Actually 50% is tight, but it should be fine for you. ~60% is normal. Defend % = 3-bet % + flat %, if that isn't clear.

Completely, but that's why you asked in the first place.

ahhh ok, yh ofc defend is those things i was just thinking it was call.

mkay cheers

i wish this thread weren't 9 months old, but maybe someone yet will jab with me on this.

i don't understand why people feel there is so much value in making the SPR smaller with hands that benefit from having a larger SPR. at 100bb i 3bet polarized (to me polarized still includes the majority of broadways and depolarized means 98s/A5s but not hands like J2o) and i see/have no problems with it in practice. in theory i could see it becoming troublesome if my opponent started 4betting extremely small (which fortunately has never happened), but even then it's still combatable by having a small 5bet range and/or beginning to 3bet more depolarized. also of course it's an issue when deeper and board coverage becomes more important. however i feel most people 3bet more depolarized than they should largely because they are unaccustomed to using only a single overcard as a semibluff or, in some cases, bluffing with ~0 equity but choosing the best blockers. there is no theoretical reason i can think of as to why we should necessarily aim to avoid these situations. additionally there will still be plenty of hands in my preflop value 3bet range that still end up functioning as mediocre to strong semibluffs. of course 3betting depolarized gives us more hands that flop and turn equity and thus more barreling opportunities, but, as always, the tradeoff is that you have to put some amount of dead money in the pot if you want to reach that game tree node.

This isn't that meaningful in the context of your argument. A polar 3b range is correct against some player types, a non-polar one against others. It's possible that you are mostly facing the former.

Neither range shape is objectively more correct than the other. It'd be incoherent to argue as such, because no strategy has an EV against a null counterstrategy -- a counterstrategy needs to be defined for a strategy to have an EV.

It seems like you're taking the position that a polar 3b range is "correct" (I've already explained why that isn't a tenable position), or maybe even that a non-polar range can't be best except in exceptional circumstances. Wrt the latter: HUNL as a whole, on the "tough sites", post-2012 or so, would disagree with you . (Although the ranges currently in vogue tend to have a bit more mixing and aren't "cleanly" non-polar.)

It also seems like you are undervaluing 98s/A5s massively; it isn't too hard for them to be relatively clear (thin) value 3-bets. Even 54s. (If that surprises you, think deeply about it.) The leading sentence, about hands "benefiting" from a certain SPR, doesn't make sense; that isn't how EV works. You determine whether a hand is more +EV to flat or 3-bet first, and then you can say whether it benefits from having a certain SPR -- not the other way around. How do you think the bit of wisdom you're referring to, that SCs/SAs "prefer" certain SPRs, originated in the first place? Did people just make it up, conjure it out of a witch's cauldron? No -- it was a conclusion drawn from estimating EVs. And of course it isn't always correct. E.g., commonly in the specific spot we are discussing.

On the last sentence: Yes, 3-betting re-opens the action, but by definition -- literally -- under the circumstances where it's correct to 3b a depolar range, re-opening the action doesn't pose a significant enough problem for the BB to change strategies. Because, generally, where it's correct to 3b a depolar range, the BTN's 4b-call ratio is tame. (This has been discussed upthread.)

Well, this would be the wrong reason to 3b a depolar range. That isn't how EV works either.

*mumbles something about EV not working that way*

I mean, if the goal was to maximize barreling opportunities, we'd just 3-bet a range like [AA-QQ, AK]. Maybe a SC or two to be tricky!

Don't use that as a reason for anything. Crunch numbers. Estimate actual EVs. Don't work with weak correlators. Verbal reasoning sucks smelly donkey taint on the earlier streets. Seriously. The EV tree is way too complex.

sorry, i haven't had to be very precise with my language since college so i'm a bit out of shape. but yes, i'm conflating multiple problems. the first is how these strategies perform against the nemesis. the second is, if the polar strategy exhibits a lower EV against the nemesis than the depolar strategy, what sorts of tactical exploits lead to this and cause us to want to depolarize our 3betting range. the third is whether or not most opponents utilize these tactical exploits. but we need to solve the first problem before we can tackle anything else, so i'd like to focus on that.

i'm taking the position that at sufficiently shallow stacks a polar strategy isn't obviously inferior or superior to a depolar strategy. frequently i take the agnostic stance on preflop problems because they're so intractable. where did you explain that a polar strategy isn't tenable?

how can you deal with preflop problems except in broad terms like these? i'm aware how EV works and that my SPR statement is not especially precise, but what other option do we have? are these calculations you're talking about in public record somewhere? or at the very least, is the methodology in public record? afaik tipton's books are the most in-depth and mathematically robust ones around, but even he doesn't begin to address preflop in the manner you're describing.

my SPR reasoning is roughly as follows:

in toy games we see that hands with non-nut potential have more difficulty retaining their equity at higher SPRs than at lower SPRs. we also see that hands with nut potential retain their equity relatively well over multiple streets at higher SPRs. it stands to reason, then, that hands with nut potential generally prefer higher SPRs, and hands with low nut potential generally prefer lower SPRs (assuming we are up against some constant range)

i realize that statement is a generalization because there doesn't need to be a linear relationship between SPR and EV. for instance, with A2o, an SPR of 0 is significantly better than an SPR of 6, while an SPR of 6 likely isn't that much better than an SPR of 12. EV also doesn't have to decrease or increase indefinitely wrt SPR (and i'm guessing it probably doesn't & reaches some maximum somewhere for most hands) however, it seems that relationship will largely hold true across most SPRs, and if it doesn't, i believe the burden is on the dissenter to show why it wouldn't (it seems to me saying "these toy game results do not generalize to full-scale poker" is slightly more unfounded a statement than "these toy game results do generalize to full-scale poker")

so what i'm doing is looking at the results of a toy game which has concrete payoffs and attempting to extrapolate those results to full-scale poker. of course SPR isn't the a priori argument. anyway, i don't understand how it is possible to approach preflop in a more precise manner than this. if you know how, i'd love to hear it.

ofc that wasn't an EV calculation. i'm addressing some cognitive biases that i assume people have against 3betting a polar range.

if i could sum the payoffs for every possible line against a maximally exploitive opponent and compare them, i would. my understanding is that BECAUSE the EV tree is way too complex we have no option but to resort to verbal reasoning and weak correlators.

I didn't say that.

Working with SPR alone (or SPR primarily) leaves out a lot. It's not like 3-betting magically lowers the SPR and does nothing else: the EV tree has other branches, and even along the two main branches (calling the open, getting a 3-bet called) you can't isolate SPR as the only relevant difference (e.g. range composition is influential too -- possibly even a lot more influential).

It's also a walking irrelevance / tautology risk. For one thing, if it's more +EV to 3-bet 98s than flat it, then who cares if it would actually prefer a larger SPR? And I don't think flat > 3-bet (or 3-bet > flat) is an emergent property of 98s preferring one SPR over another.

I didn't say that it was untrue, or that it doesn't (sometimes) apply to real poker. I don't think it's particularly useful here.

You could work with simple quantitative models.

That's guesswork too, but I think it's harder to delude oneself that way, easier to see when the results are silly, easier to be constantly aware of what you don't know.

yeah I know -- was directing that comment at the people who'd think that way

What assumptions for BTN play are you using?

Sauce has talked about 3-betting non-polar ranges on RIO; I'd recommend tracking down all of his posts on the subject. Here's one. Answering his question might be helpful.

ah my bad. i got very excited for a second!

i agree... selecting an SPR independent of everything else isn't a move in poker so, yeah, probably nothing i said is especially useful.

such as? the simplest thing to me that seems not-useless would be to lump together different types of hands we can flop and attempt to estimate the value of each one by again lumping together various turn & river combinations. then perhaps we can assign some reasonable looking strategy to our opponent and calculate. but first, this is already a fairly large problem. second, it's not clear what a tough strategy is (we are probably all still terrible compared to GTO). lastly, a tough opponent will incorporate multiple betsizes into his strategy, so already the problem seems too complex for a human to solve, and this is for a gross oversimplification of the game! anything simpler than that seems like it would have very questionable value.

without going into too much detail, i generally analyze BT opening 100% for a minraise, BB 3betting an undefined range to 8bb, and BT responding with 50-55% folds, 10% 4bets, 35-40% calls.

to answer his specific points in that thread, the less aggressive our opponent is postflop in single-raised pots, the less value there is in flatcalling relatively strong (or, shall we say, nut potential) hands. the less often our opponent 4bets, the more value there is in 3betting everything (our opponent can 4bet less often with larger sizing, so his choice of 4bet sizing is also nestled in this statement).

still, without knowledge of what equilibrium is, i don't see how we can apply these ideas confidently. for instance, implicit in his post is the idea that you don't need an especially strong flatting range, and when your flatting range is too strong it will cause your opponent to dial back his aggression to the point where certain hands become higher EV as 3bets, but who's to say where that cutoff point is?

also, no offense to sauce, but i'm not particularly trustworthy of him on the more complex topics simply because i don't think it's possible to be well-versed in them without a strong command of math & programming, which iirc he's admitted he doesn't have. a number of other high stakes HU guys also seem to be decidedly unafraid of playing sauce. although, from what i can tell those same guys all seem to employ a depolarized strategy even at 100bb, so i'm willing to admit that it's likely depolar is strictly better than polar. i'd just like to understand why (in a more specific way than EV(3bet)>EV(call)), since i find prevailing public opinion on the matter to be unconvincing.

fwiw, sauce seems like a relatively smart dude and would still probably crush me HU. i just don't feel he has the necessary qualifications here.

thank you for taking the time to read and respond to my posts, by the way.