Quote:
Originally Posted by RustyBrooks
The kinds of games that have been solved are *so* completely simple compared to NLHE.
I'm not a specialist by any mean but yet, I think there's so much misunderstanding going on here (and basically on almost any thread about game theory for poker).
RustyBrooks raises a very elementary but overlooked issue. Game theory studies "models of games". For some (classes of) models, we are currently able to prove the existence of GTO strategies. For very few of them, we are currently able to exactly compute them.
First and foremost, game theory may or may not help you prove the existence / approximate / exactly compute GTO strategies for models that more or less accurately describe real poker. But it's just models of it. Not the true game we are actually playing.
And yes, at this point, we can exactly compute GTO strategies for models that describe poker so roughly that they are very informative regarding what a GTO strategy would be for something that even starts looking like real poker (at least for multi-way, NL games).
This being said, it may not be necessary to be able to EXACTLY find GTO strategies. Find approximate solutions can be of great interest. From a theoretical point of view, though, it can only be satisfying if you are able to quantify "how far" from the optimum your approximation is. And this is not a trivial issue. Even defining what a relevant distance (to measure this gap) is non-trivial. What we seem to be able to do now is, given a fixed strategy, to compute the optimal strategy against it. Then, we can evaluate how it performs versus this optimal counter-strategy. If it break evens, it's GTO, if not, it will necessarily be losing and the amount by which it is losing can be a measure of "how fare we are". But it is a pretty bad measure, though. I don't want to get too technical, but GTO strategies are solutions of optimization problems (ie minimzing/maximizing a function). If the function you are optimizing does not have some desirable (regularity) properties, the EV gap tells you nothing about how far the strategy itself is from GTO. You could have a huge EV gap with a strategy that is in fact very close to optimal (if the function varies very fast around its optimum). You could also have the opposite: find a solution that has a very tiny EV gap, but that actually is very very far from the true optimum.
All this to say that there is not necessarily anything wrong with pokersnowie. But to evaluate that, they should provide more details about a) what model they are studying, b) the function they are optimizing (and some of its properties), the algorithm they use to approximate it, or at least some analysis of how their approximation relates to the true optimum of their function. I checked their website. I found none of that.
And no, even if they made public the full characterization of their so-called GTO strategy, it would not be enough. We would not be able to say anything about it, except that it would not be truly optimal (but no one should be expecting that anyway). We need the solution and how they reached it. Else, we just can believe them. Or not. Because it's so full of imprecision that I doubt it can be scientifically sound.
Last edited by Piconzaz; 11-15-2013 at 01:26 PM.