No, the above quote was a response to BackBlood asking why I 3-bet more pocket pairs against a 2x than a 3x 100bb deep. I have never answered a question about why I'd be more likely to 3-bet KJo vs a 3x open and more likely to 3-bet 77 vs a 2x open, and I never would, because the question contains a false assumption. I would 3-bet 77 100% of the time against both opening sizes and KJo <100% of the time against both opening sizes (more precisely, I should say that I think it's probably theoretically correct to - in practice, I play a pure strategy because it's easier).

The specific numbers are less important than the simple fact that 3-betting a smaller open at identical stack sizes results in a higher SPR, which implies that we ought to stack off less frequently post-flop (but with stronger hands when we do). This suggests to me that if our 3-betting range should be different against different opening sizes (as I suspect it should), then we should be less likely to 3-bet our weakest offsuit high-card hands (like KJo/ATo) and more likely to 3-bet some of what would otherwise be our strongest flats (i.e. offsuit connectors like QJo/JTo, some weaker suited 2-gappers, and perhaps more suited aces).

Correct. If you think you need >1p to win, then you should almost always just fold pf. After calling a 4-bet, you will usually need to stack off if you make a pair, which is why it's important to choose the right hands to call 4-bets with (i.e. not 98s, except in special circumstances).

100-200bb deep, with 77, do you 3bet/fold, 3bet/flat 4bet or 3bet/shove over 4bet?

Depends on the size of the 4-bet, but 3-bet/flat 4-bet against most standard sizings. I NEVER 3-bet/fold a pocket pair (except theoretically against very weird/large raises). If I don't believe a particular pair is strong enough to call a standard 4-bet, I either fold or flat it the first time around. 77 is plenty strong enough to call a 4-bet HU (it would not be against an UTG raiser in 6-max or full ring obv, hence I would either fold or flat it).

Spladle...I am only halfways thru this thread and I have to admitt, I am overwhelmed by all the knowledge you have about poker theory. I would appreciate if you could tell me how on earth you learned all of this?

Also, what approach would you recommend a novice like me to take if I have a goal to become better at poker theory stuff?

Thank´s!

Bump

huh, interesting thread, though it still not clear who was in the right here. It would appear that ronin was making a point about minimal defence frequency (mdf) and how it should be a baseline for our strategy, while spladle was saying that mdf is a one-street concept and is therefore useless in a multi-street game. However, mdf is still used today, exactly like ronin described, to create baseline for how much do we need to defend. So, it would appear that ronin was right? But mdf IS a one-street concept, so it shouldnt work like that?

also, this was kinda lost in all the other talk, but Spladle accidently gave an excellent argument as to why we should use very small sizings on dry boards like 884r, showing that betting 3/4 can be easy countered with strategy with super high x/r (he said he is x/ring 30% there)

I didn't reread any of the thread but vaguely remember its content. The mdf still applies, you would just need to adjust it for the street and board type. Each street will have a modified average mdf unique to it. It will be the average that the GTO agent defends across all board types.

The board type will have a far greater effect on the mdf.

As I think you have stated elsewhere, this sort of GTO approach is selling bicycles to fish, especially when you're paying >10bb/100 in rake.


Might as well brood over whether red is better than black at roulette. GTO uses every sizing by the penny. Almost no one who plays serious poker does that. If you habitually use a smaller size, you can legit widen your value range. If you don't, you can't.

If we like to bet a lot because we can get folds, then the board is being overfolded. Do smaller sizings actually get higher returns?

As far as xring 30%, anyone who's read and assimilated the useful lessons of Will Tipton's books should immediately recognize why a 30% checkraising frequency on almost any paired board is far enough from GTO that you couldn't hit it with an arclight.

Any strategy that did so would find itself with something like 150-175 checkraise combos versus a range usually containing every single nutted hand. No bueno.

I thought that MDF is pure bs argument by now?

To make villain indifferent from bluffing you need the assumption that bluffing has 0EV and that villain checking has 0ev, neither of which is true.

Especially OOP facing a bet- the in position player needs to do better than checking (or indifferent as in the vast majority of cases) with his "bluffs", and the EV of checking is quite a lot higher than 0. I don't think I've come across any boards where vs a correcting betting play defending >= MDF occurs.

Idk if you are serious here, but it has been proven mathematically that the number of betsizes GTO uses in ANY game is bounded by the number of distinct holecards.

So on any street GTO would have at most 169 sizes (this is just a mathematical upper bound- could be far smaller in a lot of cases).

I found this out recently, and it's cool to know that NLHE can be truly solved one day.

Also what you said about xr 30% being wrong couldn't be further from the truth. Actually in raised pots <25bb deep most paired boards have a far higher x/r freq than x/c.

The board doesn't even need to be paired. If you put in reasonable ranges for SB limp and BB check vs limp at 10bb, on AK9r OOP has 0 x/calling range and x/r it's entire continuing range (logic is OOP doesn't 2p as no K9s or K9o, Ax or KT+ and SB is betting 100% of air- apart from the pairs OOP has extremely defined and vulnerable hands- any undercard to the 9 is a bad card for him if he x/calls). The SB 3bets flop with TT and gets it in vs Kx 9x and JT QT QJ, and even has a min3b range on the flop.

I didn't know that, interesting, thanks. Do you have a link? Is it a coincidence that it's the number of suits squared?

It does sounds kind of suspicious though, especially if the largest bet size is anything near the stack. Maybe it's not. It would certainly make sense that GTO wouldn't, for instance, open shove a 7h6h5h flop. OTOH, if there were no upper bound, then in a 100bb game that means GTO's smallest size is like 35 cents*? That wouldn't quite smell right.

Yeah, that will be almost as cool as every reg on ACR down to HUNL5 perfectly understanding bb defense ranges.



Lol. As I recall, the thread is about HUNL, not the last round of a HUSNG.

There are other boards where oop is weak, but we're talking very specifically about paired boards. That's important because even on the most favorable paired boards for OOP, like J88, OOP is still missing something like 20 out of the top 50 combos and another 25-30 out of the next 50. Boards like Q22 are totally devastating for OOP's range.

The problem with being that weak with a bloated range, even in the first case, is that villain can take the anti-Spladle line, putting in big bets, and quickly get an EV of close to the pot. And that's if OOP knows how to play his range perfectly, which is unlikely given where he just ended up. That means he needs now to be expertly selecting from a palette of turd-hued options, for no reason other than pseudogtosis, of which this thread serves as a passable epidemiological study.

Which segues nicely into your next point,




While checkraising an entire continuing range may be fine 10bb, at 100bb deep its bump-stock night at Mandalay Bay. You list one of the psycho options OOP would be forced to choose if he were hell bent on doing something that crazy, even on an AK9 board. On Q22r, it's 767 lessons without landing class.


*a slip of small stakes solipsism. My frame of reference is NL50.

Talking about poker is tricky because the difference between phrases like "0 EV" and "zero relative EV" can radically change the meaning of what's being said. It doesn't help that I just coined the phrase zero relative EV because I don't even know what phrase to use there. Having to coin terms constantly and lack of a standard lexicon has been a main impediment to people learning poker.

Some would argue that's a good thing.


On the flop, it's possible the GTO defense frequency is >mdf on a board like 7h6h5h. The flop GTO defense average is probably about naive mdf - 5%. Turn will probably be like naive mdf - 3%. I am talking about raw percentage points ("points" to gangsters and banksters, of which gamblers are a subset), not percents of stats.

Above, the part that says

should read, "if it does open shove flop." And obv "number of suits squared" should be "number of ranks squared".

I think you could be right about 100bb+ paired boards in SRP OOP not checkraising >30%. But I take HUNL as a game of any stacksize >1bb.

Also 169 was my attempt at counting unique holecard combos (and making sure I was correct with the upperbound)- I guess in reality it's way less (AKhh = AKss and should have the same strategy preflop). In any case it's the idea that there is an upper-bound at all that's the interesting result. You can take this to the flop or any other street as well- but e.g. on an AsKsQs flop having Th5d is not the same as having Th5h- due to some subtle blocker effects (but obviously Td5h is the same as Th5d).

Unfortunately I don't have a link, and you can choose to not believe me but I heard it from a credible source.

Regarding MDF- still not sold on 7h6h5h. As I understood it on wet boards cbetting freq goes down, defending freq goes down as well and x/r freq goes up. I still think it's a useless concept.

IDK, I toyed around a little on PIO a long time ago and seem to remember increased frequencies in both cbetting and defense on wet boards, but that was on turn. If that's true, than it's one of the things that Spladle correctly predicted. Would be interesting to see actual PIO or equivalent flop play.


It depends what you're after. If you're concerned with academic precision, it's pretty useless. If you're concerned with highly accurate, real-world GTO play and you have access to a flop solver, a solver-adjusted MDF could be very useful in game, with some practice. Knowing the solver-adjusted MDF would involve knowing the average GTO defense frequency for the given street, knowing how different board types affect the GTO DF on the given street, then estimating the board and street-specific MDF for the situation.


In naive form — that's non-board or street-adjusted — the MDF is still extremely useful. Unless you're paying less than about 5bb/100, being able to roughly generate the naive MDF across all boards is a big step towards becoming effectively unbeatable. Doing something like using MDF - 5 on the flop and MDF - 3 on the turn would go a long way towards denying your opponent any rake-beatable edge.

Hey, thanks for the compliment. I learned a lot from reading and posting on 2+2 over a decade ago, then did some additional study on my own while I was playing for a living. Mixed games are great for teaching poker concepts that people who specialize in a single game often never learn. If you want to become better at poker theory stuff, I'd advise you to read/post on the forums and read poker theory books; not much more to it than that.

Wish I'd seen this sooner, but better late than never I suppose.

Even without knowing what you're talking about, I can guarantee that I was right.

MDF isn't useless in a multi-street game, it's just inapplicable in certain situations, i.e. after calling a raise from the BB and facing a flop bet OOP. The IP player will sometimes (perhaps even usually) be able to profitably bet two blank cards in this situation. On the other hand, MDF is very relevant when facing a PF 3-bet or flop raise. Your opponent should never be able to raise (rather than bet) two blank cards.

watergun7 is correct that the upper bound on bet sizes in any given situation is the number of unique possible hole card combinations. So pre-flop that would be 169, but the number actually goes up after the flop, not down.

This is not correct. "Minimum defense frequency" refers to the frequency with which you'd need to not fold in order to prevent your opponent from betting or raising any two cards. It can be calculated very easily if you know the pot size and bet size. Sometimes it's relevant (i.e. when facing a raise) and sometimes it's not.

It wouldn't shock me if the GTO c/r frequency in this spot (the one in the OP) was closer to 60% than 30%. Nothing wrong with playing raise-or-fold when facing the flop bet here.