Read up on what a Nash equilibrium is and realize why this is not possible. If snowie truly pretends opponent is playing gto and snowie were gto, it would actually not be possible to improve snowie's ev even in a vacuum, even if it just means playing one single hand differently.

And just want to reiterate although it seems to be falling on deaf ears that the snowie team is showing themselves more and more to be frauds. Instead of answering questions on why they lie and promote themselves with false advertising they answer start questions pretending to be an authority on anything poker related when they have no credentials whatsoever.

bump

well i think they have shown that their product has bugs and the algorithm is not perfect and still is improving. Every software product is like that.

however they have stated these things extremely clearly. It seems to me most people bashing them have not read their website, nor actually studied the program (which u can do for free)

They are also answering questions very clearly.

Every possible move snowie makes in any situation is available for you to review and analyze.

You sounds so much like all you want to do is bash these guys that its just not productive. Which is actually really bad since i am sure you might actually have valid points that should be addressed.

I think u are using snowie wrong. I have used snowie to learn HU and i have def. a fast learning curve than with any other tool i ever used before.

U dont need to download snowies hands or try a million hands urself, the software shows you all possible combinations for any situation. So you can check out what snowie does postflop on certain board textures and after what preflop action.

And no, you will not be able to memorize a GTO like strategy even in the very simplified form that snowie is using/determening.

Snowie however does not explain why. That is not avoiding the question like some people here falsely think. Maybe read the website and listen to some interviews the guys have given if u actually care how this thing works. This is essentially data driven. its up to us to understand, but that is always speculation even if it comes from the snowie team. They have also explained that even in this thread.

Again it would be nice if folks could come up with arguments that can be discussed and put them forward in a constructive way instead of bashing the team because the know how to market their product well.

maybe u can give me a better model of GTO than they do. Maybe also in a way that i can put in any possible poker situation and see what the right play is what the EV is against perfect players and a game where i can play with real time feedback when i make mistakes so i can learn this gto strategy?

Should be easy for you right?

Oh also maybe you can explain to me how you got to your model so that an idiot like me can actually understand why it actually should be close to GTO.

Thats pretty much what they have done. they also explained that their program has limits and is not perfect GTO but an approximation and there are certain rules/assumption (like only 3 bet options). they've explained this ages ago.

Nice shillling......

Here are two examples off the website which prove my point...

Try stating inaccurate / dubious things like that in an academic paper for submission....


Again you are doing the same. We have absolutely no idea if it is any closer to GTO than my normal play, the creator haven't made any attempt to prove it. Limited bet sizing options is a huge problem from a theory perspective, not an aside.

If they want to stick to talking about having created a very good AI etc, thats fine. Just throwing around claims of GTO is what I am talking about.

I work in academia and would be laughed out of town if I put the sort of marketing BS in my submissions for publication.

I have a cure for cancer. You drink my secret potion and are suddenly cured. I can't prove this in the slightest but cancer patients have testified that drinking my potion helps them fight cancer even though it hasn't actually improved the timeline for people dying compared to a placebo and the testimonials are on my web sites and from a few anonymous accounts on a cancer forum.

And if you disagree how about you come up with a cure for cancer that's better.

Also fwiw the way you measure how close to go you are is measure your winrate (lossrate) against the nemesis strategy. How come the legitimate limit bots people build for ai competitions do this yet snowie hasn't even mentioned that as a metric they're looking into? Maybe they're worried people won't buy their **** once they realize how far from gto snowie actually is?

LOL...I will try that approach with my next submission for a peer reviewed journal. I'm sure I will get it published.

I have proofs of this cure.

I'd like to thank doctor Zachvac for his great potion which has helped me fight cancer. I've tried it yesterday and I already feel better, I don't need my chemotherapy anymore, thank you !
Mary

At first, I was skeptical about doctor Zachvac's magic potion, because I'm smart and skeptical and wouldn't fall for a random quackery. But after discussing it with my friends and my grandma, I thought I should give it a try. And I must admit I am amazed at the potency of this potion ! And also, I know it's not a placebo (because it's written "not a placebo" on the back of the potion)
Jennifer


As a very serious scientist myself, I'd like to say that through his recent researches, doctor Zachvac has achieved a scientific breakthrough which will make the world better for everyone. Plus, it's really scientific because there are some equations and he uses complicated terms like neoplasm and GTO.
Peter, a real scientist (well not exactly but I have a highschool degree where it says I'm good in science stuffs)

To reinforce zachvac's post here is more concrete information:

The computer poker research group from the University of Alberta published a paper 3 years ago that describes how they are measuring the exploitability of the agents submitted to the annual computer bot competition:
http://martin.zinkevich.org/publicat...i2011_rgbr.pdf

Why there is no data on Snowie's exploitability?

I haven't read the whole paper, but AFAIK it's only applicable to limit hold'em so far.
However, given the poker abstraction snowie uses, I guess it should apply inside this abstraction model, but I don't think it's possible to use this method in NLHE yet.

Dear MidniteToker and all 2+2 readers,

after reviewing our public messaging, we realized that on the first layer of our website and communication materials there were some potentially misleading statements.

As an example, we appreciate the fact that simply stating “Play perfect Game Theory Optimal”, could be misleading to “PokerSnowie plays perfect Game Theory Optimal”, which would be an untruthful statement. This was not our intention of course, also because if you read the articles on our website and on our blog, you would realize that we are very honest with what PokerSnowie currently is and how we plan to evolve.

Having said that, we felt that the many criticisms we got about this (some of which very “colored”, like the one of MidniteToker, which I’m quoting) are understandable and we started a review of our statements in order to amend this. You might notice that we have already changed the main title of the home page, as well as the first two most relevant headlines. These three things were the most visible and criticized ones.

We are open to any additional feedback you would like to give us and we will take into consideration any comment about untruthful statements that you feel we are making on our website.

Best Regards,

Roberto Gobbo
CEO - Snowie Games Ltd.

You're right the paper addresses LHE. If Snowie's abstraction is too large then one-on-one performance on the competition should give interesting empirical data on how strong it is.

Front and centre on the main page....


Even...

at best you aren't presenting facts to back this up, at worst this isn't true.

If you stop trying to make these outlandish claims that are just marketing BS and stick to claims that are true, you would be so much better.

If NLHE was a 1 street game only, the value of having position wouldn't be great. The value of position increases the more streets that are available. So, how come Snowie recommends bigger betsizing later, allowing villain to bloat the pot early and allowing him to bet flop, jam turn?


Enter your Snowie into the annual poker bot competition. Prove that you have the best bot. Anything else is just an admittance of being a scam.

Dear Roberto,

first of all, thumbs up for your statement! It's definitely the right strategy to address the criticism present throughout this thread and alter your marketing statements. I would also like to say that the statement “Play perfect Game Theory Optimal” is in fact misleading.

As oracle3001 pointed out, there are still some very misleading statements on your website. Here's another one, found in the "Challenge PokerSnowie" section:

I think there are two major questions left, and most people using or criticizing Snowie would appreciate more transparency in regards with these two claims:

(1) Strength of PokerSnowie's gameplay
You claim that "PokerSnowie is probably the world's best NL Hold'em poker player", yet we're missing (as far as I know, happy to be corrected here) any proof of that. Not only have human players (over arguably small samples) beaten PokerSnowie, but Snowie also hasn't played vs other "bots". There are two ways that have been outlined in this thread how you could at least provide a benchmark for your claim: (a) measure the EV of a complete heads-up strategy that maximally exploits PokerSnowie's (current) heads-up strategy (aka compute the EV of the nemesis) and see how "far" we are away from GTO (b) let PokerSnowie compete with other "bots", so that we can gather some data (producing results that may or may not turn out to be statistically significant) on PokerSnowie's profitability. I understand if you do not want to pursue either one of these options, and that's of course completely within your rights. However, if this is the case, I would at least expect a general statement regarding your perspective on these things, in addition to some sort of "proof" on why you think PokerSnowie strategy is really as strong as you advertise it, given you have provided no (objective) benchmark.

(2) Convergence of the training algorithm into GTO
You explain the "technology and training" here: http://www.pokersnowie.com/about/tec...-training.html. You basically say that you're created an AI and a "learning algorithm" for poker based on "neural networks". You then state that in the first stage of learning you let PokerSnowie play vs itself completely at random, and that the learning algorithm allowed Snowie to learn the "basics" of poker (aka calling an all in on the riv with 4 high is -EV).

Then comes the most interesting, but also very confusing section: "PokerSnowie on the way to Game Theory". This section is supposed to educate the reader/user how your algorithm converges into a GTO strategy. Let's recap, you start with:

Basically, you're saying that you're applied some sort of additional algorithm so that Snowie "balances" its strategy in a way that its strategy becomes "unexploitable". You then say:

My question is: Why? Do you have any proof that your algorithm will converge into a GTO strategy? I'm not a GTO expert by any means, and although the intuitive description of your algorithm makes sense at first glance, I'm quite sure that one can program various algortihms that do exactly what you said yours does, and I'm also sure a bunch of them wouldn't converge into an equilibrium in full HUNL, even with some betsizing abstractions. The burden on the proof, as others have pointed out, is on you, since you claim it. Without a proof that PokerSnowie's learining algorithm indeed converges into a GTO strategy, you can't really use "GTO" for marketing purposes. If you had access to a supercomputer today that, say, allows Snowie to play another 1000000000000000000 hands in one day, are you certain that Snowie's strat is very close to "true" GTO tomorrow? Or can you go a bit more into detail what algorithm you're using?

In addition, what is your perspective on the doubts raised in this thread towards the "solvibility" of n-player NL (n>2)?

I'd like to conclude with addressing two statements on your "PokerSnowies's weaknesses" section (http://www.pokersnowie.com/about/weaknesses.html) that are very at odd with my knowledge of game theory:

You give an example of an obvious mistake, where Hero faces an all-in on the turn. You then say that a human player would usually (a) estimate his equity vs Villain's range and (b) calculate pot odds. Then:

Seems even more unlikely to me that your learning algorithm converges into GTO when equity and pot odds aren't first-order variables in your algorithm.

Then, you talk about the betsizing abstractions you've made and state:

Bolded part seems also very odd to me.

It would be great if you could take some time and address the above points. Thanks in advance.

I have used snowie extensively and am generally impressed however I've noticed a few problems or bugs

When facing a close allin in certain spots snowie will say allin ev 0.01 or fold ev -0.01 . It does this far too often for it to be correct , like having just a 0.01 bb diff in equity in a lot of spots is super unlikely . Reason for this ?

Also it advises some ridic folds . An example just now is 100nl 6max . Btn minraises to $2 . SB calls . I call from BB with Tc6c . Flop is 5c4c2c

SB checks , I check , btn cbets 75% pot . SB folds and snowie advises me to fold here after flopping the flush !?! Yet if I change my cards to Ad6c it then advises me to call ?! Only possible reason I can think of is that we will def lose a lot v bigger flush or fullhouse with Tc6c whereas we wont lose a lot with Ad6c if the board pairs on the turn for example . I guess it doesn't expect btn to ever cbet much there tho , probably puts him on sets or flushes ?

Another hand there were 2 limpers and I had 55 . Flop was 665 and a bet and raise in front of me and snowie told me to fold . I understand this one a little more since snowie prob doesn't understand limpers ranges very well but still seems a bit crazy

Kind of undermines confidence in it's other advice when you see stuff like this

Its wining 17 bbs in PLAY MONEY , lol
Master ;P

obv: sarcasm on

Hi Babarberousse,

My name is Mike Johanson; I'm the first author on that paper, and a PhD student with the University of Alberta team that made Polaris and Hyperborean. I'm going to stay out of the conversation about Pokersnowie (I don't know nearly enough about it to have a useful comment) but I can say something about the paper and computing exploitability in no-limit.

In the paper we only used the algorithm on heads-up limit because there were lots of unanswered questions there (nobody had ever done it before!), but it's absolutely applicable to no-limit or Omaha or any other poker game (even beyond heads-up, but it's most meaningful there). There's no theoretical problem at all with applying it to no-limit, but there is a practical one - if you really want an exact exploitability value, it would still take too long to compute in practice.

However, it's very easy to use that algorithm to get a lower bound on exploitability, so that you know a bot is exploitable for at least X, and possibly more. X can be surprisingly high in no-limit, even for bots that are competitive with human pros. That's just like the case described in the paper for heads-up limit, where the version of Polaris we used in 2008 to win the Man-vs-Machine match was still beatable for 11.75 big bets / 100 (or 235 milli-big-blinds/g), which was awfully high compared to the win-rates you see in real games. But if you find out that a bot is beatable for at least X, and X is big, then you know it's definitely nowhere close to equilibrium.

Heads-up limit has 3.162 * 10^17 game states, and the type of heads-up no-limit we currently play in the Annual Computer Poker Competition, $50-$100 with $20,000 (200-blind) stacks, has 6.311 * 10^164 game states (cite). The best response computation is about proportional to the size of the game. So while evaluating a bot in heads-up limit takes about a day (using a cluster of computers) and is thus pretty convenient for us, exactly measuring a no-limit bot's exploitability would take an absurd about of time.

But that's to measure how much a no-limit bot can lose against an absolutely perfect opponent that does no simplification on their view of the cards or the betting. If you want to make a tractable computation and get a lower bound on exploitability, you can always run the algorithm but restrict the best-response player to only make a handful of useful bet sizes, like 0.5-pot, 0.75-pot, pot, 1.5-pot, and so on, instead of dollar amounts, like $50, $51, $52, ... $20,000. So, say we use 5 useful bets, instead of all ~20,000 exact bet sizes. That simplified computation is far far easier (and we've already done it a few times for our no-limit bots) and gives you a lower bound on how exploitable the bot is. A "better" best-responder who had more betting options is guaranteed to win at least as much (since they could always just use the same strategy as one with less) and might win more.

One of our team members, Josh Davidson, did this computation last year to evaluate the no-limit bot that we submitted to the 2011 Annual Computer Poker Competition. We had done a few tens of thousands of hands of testing with it against human pros, which isn't enough to get statistical significance in no-limit, but neither side showed an edge and the feedback we got was that it wasn't bad. When we ran the best response restricted to the same restricted betting options that the bot used, but with a perfect card representation, we found that it was exploitable for a pretty huge 3,367 milli-big-blinds / game: more than 3 big blinds per game. That's huge. And even worse, that's a lower bound: an opponent that had more betting options could win even more. Possibly a lot more, since one of the best ways to exploit these types of bots is to make bets that fall in between the bet sizes that it uses (like 0.75 if the bot only understands 0.5 and 1 pot bets). So even though our 2011 no-limit bot was trained using game theoretic techniques, and it wasn't bad in games against human pros, it was still massively far from equilibrium in the real game.

The computation is much harder for our more recent no-limit bots, since they use a much larger number of bets at each decision (this helps a lot defensively against humans and other bots that attack the betting abstraction like I described above), and we've surpassed the point where we can efficiently do best responses that use that same big betting space but no card abstraction. The best response algorithm still works, but it's just not fast enough to be practical - we'll need to find one or two more computational tricks to speed it up. So for now, we can't make any real claims on how close to equilibrium our more recent no-limit bots are.

But for smaller betting spaces, say for bots that only make 0.5-pot, 1-pot, and 2-pot bets, this type of best response computation should be feasible using the algorithm in the paper. In fact, the 2011 bot that we already evaluated had those three bet sizes and a few more as well. And even if that was too hard to compute, you could always try evaluating a game with smaller stack sizes, like 100 blinds or 50 blinds instead of the 200 blind stacks that we play with, just to see how well the algorithm that's learning that equilibrium strategy actually works.

-- Mike

Awesome post, thanks for all these clarifications and thanks for updating us on some important poker researches.
When I said "I don't think it's possible to use this method in NLHE yet", I indeed should have added "from a practical point of view".

But if I understood correctly your post, it is indeed realistic to use this method to find a lower bound of pokersnowie's exploitability.

As you are certainly the most competent person in this thread, could you answer a few game-theoretic questions ?

How accurate do you think that this lower bound is ?
In other word, what do you think of snowie's claim quoted below ?

How relevant do you think Nash Equilibrium is for nlhe with more than 2 players ? How strong do you think the best current nlhe bots are in these games ?

Lastly, have you published any feedback from the pros or recent analysis about the strength of your no limit bots in HU ?

I don't want to derail the thread, so I'd rather not talk about our bots or equilibria in ring games, or even speculate about Pokersnowie, because I don't know enough about it to comment. I just wanted to clarify the best response computation bit.

As for how accurate the lower bound would be, you could do the (restricted betting) best response and get an exploitability of zero, and still be far away from Nash equilibrium in the real game. It only tells you something useful if it comes out high. It couldn't prove that you are at equilibrium, but it could definitely prove that you aren't.

As for the 0.75x bet, there's actually two problems: an easy one and a hard one. The easy problem is that it might be optimal to bet 0.75x but your bot can't make that bet size, and so you lose some value. But it's probably not too much worse to make a 0.5 or 1 pot bet, so maybe you haven't lost much. The far far more dangerous problem for most of the game theoretic strategies I'm familiar with is when your opponent makes a 0.75x bet and your bot doesn't know exactly what that means, and you have to treat it as being somewhere in between 0.5 and 1. Or, far more dangerous, if the bot doesn't have a bet size in between 2-pot and all-in, and a 12-pot bet is wildly different from either side of that range. There's been a decent amount of research by my team and by the team at Carnegie Mellon University into "translation" techniques for patching over these betting abstraction holes, but it's still probably the easiest to exploit weakness in these types of programs. You can plug that hole by adding many more defensive bet sizes, like we do, but that's expensive in that it makes the game you're solving much bigger. This is the actual dangerous problem, and it's what could make the lower bound computation not meaningful: even if you are unexploitable in the restricted betting game, you could still make big mistakes in the real game when your opponent attacks these gaps.

Thanks for these explanations.

I understand that you don't want to have a childish argument with snowie in a 2+2 thread, but if I understood you correctly, what you said basically implies that the abstraction model described by snowie should be highly exploitable (unless they use, for example, more "defensive betsizes" as you explained). It seems like an important question they should answer.

I'm guessing there are no good method to find any useful higher bound of exploitability ?

About the other questions, could you answer me in private message if you think this could derail the thread ?

It hardly comes as a shock that abstracting an infinite number of bet sizes down to 3 or 4 will result in a strategy that is highly likely to be very exploitable in theoretical sense / a long way from equilibrium.

That doesn't mean it can't be a tough bot that appears difficult for a human player to easily "exploit".

You are right (well, except that the number of bet sizes is never infinite in poker).
But what the snowie team seems to believe is that this is not "critical".