +EV, then that is implying that player 2 is playing in a way that is -EV, meaning that player 2 is not playing GTO. If players 2 begins playing in a way that is +EV, this means that player one is obviously not playing GTO. The only way that players in an HU game can play GTO is by playing in a way that their EV is 0, right?

The example used was that both players play EVERYTHING GTO EXCEPT a specific scenario in which player 1 checks back the nuts on the river (and I already stated that it would be impossible to actually do this because to play GTO, every aspect of the strategy must be played perfect I think)

I bet the nuts on the river because it is a + EV play which is greater than the alternative (0 EV)

I would not even consider this playing. This would be 2 people doing nothing

Another example to think about would be a GTO player playing against a river bet from a player that only ever had the nuts. Would the GTO player call that players river bet with hands worse than the nuts?

The GTO player would and it would be a -EV call, however he would be gaining EV from other areas to make up for it.

It's as valid a form of 'playing' as anything else. (The example wasn't necessarily for you. It was just to show conclusively that unlike the RPS example, it's possible to do much worse than breakeven vs a GTO strategy)

were you implying that the GTO player is the big blind and the other player just folds every hand without the GTO player acting? If so then this is doing nothing.

I think even if you are implying that the GTO player raises first and then the other player just folds every hand, that would still be considered doing nothing.

If player 2 has the nuts on the river and there is money in the pot then there is absolutely nothing player 1 can do to stop player 2 having an EV edge in this particular situation even if it plays a GTO response to player 2's actions. Mathematics of Poker even went as far as to show that two GTO strategies playing each other perfectly on the river with a non-0 pot gives an EV edge to the player acting last which I found quite interesting.

If the only option of one of the "players" is folding, then it really isnt a game

What I asked in the first place was whether or not a HU GTO player in poker was 0EV or +EV. The more I think about it the more I am pretty sure that the GTO player is 0EV whether they are playing against another GTO player or a fish.

Within a GTO strategy, I am sure you will always be able to find specific instances where something is -EV or +EV, but the point is that the whole strategy will yield a result of 0EV.

Doing nothing ≠ folding.

I never said it was Player-2's only option, just the one that he's chosen. (And this strategy will perform better than others given sufficiently large stack sizes).

If you fail to value bet in a situation where the bot would have bet you will not make as much as the bot would in the same situation. If you are making less than the bot in some situations and not making up for it in others (which you can't against a GTO strategy) then in the long run you will lose to the bot. No different to a strong player against a passive fish who misses value bets - the strong player bets good value, the fish misses heaps of value. In the long run the strong player wins.

you are completely incorrect and your lack of understanding despite some really good examples being given leads me to think you are maybe trolling?

No. See post #236.

You said all he will ever do is fold. Not really sure how this example is correct. If all he ever does is fold, he is losing everytime all the time. By folding every hand except the nuts and shoving that, he will do better than folding every hand.

Im not trolling. Trying to understand it better. Maybe I am missing something obvious?

So...this super nit fish's whole strategy is not 0EV against a GTO strategy, right?

good rule of thumb for this thread: give one easily understandable example, if they dont figure it out they should hit the books or stop trolling =/

The GTO strategy would be +EV over a large sample against all other strategies except for another GTO strategy. This is part of the definition of GTO. Sauce's example in the OCT 2011 HSNL Reg's thread of playing against a 5bb HUNL GTO push/fold bot with his own strategy and losing 2.37bb/100 is a good example. Not exploitable means that every other strategy is exploitable, and over a large enough sample the GTO strategy will win.

As for your betting the nuts on the river question, the EV lost by not doing so would make the overall strategy EV negative, thus the EV neutrality of the check is irrelevant, because the repercussions on the whole decision tree would make it non GTO.

What can I say, I'm a sucker for getting someone to admit I'm right.

Post 236 said that Polaris was beatable. Wasnt the goal of Polaris to be unbeatable (meaning it was beatable for 0bb/100?), which would be GTO

yes it is, because the GTO strategy will call the fish's shove with a certain number of non nut hands making a shove 0 EV

It's goal is to be unbeatable, sure. It has not yet obtained that goal. Also, notice though that post #236 gave Polaris' EV against a GTO strategy, which was...negative.