Intuitively I agree with this, but I am having trouble verbalizing my reasoning.

Has this statement been proven for NLHE?

How can anyone think that when two GTO players play head up holdem the button doesn't have an edge (as long as stacks are big enough to allow for folding and the button has the smaller blind)?

Also the fact that the button and blind GTO strategy are totally disconnected has real world consequences. If you are a good exploter and also good at coming close to GTO you may well find yourself against an opponent who plays one side well enough that you stay GTOish but plays the other side weak enough that you should switch hats. For instance, I'm guessing that there are guys who play strong on the button but in first position make significant mistakes (such as almost never donk betting.)

that makes more sense, you said it the other way around

You generally can't just bet arbitrarily large in NLHE because at some point you simply become exploitable by the strategy of never continuing against your bet with anything other than the nuts (and going through whatever contortions are necessary to be able to have the nuts in any given spot so that you can pick off your opponent's billion BB bluffs). The only exception to this is when you can bet a range composed entirely of the nuts and blockers to the nuts. At this point, you can bet arbitrarily big and as your stack goes to infinity your ratio of bluffs to value can go to 1 : 1. For this reason alone, 200 billion bb deep NLHE would be slightly different from 100 billion bb deep NLHE, but it's a really inconsequential difference. In practical terms (and this is pretty much pure guessing) I'd expect things don't change much past 1000bb or so.

Thank you for the detailed reply Ike

Clearly, Ike didn't read Durrrs J6hh 8h9hTh 1million bb deep example. Sad that some of these math geeks think they can play there 'GTO' math poker vs some of the best poker players in the world. If they could, they'd be with Durrrr making millions in the macau games not on team online plotting strategies with eachother on Skype and sharing hud stats! Cant wait for durrr to teach these nerds a lesson (if they can come up with enough money to make it worth his time!)

In some games it can...

Clearly, Ike didn't read Durrrs J6hh 8h9hTh 1million bb deep example. Sad that some of these math geeks think they can play there 'GTO' math poker vs some of the best poker players in the world. If they could, they'd be with Durrrr making millions in the macau games not on team online plotting strategies with eachother on Skype and sharing hud stats!

Lol......?

Durrrr plays Macau because those are the biggest stakes he can crush. Ike and/or Sauce may very well be better than him at HUNLHE.

level/joke i assume. lol regardless if not though. "Clearly, Ike didn't read Durrrs J6hh" somehow reminds me of howard lederer's "one time, at a party".

i think all ike, sauce, kanu and jungle are much better right now at HUNL (online settings anyways). That might change if durrrr puts in enough volume anytime soon if he`s any motivated obviously (hes still a brilliant poker player, its more the matter of who`s in better "shape")

I feel like such a fish with reading this debate. Do You guys think Negreanu knows all these equations?? i.e. I just recently got to where i am making a consistent profit in live 1/2 games and that comes after extensive reading and practice online and in home games my reads are what is making the profit though i think as i have far from perfect strategy?!?!?! as i kinda suck at math outside of simple odds calculations now i have to wonder if my skills are somehow inferior to a math problem?? Input anyone -superfishguy

LOL

My understanding of what you're saying is that the reason there would be a difference (albeit inconsequential) between 200 billion bb deep and 100 billion bb deep is as follows: because the stack to pot ratio is slightly larger in the 200bil bb game, the GTO strategy will have to bluff slightly more often in the 200bil game than the 100bil game in order to avoid being exploited by an insta-fold strategy by the non-nuts-holding villain.

In other words, as the GTOHero's stack size increases toward infinity, the GTOHero's bluffing frequency must increase toward a 1:1 value to bluff ratio. For this reason alone, it could never be proven that the GTO NLHE strategy is the same once stacks reach a certain large size.

I might be way off in my interpretation and understanding of your post, but I will say that this is the most deeply I've ever thought about poker, so thanks for indulging me.

I tried to edit my post above, but didn't make it in time: If it wasn't clear from my post, all of my analysis above only applies to the very narrow situation you described, where GTOHero's range is only the nuts and nut blockers. For example, {Ad, Xd and Ad, Xnond} on a 3 diamond unpaired board with no straight flush opportunities.

This is only true if stacks are infinite, which they never would be (also, assuming bets cannot be made in arbitrary fractions of a cent).

Agree. For all practical purposes the size of the game is limited by (i) discrete bet sizes (all games have a minimum chip size for example); (ii) limited stack sizes; (iii) the solution being (for practical purposes) the same above a certain stack size. However, its fair to think in terms of either (a) different solutions for each stack size (so we would have to talk about solving eg "100bb HUNLHE with 0.1bb minimum unit"; or (b) a very complex compehensive solution where stack size is one of the game tree factors.

Yep. If durrrr sees sense and ducks the bot challenge I would def be willing to bet on Ike/Sauce vs him instead (HUNLHE)!

Hey guys, I'm sorry if it was discussed before (im only on page 51 so far, lol), but reading this thread I've though of an interesting dilemma. I'm pretty well-versed in academic math in general and (especially) logic, but I'm completely new to game theory, so if I'm just misunderstending some basic terms, please, do not hesitate to correct me.

The question is: how (or if) does gto strategy "distinguish" bluffs from semibluff and valuebets? I came up with following answers:

1. It doesnt. Most counter-intuitive answer, pretty clearly wrong, but worth considering for a second. The idea is that except for nut-high and nut-low situation gto just randomly "balancing" bets, as if "not looking" in own cards. We can falsificate it inductively, by looking at nash equilibrium for push/fold hu, where it's pretty clear that our pushing ranges exist also for non-aces and non-23o. I'm pretty sure it can be also shown deductively, but why bother?

2. It has some built-in "absolute hand strength" term - for example, we say that valuebetting is betting top x% of possible hand combination on the flop, y% combination on the turn and z% combination on the river, semibluffing is betting when our hand is non-valuebet, but there exist at least x'% cards on the next street that turn our hand into a value-betting hand and bluffing is all the rest. The problem with this idea is that our actual hand strength depends on likelyhood of our opponent holding a hand stronger than ours, and it depends on many things, one of them being board structure. And including that in our estimation of hand strength would be assuming some strategy for opponent (look point 3).

3. It assumes that opponent is playing some strategy (most likely gto as well). This seems like the best answer to me, however also raises some questions. First of all, it's clearly correct for before-mentioned nash equilibrium for push/fold hu (where it is said explicite). It also seems rational, BUT:

a) from what I understand, gto does not adjust. Wouldnt assuming some strategy for opponent and playing accordingly be some form of adjusting? Or do I understand "adjusting" wrong in this case?

b) wouldnt that be exploitable by conciously taking sub-optimal lines, to lead our gto opponent to make decisions sub-optimal in relation to our actual range (in opposite to assumed gto-range)? Or is the whole beauty of gto that we have to sacrifice at least x% equity to gain maximum x% equity by "confusing" gto-opponent (thus making gto unexploitable)? But isnt it supposed to be truth that any sub-optimal to gto strategy HAS to lose vs gto? Im kinda confused here

c) assuming that opponent plays gto is clearly not true in most/all cases (since from what we know no gto for poker exists yet). Wouldnt deducing our action from false assumption be non-optimal course of action? Or is assuming that closest to perfect we can achieve (and therefore optimal). But what would make it so? Is it because gto-opponent is "worst case scenario" for gto and it has to be prepared to at least break even with it?

4. GTO doesnt exist, Nash was wrong and durrr is right. No comment here I guess

Summing up, it seems like option 3 is the answer, however I still have some doubts there and would appreciate some clarification. Sorry if I'm not clear in some points, but I'm not a native english speaker and have some problems expressing such theoretical and complex thoughts

I don't really understand the question you are asking (perhaps you can clarify that part?) but I can say that 3) is not the answer to whatever the question is.

The basis for a GTO solution is that it doesn't make assumptions about the opponents strategy. It is designed to be unbeatable whatever the opponent does.

I don't know how to make it more clear. I'm asking if (and how) gto strategy "distinguishes" vbets from bluffs. For example, if the gto play is to bluff 30% and c/f 70% on the river, our strategy needs to "know" whether or not betting 3rd pair is a bluff or a vbet. I'm saying that it seems to depend on our opponent range, and this requires some assumptions. If not, we are left without a definition of one of the most basic terms in our strategy.


Actually, the 3rd pair example might be a little blurry, let's consider having 3rd nut-low on the river. How does our strategy "know" betting here is a bluff (it obviously is) without assuming that our opponent's range DOES NOT consist nut-low and 2nd nut-low only? Why it needs to know whether it's bluffing is shown in point 1 (I hope).



Yup, that's what's disturbed me.

If I understand your question, it's kinda 2. But, "our actual hand strength depends on likelyhood of our opponent holding a hand stronger than ours" is not true from an overall strategy point of view. You're thinking about individual hands, not overall strategies.

I think what you're trying to say on 3 is also true, but the word "assumes" is poorly chosen, and overall it's kinda missing the point.

"Or is the whole beauty of gto that we have to sacrifice at least x% equity to gain maximum x% equity by "confusing" gto-opponent (thus making gto unexploitable)?"
Yes.
"But isnt it supposed to be truth that any sub-optimal to gto strategy HAS to lose vs gto?"
No, see rock-paper-scissor

The GTO solution doesn't need to "know" its a bluff or a value bet. It just specifies for each hand it can still have at that point in the game tree:

- what % of the time to bet (and bet each different amount)
- what % of the time to check

The idea of "knowing" whether it is a bluff or a value bet assumes the bot knows "why" it is taking those actions (also assumes those are the only reasons btw). That false assumption is perhaps the source of your question? It has no "why" other than, when taken together in combination with the rest of the strategy, that is the optimal thing to do.

K, thx. As for point 2: let's say we've raised 3x preflop, get called and see a board QJTr vs 456r. Vs most opponents, we know that likelyhood of hitting board 1 is much bigger, since most decent players choose to flat broadway-ish card vs 3x and 3bet or fold low cards (just an example, nobody 3x in hu anyway nowdays ). However, that knowledge comes from assumption about our opponent's strategy, therefore our actual hand strength also comes from that assumption, therefore drawing a line between bluff and vbet seems impossible without assuming something about opponent's strategy.

Anyway, the more I think about it, the more obvious it becomes that it is definetly 3, I just used the word "assume" too liberaly here. I could give some examples if anyone else struggles to understand the problem - for starters, try considering btn play vs opponent in bb who always folds, except for calling 23o specifcly and playing postflop normally and see how defining bluffs and valuebets looks here (hint: gto is still vbetting aces on 233 and it's part of winning strategy). Gto doesnt "assume" playing vs gto, it just plays as if it was playing vs gto. I think i got it now

edit: raidalot, that's not what I was talking about, I used quote marks with "know" to show that I'm using it metaphorically, "know it's a bluff" sounds much more intuitive than "assign action to sub-set of set of all actions that people call bluffs".

Demonstrate that HUNLH has a specification of payoffs for each combination of strategies (and a quantifiable set of strategies). And what form of game is it? Are you including husngs?