Quote:
Originally Posted by MT656
After I get flop calcs commercially launched, depending on user feedback I may go back and investigate bet sizing in more depth, but in my limited early experience the potential EV gains weren't enormous.
Thanks for responding; two follow-up questions.
1) Is there a way to get some kind of estimate on the difference between a truly "optimal" bet-size and the best solution from a (given) limited range of options?
In other words, is it possible to take the salient features of the calculation and generalize them produce some kind of bounds on the "user error" value which can actually be displayed to the user?
2) Is it correct to assume that the problems you're currently working on are actually kind of elementary (but important) problems compared to actually "solving" poker?
In other words, is there some kind of huge leap in complexity when you want to start actually solving for pre-flop strategies? It seems like this is where the lion's share of the work is.
Also, I think that $49.99/month for your product is a steal, and I wouldn't think twice about paying double for the turn solver (or the river solver, for that matter).
Glad you like the software and think its a bargain for the price!
Regarding 1, you can compute epsilon equilibrium distance without knowing a GTO solution which is a bound on error. For more on that see my youtube videos:
https://www.youtube.com/watch?v=j7xSHC90_Og
https://www.youtube.com/watch?v=-UenhnsjiOY
This is the standard way to measure the accuracy of an approximate GTO solution and the "Nash Distance" number that GTORB shows you at the top left of every solution is exactly that number.
However, the calculation that GTORB shows is the "in model" epsilon equilibrium distance, that is it is the distance assuming that the only strategic options are the ones in the game tree that you specified.
In the future I plan to add options to do stuff like see "If I play the GTO solution to the game where people can only bet 50% pot but they are actually allowed to bet 40%, 50%, 60% what is the out of model equilibrium distance", i.e. how bad is it to treat 40% pot bets as though they were 50% pot bets.
Unfortunately I don't think there is only way to do that type of calculation to generate bounds for arbitrary bet sizes. Anyone being scientific about their work should always have in-model epsilon equilibrium distances calculated, but out of model ones in full generality are very hard.
Regarding 2) Yes I'd say that is correct. I don't really think of GTORB as a tool to solve poker but rather as a more practical tool to help players win more money. Its entirely possible that the "standard" pre flop ranges (and bet sizes) people use even at high stakes are very wrong, solving poker would involve figure that all out exactly. Regardless of what optimal play pre flop is, most people play one of a few reasonably predictable and static ways. Answering the question "if we assume they play that way preflop, how do I play post-flop optimally" is a very directly useful and +EV question to answer. In fact, if our opponents do not adjust their pre-flop play, answering that question is going to be higher EV than knowing "assuming everyone plays GTO pre flop what does optimal post-flop play look like".
Finally regarding Snowie, my understanding is that they removed all claims to snowie being GTO from their marketing, I think their CEO posted on 2p2 a while back correcting some of their early marketing that claimed the program played GTO. I think that they are solving a very different problem them I am, they are trying to make a strong poker AI, not solve for GTO play. They want their AI to be non-exploitative but that is very different from it actually being GTO. Of course just simple epsilon equilibrium measurements (which you can make with CREV in simple cases) would be enough to spot non-GTO play that it might make in simple spots (e.g. on the river).
In terms of the value of AIs, obviously an AI that could just play true GTO in all spots would be the holy grail, but it doesn't mean that a non-GTO AI couldn't be better than any player in the world theoretically speaking and thus very valuable to play against/learn from. This is the case in chess and people regularly train against AIs despite chess being far from solved and unlikely to be solved this century. Whether Snowie is a good enough AI to constructively practice again and learn from is in the eye of the beholder.
Every year there is a computer poker championship and my understanding is that the winners of that are still not generally at the level of top humans. I think one of the former champions stated their bot was comparable in skill to a winning micro stakes grinder.
Some AI approaches solve abstracted (simplified) versions of poker for GTO strategies, often ignoring blockers, simplifying bet-sizes, making strategy assumptions etc and play that way in the full game, including the winner of this years event. A GTO focused bot both won the most chips total against a pool that included fish and had the best record against tough opponents this year which I think should convince a lot of people who think GTO would break even against weak players that they are mistake. There is a neat article on it here:
http://www.cardplayer.com/poker-news...apon-for-poker. However, I think most academics have never played poker at a high level and greatly overestimate how well their bots would do against top players so I would take the hype with a grain of salt. AI research in incomplete information games is a young field. The AI tournament this year was the first to feature ANY 3-handed play of any kind and they played limit Kuhn poker (the AKQ game), which is infinitely simpler than NLHE.
Last edited by swc123; 12-17-2014 at 07:28 PM.