I do get what you are saying. I guess I am agreeing with Durrrr in that many poker games are unsolvable, that GTO does not exist.

Going back to the draw example, I realize that the GTO strategy does not care what I do, does not adjust, only plays based on its own hand ...... I am making an observation, that in this specific game, that if an opponent was unable to adjust to certain strategies, it could not win. I realize it would play counter intuitive and not care what I do. I still insist that it would be impossible to solve this game in a GTO way, because without adjusting to some specific things, it is impossible to not be exploitable. The Standing Pat problem is just 1 way to describe this. I do not think a strategy that was unable to adjust to opponents could be unexploitable in this game, it is not possible. The GTO would have to come up with some frequency that it thinks it should call when its opponent 3bets or raises pre, and then bets post after standing pat....... obviously no matter how often I do it, it isn't going to adjust... There is simply no frequency for it to have that isn't exploitable without making adjustments to how often I am doing it

the game is solved? what? from what I understand you play differently against different opponents. It can't be "solved" because you can't always know what the other player is thinking. you can't just apply x strategy to every opponent. x needs to turn into a,b,c etc. If you somehow became aware of everyone's strategy and thoughts in every situation then you could play perfectly. But that is not possible. Even if you play exactly like a computer you could auto pilot to win some amount, but if you are adjusting to noncomputers then you will win more. It is stupid, and when HS players come in here and try to say something different I become optimistic.

Yes. If the GTO solution adjusted to the player then it would be possible to develop a solution to exploit the GTO solution by acting in a fashion identical to the player the GTO solution was 'adjusting' to and then act in an opposite or otherwise exploitative fashion.

Are you actually saying that the GTO strategy would not even take into account how many cards I discard whatsoever in its decisions?

so much fail in understanding gto, durrrr included.

Yes.

It would consider all possible distributions of hands you could have after the discard but it wouldn't make any assumptions about the cards you did or did not discard since, as you mentioned, that would lead to trivial exploitation by working in contradiction to those assumptions.

Do you understand that what you're saying directly contradicts one of the most famous and significant results in the last century of mathematics? Do you think everyone who is telling you you're wrong is misapplying the math or do you think you understand something several generations of mathematicians have gotten wrong?

Also, can we please bet on you vs a LHE bot of my choice?

how can it know what is optimal without knowing how the other player plays? If I 5bet every hand preflop then does the GTO just know to 6bet a huge % of the time. And if he does, then isn't he adapting therefore making it exploitable?

You're wrong about this. Discarding is an action in a draw game. A GTO draw bot would take account of draw decisions just the same as it would take account of whether you called or 3bet preflop.

If this is true, then I reiterate it would be impossible to not be exploitable.

Again the optimal in GTO does not have anything to do with 'best' or maximally exploitative play. What GTO is concerned with is simply minimizing its maximum loss.

Consider something much more simple - you are playing heads up and your opponent open shoves 100bb. A GTO solution doesn't care if you've folded the past 100 hands in a row, or if you've shoved the past 100 hands in a row. It would have a strategy that would have the minimal max loss against any possible strategy. In many cases, like the two above, a non-GTO strategy would be vastly better. Again, GTO does not mean best.

I think ike would be better equipped to handle the swings here (or any other nosebleed player w/ an understanding of GTO and a familiarity with the LHE bots would also probably take you up on this)

A GTO bot would be unable to take account of any action that doesn't provide additional information without assumptions. Any action based on information that is based on assumptions can be exploited. You know before the discard that he has 5 unknown cards; after the discard he has 5 uknown cards. That game state is not changed at all by the action of discarding.

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This doesn't matter; I'm not sure why you think it does.

Exactly.

Distributions that draw 2 are weaker than distributions that draw 1 etc. Ofc the draw provides (public) information, similar to the upcards in stud.

Since the BOT is never adjusting to a range... it can't come up with a proper calling % against a stand pat. Pre draw, If I stand pat, the GTO bot is going to correctly know that my distribution is any 5 cards.... and it is not making any judgement on whether or not i would stand pat without a made hand or whether I would would stand pat with any 5. Using this only info it has, (i stood pat) it can only know my distribution is any 5. It can then find some % that works against any 5, but then I can adjust and not do it with any 5. I realize it is using a strategy that should work against me no matter how often I do it and no matter my holdings when I do the play...but If it doesn't know how often I am standing pat, and doesn't adjust to it, it is exploitable. With me knowing that the GTO bot is calling with some set frequency against a Stand pat, I can figure out that frequency and exploit it. There is no magic amount it can call that will be not exploitable. I can adjust to its frequency but it can not adjust to mine. I realize GTO means that by definition it is not exploitable, which is why i am saying that for this game GTO does not exist.

Basically if the GTO bot calls the exact same % against someone who stands pat every single hand as it would against someone who only does with an actual made hand, and makes no distinction between these polar opposite styles, there will always be a way to exploit it. 5 Card draw is not beatable without adjusting.

Do you also think that a GTO bot plays identically when the action goes button raises, BB calls as when it goes button limps, BB raises, button calls? In both cases there are 2BB in the pot going to the flop, but these are not identical game states.

so you can program a bot to have specific %s and no player can win against it? I have to be missing something.

Yes (hypothetically, of course).

Yeah. To be fair, it's a bit counter intuitive.

I know it wasn't really your point, but that is not true if we are talking about 5 card draw high. 1 card draws are 99% of the time either two pair or a flush/straight draw or a set being disguised as a two pair/draw. 2 card draws do not have the draws in the range, as nobody discards two to flushes in this game above the 1c/2c stakes. 2 card draws are either a set or someone holding a pair and a kicker. 2 card draws are much stronger range then 1 card draws.

My rock paper scissors bot: 1/3 rock, 1/3 paper, 1/3 scissors.

There's an example where I gave you specific %s and you can't win against it. Why is it so hard to understand that although wayyyy more complex, the same can be done with poker?

Meant 2-7td of course

Upcards in stud provide information without assumptions, draws do not.

It's similar to how somebody shoving 100bb heads up is presumably a stronger range than somebody minraising. But GTO doesn't have the luxury of making such assumptions as those assumptions are exploitable. All GTO cares about is the known information. The 100bb it would defend against with a much tighter range, not because it assumes 100bb shove is stronger but because the pot odds it lays means GTO 'needs' to defend much less often to minimize its maximal possible loss against any possible strategy. The 100bb vs 1bb changes the game state in a fashion without assumptions, drawing does not.

Drawing is an opportunity to increase the equity of your hand by discarding bad cards and having the chance to draw better ones. Not drawing, forgoing that opportunity, can be thought of as an "expenditure" the same as putting a lot of chips in the pot. GTO play can fold more often vs pat and bet than vs draw and bet for the same reason GTO play can fold more often vs a larger bet. Starting from the draw decision point, pat and bet "risks" more than draw and bet.