I think it really depends what your current style is like and how close your own play is to Snowie's attempt at GTO. I think a lot of players are amazed at Snowie's (low) c-bet frequency when it's OOP. Comparing your flop c-betting ranges to the ranges that Snowie recommends can be quite illuminating or indeed shocking. (There are some spots where I know most microstakes regs will c-bet close to 100% of their range. In the same spots, Snowie c-bets close to 0%).
The charts for balance and stats can be quite interesting too. If you find - for example - that you are too value-heavy with your river bets, then that's something you might want to work on.
Playing the challenges can be a lot of fun too.

The Callingrange from pokersnowie from the position SBvsBU against a raise (vs 2,5x) only contains 44 (100%) and K9s (50%).

How can that possibly be correct? Anybody has an idea how it comes to that conlcusion. Because usually pokersnowies preflop play is quite good imo and makes a lot of sense to me but this does not at all.

Snowie doesn't like calling in this situation at all, which is understandable.

Snowie does not like playing OOP. Calling would definitely put you in that spot. Also, calling would give a BB very good odds to call, so it would put you in a 3-way pot OOP, which is something you want to avoid. Raising gives you a chance everyone folds. Even if you hit a big hand playing OOP reduces your chances to realize a full equity.

Those two hands 44 and K9 Snowie would call just for a balancing purposes I believe.

Regards,

Isn't that small of a calling range super exploitable? When the opponent knows that you only have 44 and K9s in your range, he will have a very easy time playing against you in that situation when he opens BU and you call in SB. I do understand 3betting pretty much all of your hands in the SB is the right play but I don't get why Pokersnowie would then suddenly call with only two hands.

If you know exactly what is your opponent calling range in that spot then yes, it can be exploitable. But in the real world we don't know that. You could be raising 100% of your range in this spot, but it's always better to keep your opponent guessing. You could change the calling hands to be unpredictable.

Snowie doesn't "think" about exploitation like a human does, and it doesn't try to be "balanced" as such. If it flats those hands in that spot, it's because when it did its training, it found that the EV was maximised by choosing to call with those hands, but the EV of other hands was maximised by 3-betting or folding.
I presume that the EV of calling with 44 or K9s is very close to if not exactly breakeven, so if you were playing against a bunch of snowbots, it wouldn't actually matter if you just folded instead.

But cant someone see you call and know you have hands like these - that somewhat a massive chokepoint?

Typically with theory it doesn't matter if villain knows your strategy - in fact candidates for optimal strategies are often evaluated based on their exploitability by a perfect counter strategy (which assumes your opponent knows the entirety of your strategy). If you had an equillibrium strategy you could tell your opponent your exact strategy and the best he or she could do would be to implement the other strategy of the equilibrium strategy set, breaking even in the process.

Those hands being in Snowie's SB calling range simply means that over all the hands it has played it has found that flatting 44 and K9s have at least the same expectation has folding over all possible outcomes (as Arty has said). They could be anomalies due to the fact that Snowie hasn't played enough hands to purge them from it's calling range or they may never get purged and have at least the same EV as folding. Only time and more hands will tell.

He's right though, there's no way 44 and K9s provide enough board coverage to be part of a NE. I'm sure anyone who would be willing to put the time could get pretty close to a mathematical proof. Snowie's range is going to be super capped postflop and it's going to be easy to create a super profitable polarized range with BTN.
It's also going to be pretty hard for snowie to vb its sets and Kx.

I don't think your hand being face up is necessarily a problem. Just because your opponent knows what you have doesn't mean your screwed. I'd rather have AA every hand being face up for everyone to see at a FR table than to be given two random cards, but have them be hidden. People will be able to see what I have, but that isn't going to stop me from collecting huge amounts of money.

I don't think 44 and K9 are there to play back against strong holdings, but more so for weaker holdings like 96s or Q9o. A runout like AQ722 might come out and 44 might need to make some weirdly loose call downs on certain runouts to keep the weak hands from bluffing all the way. On some run outs you'll just be screwed and there is nothing you can do about it.

I don't really like it either. To compromise throw K9s in your 3-bet range and fold 44 or vise versa.

When you fold he has a very easy time playing against you.

You're calling far less than 1% of the time and only because it's slightly more EV than folding. Do you have some proof that the button would have such an easy time that you'd be better off folding?

Or looking at it in another way, do you have some proof that to be unexploitable, or difficult to play against, you need to call with a large range of hands from the SB?

Imo the burden of proof is on a side claiming it's not an easy time. The range is very limited and very weak against BTN open. It means on most flops OOP will have EV 0 and on the ones it's not 0 it will be very easy for the button to play reducing implied odds (for example it's clear where OOP hit a set).
OOP gets a lot from set but tha "a lot" is still a bit less than the whole pot. I run some postflop cases and for example it's 86% of the pot on 964 rainbow and only 22% on 963 rainbow. They get 0 if they doesn't hit the flop. They can't defend vs BB 3bet making the call almost dead money as well. It's just obvious the range is wrong and a result of calculations not being run long enough yet.

It's not about large range of hands it's about stronger range. K9s/44 is very weak and won't realize any sigficant part of their equity. It's easy to prove as well by running some postflop simulations and seein what the results are.

Although having AA face up might still be profitable with a small SPR, it still highly decreases the EV of this hand. If you were to limp your AA face up at a FR table vs competent players, you would probably lose money.

And AA is a very particular case as it retains strong equity on almost any flop, and therefore it's very difficult to get bluffed when holding it.

K9s and 44 are much more vulnerable and will obviously miss too many boards to yield a positive EV.

Put in a simple way, let's say you are always dealt 22 (and I know it) and I'm dealt any two cards that are not a pocket pair, so that we always have close to 50% equity preflop. But whose range is going to have the highest EV postflop?

And we're not even talking about the insanely profitable squeezing spot BB is getting.

I think if I was forced to open limp with AA face up I could very well make a profit even against competant players at 100BBs. As long as one is disciplined enough to find the fold button I think it would be an easy game. AA is just too strong of a hand to be able to bluff off all the time. Just pick your spots sparingly and take the money.

I think a lot of players who's range consist of only AA or KK in a spot get cracked a lot, but only because they aren't aware that other people are putting them on that exact range of hands and they get the money in when they are beat. If you know people are putting you on that range then you can beat them.

People limping in behind with handss like JJ, 77, 65s, and 33 won't be enough to stop AA from picking up the pot a majority of the time. True that other players can bluff by playing draws aggressively and over betting the pot on certain run outs. But still, AA will be able to win.


I do agree with your point about K9s and 44. There are so many runouts where you could easily be screwed. I think this is probably an error in Snowie's strategy. I do wonder if there are GTO situations where taking a -EV line could actually be correct to keep an opponent from making too many +EV lines against you.

An example of this might be folding to 3-bets. Do it too much and you can get bluffed with any two cards. You might want to fold TT, but call anyway because you don't want to get exploited by getting 3-bet and then folding too often.

If I have 22 against two overcards, and we make an agreement that when I shove you'll always call, then it doesn't matter whether I shove pre-flop, flop, turn or river. If your equity changed after the flop it, then when we shoved would matter.

SB needs about 29% equity to call. It has about 50% equity against a button limping range. On average it'll have 50% equity pre-flop, flop, turn, and river.

I'm almost certain some 2+2ers have already tried this experiment HU 100bb deep. IIRC, they realized that it was kind of close. That makes me think that in FR AA would end up losing, or show a very marginal profit at best.
Anyway, the idea is that having your hand face up highly decreases its EV. I don't think there's any debate over that.

Dude, you know what a Nash equilibrium is, right? It doesn't allow -EV lines because that would mean an unilateral change of strategy would increase the EV of one's strategy. Sure, calling a 3b with TT oop is -EV vs some opponents , but it can't be -EV in a NE because the EV of folding would be 0... If you get confused on this sort of stuffs you should read up on some game theory basics to clear your mind.

Sorry but I don't get your point.
Obviously we don't allow the player with 22 to shove preflop. And obviously the other player has the right to fold his hand postflop.
The idea is to show that there are obvious situations with close range equity (and probably with a positive EV postflop in regular situations) but which turn to be -EV because your hand is face up postflop.

Unless you flop top set at a ridiculous frequency, I think this is highly doubtful. If a villain knows your exact hand, but you have no idea what his is, he basically becomes a super-user that can bluff you off your hand on any board where you don't have the nuts, since villain has complete information, but you do not. Sklansky's fundamental theory of poker is at work.
e.g. if the board comes Q87, villain can rep a set, but you obviously can't. Your range isn't just capped. It's literally face up!

K9s and 44 have about 50% equity against a button limping range. We need 29% equity to call a 2.5x raise out of the small blind. On average we'll have 50% equity on the flop, and we need 29% to breakeven.

A couple people, including you, saw that it's obviously a huge mistake because our range is face-up. I was hoping you'd provide an argument that I could rebut beyond Proof By Obviousness.

Instead I'll argue with myself:

1. Assuming the Villain doesn't have blockers, 43% of the time they'll be a 4 or king on the flop. He can't bluff every flop. We can bluff/value-bet flops containing 4s and Ks -- maybe even nines.

2. On any 2-tone or montotone flop we could have a flush or flush draw. Villain can't safely bluff those.

3. We only need to realize 60% (29%/50%) of our hand's equity to show a profit.

That might not be a good rebuttal, but I don't know what your argument is in detail.

My argument was this:
So yeah, it's pretty much a proof by obviousness. Getting a better proof is probably very tedious.

I do not understand, if someone got AA every time in HU, regardless of having the nuts, he could go all in every time and would have more equity and pick up the blinds, he could only be matched by another AA

theoretical situation was stated as having AA and only the option to limp pre.

theoretical situation is silly and I wish there was a viable way to gamble on it.

@BrbCale:
For the scenario we were assuming that AA is forced to limp preflop, because then there would be no debate.

@Babarberousse:
I think I remember that HU challenge. The guy who had AA didn't ever value bet which I believe is a mistake.

I've tried it out with my brother and AA was a huge favorite every time. Then again, we aren't poker wizards.


In some situations it is correct to take a less +EV line for balance purposes to protect other parts of your range. I was thinking the take -EV line would be kind of the same thing where you prevent someone from 3-betting you with any two cards.

Not sure what you are talking about but it has nothing to do with a NE as explained above. I think that what you don't understand is that the EV of a specific strat or hand always depends on the strat it is facing.
A GTO strat is a popularized poker name for a strat that follows a Nash equilibrium. At such an equilibrium, both strats are always taking the optimal lines with every single hand, that's why it's called an equilibrium. Noone has any interest in deviating so noone deliberately takes "a less +EV line".

But very often, you'll see that a GTO strat is less than optimal against non-GTO strats. In these cases, it is indeed possible that the GTO strat takes a less +EV line (or even a -EV line) against the specific strat it is facing.

For example, let's assume X is a HU strat where the player open shoves AA and open folds everything else. A GTO strat will call with hands like TT+/AK which is clearly suboptimal. However, at a Nash equilibrium, the GTO strat is indeed taking the most +EV line and even the bottom of its calling range is still +EV.

Balance is not the aim of the game. Profit is.
A range might look "balanced" in post-game analysis, but the reason to check, bet, raise or fold is because it maximises the EV of your range. The importance of "balancing" or "protecting my checking range" is wildly over-estimated imo.

There are plenty of spots where checking top set (for example) might give the appearance of balance (because you also check the nut low), but the main reason you check top set is not to protect your nut low checks. You check because (in a specific spot) it's more profitable than betting. (There might literally be more value in inducing bluffs, or keeping a villain's range wide, instead of betting and causing a ton of hands to fold). If betting top set clearly had a higher EV than checking, it would be a mistake to check. i.e. If you slowplayed the nuts when you could have won more money by fast-playing, you reduced your EV, which can't possibly be optimal. GTO requires the maximisation of EV. It doesn't always require "balance".