Snowie's quiz today states that when we open any hand preflop it is to steal the blinds, even opening KK utg which was its example. This sounds like something an OMC would say who is afraid of getting his KK cracked.

But it's true.

If there where no blinds the correct play would be to fold all hands other than AA. In a raked game you should also fold AA.

How is it true? Isn't a standard winrate with KK around 4-500bb/100? Winning the blinds is 150bb/100 so surely it's better to have players continue to your open when you have KK than when they all fold and you steal the blind?

KK will win a lot more than the blinds, but if there where no blinds you would have to fold it.

This is true in the abstract theoretical sense. As Sklansky says, every hand begins as a battle for the blinds.

But if you took a table of low limit live degens and told them there was no blinds for the rest of the night, take a guess whether they'd fold everything but aces or not. If you only played aces, you would be guaranteed a (long term) profit. But you'd make a larger one by playing more hands.

Playing only aces might be the game theory optimal play in that situation but it would rarely be the maximally exploitative play.

Yes that's true, but this is the game theory forum so I'm looking at things from a game theory point of view.

I have no problem with your opinion as stating, I was just clarifying.

But this isn't a game theory forum - it's a poker theory forum. And that should and does include knowing how to exploit your opponents. Knowing the GTO solution for this case is important mostly so that you know why to deviate from it.

the video also suggested that MOP supported opening close to a min raise UTG,MP,CO and 3x on the BUT?

anyone have some page numbers for MOP where i can find info on this claim?

Page 268.

What's this got to do with anything? There are blinds.

Hi.

I heard about snowie at Thinking Poker podcasts and I am using it for a few months now to analyze my play after sessions. I might say that it did improve my game, especially to better balance my ranges.

However I do not see a point discussing whether it is GTO - it certainly isnt and what they claim is only that it is close to GTO. With its limitation of just 3 bet sizes it has huge handicap so it by definition cant be optimal. It could be close to GTO n that game of 3 bet sizes, but noone is playing that. But they are still running learning algorithms, so it is clear it is not optimal in that game neither.

But it is a nice toll to use as complementary to other lerning resources - what i do is adopting the moves it suggested if I can get some logic behind it and ignoring the others. One thing I did not odopt is bet sizing preflp. I bet bigger from early and only 2 bb from button in six max. What do you thing GTO and what reasonable play in small stakes should be?

One more detail that was missed in this discussions - snowie is supposed to take rake into account for it's decisions. So decisions can be different for different stakes, since rake is relatively higher in micro/ small stakes. So having rakeback as most pros does also influences ( probably in a way the higher the rake tighter you should play).

But regarding GTO in raked games I have some doubts if all the theory holds - a lot of game theory is based on assumptions of zero sum game. But raked poker is not and in stakes i play (0.5/1) rake has huge impact on winning rate. So what do you think, does all mathematics like nash equilibrium and GTO still hold or they collapse? I can see cases with rake where both players might change their strategies for mutual benefit - paying less rake. What do you think, is there sound mathematics for strategies in non zero-sum games?

At last a common sense post in a thread of bs, wp sir!

I have a mother****ing poker snowie question why the **** does it want me to fold AJo for .5BB more ootsb when there are 4 limpers from utg, utg+1, CO & btn in frnl all 100BB deep? The stakes were 10/20 if that matters which it should not to the point where ranges would change so that we're folding for 10$ more w/ AJ here.

Not sure if this has been mentioned before but I'd be curious to know what Snowie's 6 max stats are.
Not only the 'std' VPIP/PFR/3Bet but also its barreling stats, WtSD%, W$WSF etc I doubt the creators would release this sort of info but it would be interesting none the less. Anyone tested its game game enough to have an idead? Presumably you wouldn't be able to find any leaks in its stats if it were truly close to GTO?

Some stats like VPIP, PFR, steal attempt, fold SB to steal, Fold BB to steal, and aggression factor by street are shown for coach along side the player session stats in the Playing stats section.

In a 33k Full ring Zoom sample I'm looking at, it shows the VPIP 15.57, PFR 13.36, Steal attempt 34,74, Fold to SB steal 88.38, and fold to BB steal at 64.29.

The aggression factor stats, and any post flop stat would not be the same if Pokersnowie was playing unless the player had played it the same way to get there.

These are Full ring stats not 6max.

because it thinks their ranges are a lot stronger that they actually are

that does not have to be true. Snowie tries to not be exploitable. It actually does not care about opponents range at all or even assume a range.

Just out of curiosity, I tried the poker challenge to see what it thought GTO was. While I know GTO has been solved for push botting up to an M of 10 (10 x blinds + antes) which for most on-line tournaments was about 2.5 bbs posted. With no antes that provided an overlay of around 1 BB, I'm pretty sure, GTO would suffer slightly.

I could believe that GTO might be solvable for slightly bigger stacks with a really good bot program that used a neuro-net to monte-carlo some better results with a ton of computing power but, I'm sure there would be diminishing returns on efficiency with some limit to how efficient it could be with after trying out every combination if ranges for all bet sizes which I'm sure wouldn't be practical today.

After reading the website, I saw that it wasn't supposed to adapt to any particular player but it would adapt to its collective database which was fair enough given the definition of GTO.

I could see that it seemed to imply that it didn't adjust it's ranges for how deep the stacks were. I'm certain this couldn't be correct because hand combinations value will change with how deep the stacks are.

I also saw that it was only setup to choose from 2 open raise sizes of half pot and pot size (2.25bb, 3.5bb) which again I'm certain is incorrect because as stacks increased the most efficient bet sizes must also change, especially if ranges are not adjusting.

I could see that there must be huge gaps which must be exploitable. So I decided to figure out where they were.

Another big thing I noticed was that I recall that I picked up somewhere where it couldn't account for ranges that were too far outside of normal ranges.

To be fair, it only claimed GTO for preflop ranges which is still a pretty far fetched claim in my opinion but in order to do that I new it must sacrifice ranges for postflop play.

I set it up to reveal all hole cards after the hand which was nice of them and I could see that it used suited aces as blocker bluffs as well as many suited connectors in order to balance preflop bluffs. Again, this is a mistake for anything beyond 100 bbs. The reason being, it would require removing far too many of the suited combos so I could just rep. whenever a the board made a flush against it's calling ranges.

I set it up to the max 200bbs with an auto-cap for 5-max and 6-max games. First I attempted a hyper laggy style that should have been able to play well outside of the tighter ranges by playing not only for the bigger implied odds given the 100:1 implied odds it was providing by raising only 2.25 bbs or > 200:1 from the bb but by overbalancing my bluffs anytime boards went outside of Snowie's range or at least in it's thinest spots.

This hyper exploitative style wouldn't work with humans because they would see I was bluffing too much, but again literature from Snowie said that it would not adapt to an individuals style so it should ignore my bluff frequency. I chose a VPIP range of maybe 80% and would lay claim to any boards that fell outside of Snowies range. Even if the flop would be in Snowies favor, I would float or bluff my way to any turns or river cards I could rep. It couldn't balance well enough on the flop because I was repping all turned straights outside of Snowies range, just about any flush when Snowie just called preflop, any small pair that hit, and all backdoors as well.

I started out getting myself pretty deep in the hole because I would play every hand to the river to get a sense of where Snowies boundaries were. As I hoped, it would not bluff catch thin enough when I repped a hand regardless of how much I bluffed.

Once I started using this tactic, I made up about a 600 bb deficit and was up about 600 bbs but then Snowie started hitting runner runners that would make sense how a hand was played but each time it did so, it had to get there with the thinest ranges imaginable. Often it would be a single combination that had to improve turn and hit river but it would hit these 1% ranges way too often.

I then focused on defining it's pre-flop game. I decided to work backwards and just started shoving 100% pre-flop for 200+bbs or more to see what its preflop limitations were and not expecting it to be profitable at all. After about a hundred shoves in a row. I could see that it really did still try to stick to it's normal pattern and would raise fold and even 3-bet or 4-bet fold everything but aces even though I was shoving every hand. Now I did realize that eventually it would make AA given the 6 opponents I had set up for about 2.7% of the time. Therefore I had to make more than 2.7% of my stack per shove but even though it was wasting bets by continuing it's usual style and folding, I was probably not making enough and as my stack grew it would make that 2.7% less likely. I wasn't expecting it to be anything close to be profitable but it was a lot closer than I thought it would be. Then I knew I could just tailor some variation to work extremely well.

I tried a half stack shove to see how it would react figuring I could cut my losses in half by assuming a shove would be AA and fold but the first time I saw it bluff shove a suited ace I had to abandon that idea.

BTW, if you think seeing all hole cards is too big an advantage, GTO is supposed to be exploitable even if the opponent knows exactly how it's played.

I kept making adjustments until I came up with a min raise open with ATC at 200bbs , and adjust with my stack as it grew, i.e. at 225 bbs, I'd open for 2.25 and so on. For almost all 2-bets or 3-bets Snowy attempted, I'd shove with a blocker ace. The blocker would cut AA combos from 6 to 3 plus Snowies fixed ranges were still too wide where the increased pot sizes should have been profitable. I think Snowies 4 bets narrowed considerably to some suited aces AK, QQ+ and it also would find the pot odds to call with KK and occasionally QQ so I'd just fold to any 4 bet which didn't happen enough to worry about.

I'm sure this should have been pretty profitable by itself. Whenever I didn't have the blocker, I'd just call with ATC pre-flop and stacks were still plenty deep. I noticed that it didn't open raise with suited connectors but would bluff with them so there was still plenty of room to rep flushes and small boards.

I'd pot control with 1/2 bet flop and either 1/2 pot or pot bet turn leaving plenty behind to make a massively over-sized shove on the river. I'd only shove rivers where Snowie would have missed around 95% for the nuts or near nuts it needed to call with.

For example: on a KTT board, it floated QQ, turned the Q and still folded a blank river!!? Reminded me of a certain celebrity who checked behind on the river with a similar hand on PAD.

Using this strategy I took down nearly as many pots but for much much more getting in flop and turn bets. Anytime the flop hit Snowies range, it didn't matter much because I'd either pot control for back doors or just give up when the turn would support Snowies range. I didn't do much to refine my strategy beyond that but it was clear that it should have been a massivly winning strategy that could just play according to set rules like a black jack dealer. Clearly Snowie was balanced for GTO for only the bottom most action but anything over that would just be a huge hole.

Only a couple leaks where Snowie would CR turn with an oversized bluff or semi-bluf would leave it too pot committed for me to continue or preflop action made a shorter stacked Snowie opponent pot commited to call my river shove too wide but the frequency of those hardly put a dent in the 90% of hands I was winning.

By this time I was down about 4000 bbs due to the 100% shoves and all the other exploring. But I was making that up very quickly. But the frequency of AAs pre-flop and plus nuts on the river just kept increasing so anytime I got close to money back, it would stack me again.

Call it a conspiracy or paranoia if you like, I'm just reporting what I thought was an interesting experiment, and no I didn't think it important enough to record numbers so I don't mind if you don't want to believe me.

To get some scale of the situation without actually recording and calculating the numbers, I'd say that AA came up about 5-6x as many times as any other pair. Remember all hole cards were revealed. Could my memory be biased and inflating that number? Almost certainly. Could it be variance? Well you could call a monkey painting a Rembrandt variance for all I care.

I guess they just figured that players wouldn't be getting into these extremes to notice the difference. Even with my first attempt using a hyper LAG style where I was getting to the river maybe 50%, I wasn't that certain.

Sample size was small but when looking only at the hands it was winning, it was plenty. I could have kept going to try and prove my point but once It became obvious, I didn't feel it worth the trouble. It was around a thousand hands for my first try and about a thousand hands when I was seeing the river nearly 100% of the time.

Given that it cheats when facing clearly exploitative styles. A more subtle style could probably sneak past it's radar and win over 5,000 hands which I read has been achieved but I decided I learned all I wanted to from my little experiment. I'm a US player so I don't expect to have to be facing Snowie styles online to perfect a more reasonable style that human intervention would require. Its not that hard to adjust for light 3-bet, 4-bet games when effective stacks are 200-300 bbs deep.

The problem I see with this kind of game when stacks are deep is that there's still too much playing room to close action pre-flop forcing a player to play with a range that's too well defined post flop. It just allows me to hit enough variance hands on turn and river with no problem finding enough hands to balance. Against well defined ranges, I can also use thin value bets that makes it even more profitable. This ensures enough dominance on the later streets for much more money that more than offset the -EV I'm playing pre-flop and flop for much smaller amounts.

I'm not saying any style I use isn't exploitable. They all are, but I haven't seen any style that includes too many pre-flop raises to be effective. It's just so much more important to maximize your range bandwidth post-flop where most of the money is going to get in the middle.

Hi all,

we have been following the discussions about PokerSnowie on 2 + 2 since the start and we have been thinking about the best way for us to bring value to the conversation. Therefore we decided it was time to join and answer to your question. We realize that the thread is long (27 pages) and this is going to require some time – we will do our best in the coming days and weeks.

We feel that the first relevant key topic to answer is also one of the most general: how close is PokerSnowie to perfect GTO? The answer is pretty simple: we don’t know. And it’s not so easy to measure.

Our AI has been trained with the objective to approximate as close as possible GTO, and the training is an ongoing process which we plan to continue for a long time and which is making our AI stronger every day. By the way, let’s avoid a misunderstanding: the training process is completely unrelated from the hands that Snowie plays vs. humans.

We believe that a comment that Ed Miller has written about PokerSnowie at the end of his last book, describes perfectly the situation: "While it appears today that it has not yet approximated a perfect strategy, it already plays a very strong game comparable to many of the world’s elite players. In the future, PokerSnowie will only get stronger”.

Besides this, we are not claiming that "we solved the game", but we have other professional poker players, writers and coaches who are confirming that the AI is playing at a very good level; more details about this sort of due diligence on our AI will be released during time. As far as we know, today it also appears to be the only publicly released product being close to GTO enough to be useful for analysis and training purposes. Finally, the current results on the challenges seems to confirm that the level of play of PokerSnowie is strong.

As stated above, we will patiently go through the thread in the coming days and we will try to provide answers to most of your question.

Best Regards,

Roberto Gobbo (CEO) & Stephan Samson (Head of Marketing)
Snowie Games Ltd. - Malta

And yet, the title of your web page states clearly: "PokerSnowie – Play perfect Game Theory Optimal (GTO) poker"

In other words, it's marketing bull****.

I completely agree with that.

Most beginners (and even some good players) are actually pretty confused about what GTO is. I'm glad that you admit you have no idea how close you are from GTO but this part is definitely not very clear when browsing your site.

I have a few questions that have been already asked and which I think are very important:

- Have you ever tested snowie vs another AI ? The designers of Hyperborean, slumbot or neopoker probably wouldn't decline a challenge and if your program is that strong it should be able to beat them.

- Have you ever tested snowie vs a human ? The "match" against jungleman doesn't look serious because of lolsample and lack of HH.

- You use an abstraction of poker with only a few betsizes available, how do you know how well this abstraction relates to real poker ? I think this issue was adressed somewhere in your blog, but as far as I remember not much details was given about the maths.

- How efficient do you think GTO is in 3+-handed poker ? From a mathematical perspective, there's no reason to believe that a Nash Equilibrium is a good strategy with more than 3 players. In particular, a Nash Equilibrium is exploitable in such formats. This would make snowie's approach worthless for anything but heads-up.

- Would you agree to make the code source of your RNG as well as the room you use public ? You don't have much interest in keeping it closed.

A snowie challenge was organized on the french website poker-academie against a group of coaches from the said website. Snowie performed extremely well (congrats for that) though it was clearly a lolsample where the coaches didn't have time to adapt. It should still be a proof that snowie is not a joke:
http://www.poker-academie.com/commun...9-janvier.html

However, some of these coaches have expressed doubt about the RNG, and one of the challenger even left because to him snowie was obviously cheating. Using a sample made public by one of the challenger, I showed that snowie's rungood had less than 1% chance of happening (http://www.poker-academie.com/forum/...15.html#736265).
The snowie coach "Sharp" as well as a pokersnowie employee participated in this discussion but as of now the issue hasn't been answered.

Though I don't want to accuse you of anything without a more solid proof, why don't you bring more transparency to the challenge ? It is one of your main marketing argument, so making the source code of the room and your RNG public would bring a bit more credibility to this challenge (although the fact that some player just open shove every hand still kills the credibility of this challenge).

Awesome. Could you go ahead and replace all your marketing materials to say this instead of what they currently say, which is sort of the opposite? Thanks!

Now that this has turned into a blatant advertisement thread, can it please be locked?