You are being narrow minded. Using extremes is a very common and useful tool in logic and math to illustrate a point. Folding pre 100% is a horrible strategy for sure, but it is still a strategy. Folding is an action in poker and if you are taking actions then you are playing the game.

Finding a GTO solution to poker means finding a strategy that's unexploitable and at least 0-EV vs the set of all strategies, not just the ones that "make sense".

Although I guess the point can't be proved sans solution, I think there's a decent amount of evidence to support the idea that a GTO solution will result in a ton of indifference points. If you look at toy games or even hold 'em mini-games, this is the general trend. You can come up with a lot of silly examples of suboptimal strategies that will almost for sure be -EV versus the GTO strat, but once you eliminate all of the really blunderous errors, the situation becomes less clear. Like the previous poster, I like your side of the bet -- I just think it's pretty clear from what we do know that the solution will result in lots of situations where such indifference points do exist. I'm tempted to suggest that it's theoretically inevitable, but I don't know if I really have my head wrapped around that thought well enough to argue the point.

kk

Sorry for the derail. Back on topic.

1. I think game theory is the future of poker strategy, but not every winning high-stakes pro uses it explicitly (PI, PA, zig, ect.)
2. Some high-stakes pros are sick poker players and think they understand GT, but don't (ie. durrr).
3. I think durrr would lose to the bot.
4. I think one of the HU limit specialists stands a much better chance against the bot.
5. Obviously any prop bet with durrr should have a time limit.
6. I don't see the bet taking place.
7. I would pay ~$100 to see a recorded match: durrr v. machine for 200k hands.

it was widely regarded that hoss was the best limit hold em player in the world, right? and he only lost to one person mainly- ivey. instead of durrrr, why don't we get ivey vs slumbot?

durrrr was known for making bad prop bets huh?

inb4 ftp rng rigged and mm lost over epic battle

i tend to disagree. poker is to complex.

in RPC your ev in any throw is either -1, 0, or 1. your avarage ev is 0, whatever you pick.

in poker, only calculating the ev or e.g. AT against a random hand for a preflop all-in situation requires computer-help and gives you a number like 58.7638...%, and it seems hard to construct action frequencies which would result in exactly equal evs. if not number-theoretically impossible.

also, it is shown for push/folding that gto gives you indeed a single maximum-point for equity compared for any other strategy, and the further you deviate the worse it gets. to assume that in other settings weird local maxima would exist is at least counter-intuitive.

I want to bet $1000, i have got durrrr winning AND durrrr never taking the bet in the next 6 months

would need escrow

I see what you're saying but consider situations like the following (borrowed from the previously mentioned Bryce article):

These types of situations, even though only proven in mini-games, will almost certainly occur in the full game.

I think the complexity of the game actually argues in favor of the existence of such indifference points, and it's your focus on pf concepts that is overly simplistic.

200k hands!?!??!?! he never even finished the even one of the 50k hand challenges.
Also, did I get it right that he wants odds based on the amount he's wagering? Maybe I misunderstood.

Stepping away from the awesome GTO discussion (which im trying really hard to understand) and back to the original topic and notion that all top players use these "strategies" but may not express it that way. While reading this thread last night the following came on TV.



I freaken love this show. Its worth the full watch.

Is it this unique/imbalanced distribution of electrical activity that allows guys who dont use a HUD like ivey, durrrr, zigmund, isildur etc to recognise patterns in their opponents play and adjust accordingly?

Are sauce, kanu, ike , galfond wired similarly and expedite the process using a HUD?

Im not the sharpest tool in the shed but i think this plays a major role, so ill let you smart folks watch and take it from here.

jesus christ there's a lot of people who dont understand game theory in this thread, durrr included.

"optimal" in the game theory sense means "unexploitable". it is NOT necessarily the highest EV play. it is simply the play that is part of a strategy which is perfectly balanced and is unexploitable across all boards/hand ranges/bet sizes/whatever-else. it may raise a river with a frequency that is -EV in a specific situation and thus be "sacrificing" edge in that spot, but given the ranges it gets to the river with in that spot, and given that the river play is only part of the "whole" of the entire hand, and that the single hand is only a part of the "long run" of infinite hands, it will make up for that loss in EV on that singular river spot by gaining EV in other spots, and as a whole, the strategy it employs will not be beatable. if you adjust to it's seemingly incorrect river frequency, your adjustment will lose that value in other similar river spots, and overall your adjustment (assuming here that you adjust away from gto) will cost more than it will gain, and on average against all possible situations during the infinite hand game, you will be worse off.

here are some facts:

gto in hunl does exist. john forbes nash jr proved this long ago.

gto for hunl is currently unknown, even though we know that it does exist.

unlike in RPS gto where you breakeven no matter what, in poker, you will always lose to gto.

gto does not care what you do. it does not take into account your frequencies and hand ranges. it does not adjust. it simply knows that EVERYTHING you do will end up being inferior to it and thus it doesn't care what you do. it only knows raping you.

the above point means that it may not beat bad players for as much as a non-gto good player would, because the good player would make deviations to maximally exploit the bad player-- but those deviations in turn COULD also be exploited (and thus why gto doesn't employ them) -- but the good player just knows the bad player is so bad he won't re-exploit and thus deviating is safe. gto does not know (or care about) this.

in short, gto does NOT win the most money possible, but it DOES win money IN EVERY GAME (assuming no rake).

gto cannot be beaten. not by you, not by me, and not by durrr. not even ivey. if you use your amazing human sense to know that its frequencies are off in this spot or that spot, you will only lose less against it. and you might be wrong and do worse off. regardless, the best you can hope for is to lose less. you will never beat it.

are we clear yet 2+2???

good example for sure. indifference points where all strategies perform equally well are possible.

will stop the derail now, i never said there was no such strategy possible. discussion has no practical purpose whatsoever. a strategy that is gto except in spots where it doesn't matter anyway is still gto, no?

note that the caller in your example plays gt-optimally whatever he does as long as hero's bluff frequency keeps him at that indifference-point. compare that situation with RPC where the response to gto is also indifferent. see analogies?

in before you are asked to give a source.

+1, good analogy

State is simply a block of data describing the state of the game. In my conception of some sort of GTO poker bot you'd be able to query into a table by hashing the 'state' and looking it up in a table. So for instance a state would include information including but obviously not limited to:

My cards:
My range:
Pot:
Opponent's known range:

So the state between where an opponent draws vs stands pat would be identical as your opponent's known range is still the same - 5 unknown cards. My mistake was viewing this as 'opponent's known range' which should have been something like 'opponent's known optimal range'. The draw doesn't change his known range but it changes his optimal range since the optimal weighting possibilities of trips or whatever becomes higher after the draw increasing the potential strength of his range. By assumption I was referring to changing the state on what 'ought' be without knowing something for a fact - an exploitable action.

A silly conceptual mistake that I'm happy to have been able to correct!

lol at durrrr finishing at least one of his challenges (esp 100-200k hands lol)
jungleman must be sitting facepalming somewhere right now

Example: JTs on the button 200 BB's deep. How could anything involving folding or shoving be optimal? GTO would involve x% limp y% minraise z% 4x etc.

Yeah agree with all of this, maybe if you come out with a figure of the maximum that you are prepared to lose on the bet durrrr then we can match it on the other side and that can be the buyout amount. Also there will obv have to be a time limit on the bet which if you pass you forfeit the bet. Doesn't have to be a time frame that puts you under time pressure but I'm sure none of us want money tied up for years in escrow.

Wow. Hell of a thread.

Only thing I'm confused on is how, if the hypothetical GTO bot never adjusts its play to any variable factors such as opponent tendencies, it could show a profit against any opponent.


and even if this were the case, why is everyone insisting that the GTO strategy for hunlhe would not include player-to player or even realtime adjustments?

gto means that there is no strategy that it needs to adjust against because the way it plays is not exploitable. that's the whole point.


edit: removed insult.

I'm not sure if it has been said, but since this is such a great thread, "A Beautiful Mind" is a great movie in which the guy who pretty much can rule this discussion is the main character. It is about the guy who proved this theory.

Yes, but how is it possible to not be exploited in HUNL without adjusting?

Seems contradictory.

Agree that's a great price to pay for info like that (would obv pay it).

cuz then it wouldn't be GTO strategy. GTO strategy is playing a certain unexploitable way. It doesn't care what the opponent does. Adjusting the strategy would mean exploiting the opponent (which is in turn exploitable).

if you look at one of the hundred posts about rock paper scissors that simplifies it in this thread it is easy to understand in a basic way.

throwing 1/3 rock 1/3 paper 1/3 scissors is never going to be able to be exploited in any way. so if you ever found the optimum frequencies in all situations in hunl then you can play in such a way that it is simply impossible to have a disadvantage.

No worries there. The whole thread is a derail with 3 or 4 unique discussions interwoven throughout. I kind of like it.

This is true and I was originally hesitant to respond to your post for that very reason. Your phrasing did seem to suggest you were skeptical about the idea, so I decided to reply anyway, perhaps in part because this concept plays an important role in one of my previous posts.

It does sort of matter because it shows that to achieve the goal of GTO, you often have to create such spots to avoid being exploited yourself.

That's not precisely true. If he for example folds always, his play becomes exploitable even though his expectation against the bot doesn't change. The fact that the bot doesn't respond to this behavior doesn't make the strategy game theory optimal.

It's certainly analogous in the sense that it's another simple toy game, but I think it serves to clarify how such situations can arise in holdem. There are theoretically more complicated range composition and multi-street problems that also result in indifference points; it's just the complexity of it makes it hard to present meaningful examples and thus the reliance on simple mini-games to help with conceptualization. Obv this way of trying to understand the question doesn't satisfy scientific scrutiny, but it's the best I can do. I do take some comfort in the fact that ppl who have spent more time on this than I have seem to take the existence of indifference points in the GTO solution for holdem as a given and many pros have already spent a lot of time solving and/or studying these types of mini-games in an attempt to better understand them (see the intreview from the OP, for example).

i wonder this too. sometimes I dont want to wander to far into this argument but what you guys are saying for the future implications of hu nl makes sense.

On another note, doesn't this want to make some of you just program a bot and see how good you could get it at hu nl. damn it would take a lot of time but if you could have user interfaces that made programming more fun and less of a grind, I could get it really ****ing good at hu nl with the help of the right people and feedback from other hu players. however, it would take to much work and I just dont care enough especially considering the hu economy.

i esp like when ike says he sees different preflop raise sizes (instead of just minraising every button) and correctly adjusting sizing and ranges will be a feature of the god like hu bots. can you bless us one more time ike and tell us why you think is the case? So god like hu bots wont only be 2x preflop but occasionally ...2.1-4x (how high does this # go, at some point raising more x% of ur stack with xbb is just mathematically never right)