I think all three spots are interesting, but I'm going to limit this reply to the first for various reasons. The short answer is that Phil cbets a high frequency as pfr in those spots to leverage the middling strength (overpairs, etc) portion of his range, which is where his range advantage comes from. To do this he has to size down quite a bit, which forces oop to defend more of his indeed more polarized range.

The more polar ip strategy you're describing is a very different way of attempting to maximize value, and I'm sure you size up/normally with your QQx2+ and bluffs. It's that strategy that Phil's suggesting WithColor is adopting in a multiway pot, because being up against two opponents he should polarize his betting hand selections to a much higher degree.

As to which strategy is better at maximizing value, which I think is ultimately the question you're trying to ask and might be opponent/player pool dependent, the intuitive reply I can give is this: I think Phil's method is more attuned to the specific dynamics of this situation, but as you mentioned there are factors that cut against it. The main benefit I see to your strategy is that ip gets one street closer to showdown with most of a very showdownable range, and indeed it doesn't require a lot of protection as it should be quite rich in both overcards and overpairs.

But it seems like you cap your range pretty effectively with a ~70% xb, and particularly on 22x you might want to check full range instead as it seems like a very high percentage of your 2xxx is going to have to be in your cbetting range, considering that you have so little of it. I think this is a huge problem, and one that oop will attack very naturally by leading large on a lot of turns, which puts you in a difficult spot with precisely the category of hand you'll have most often and the one from which your equity edge comes - overpairs.

By contrast, Phil's strategy allows him to remain uncapped cheaply, while also using the advantage that ip's range has rather than turning it into a handicap. This puts oop in difficult spots with a ton of his air, as it's really hard to continue a high percentage of the time on 226 type boards with hands that feel natural/have equity.

Would have really appreciated a timestamp or even a left/right table indication.

Great post, Brian. Again, sorry I didn't get back to you sooner. This could become a very large topic, perhaps worth a video to explore.

Cliffs: I agree with you.

I think a high cbet frequency and a small sizing works very well exploitatively (even against many 25/50 players), but it doesn't appear to make much sense from a theoretical perspective.

On 22x and 33x the disparity in trips+ combos is quite large in favor of BB vs. Button. If we changed the board to TT6 instead of 226, the discussion would be much different.

On 226, I'm getting:

Since BB has many more 2x+ hands and many more gutter+ draws, he probably needs to be the one doing most of the betting in theory (a lot of leading, most likely).

I think it's very interesting because BTN has a very small equity advantage, and has many more QQ-AA hands, which have BB's non-2x+ hands drawing very slim.

As John mentioned above, checking back makes it difficult to bluff (leveraging the JJ+ part of our range) since we open ourselves up to a large polarized raising range (large in raise size and in frequency) if we indeed cap ourselves.

If BB never led, I would be interested in checking back at a very very high frequency, including many 2x hands (perhaps 100% as John mentioned).

Once BB starts leading at a high frequency, we then might want to cbet more often when he opts to check (but not so often that he's incentivized to go back to checking all of his x/r hands). We probably still don't want to bet super large, as most of our range is simply trying to leverage our equity advantage (once he checks) and deny equity.

I'm not sure where it all shakes out, but I think it's clear that BB needs to lead this board quite often (in theory), and that if BTN is c-betting at a high frequency on these flops, BB can take advantage by having an insanely high x/r frequency.

Thanks for that pokerjuice breakdown Phil. Some of my wording was terribly far off, haha.

I still like the idea of cbetting a lot quite a bit, but I guess I'd acknowledge (again) that while I don't think it's amazingly better than a checking strategy, I do think that if it can be justified theoretically it does give playability advantages.

Isn't it possible to address the issue of how close the ranges run in btn's sizing? I'm not a total math reject, but this isn't something I've quantified before (and there's probably just a freaking button for it in pokerjuice, but bear with me while I talk it out, please). What I'm thinking is that if bb has x% 2x and that has y% equity vs. abcdef; average xy over abcdef and sum with x(sub)1y(sub)1 for other parts of bb's range, and I think you get an answer.

And I think the answer is that btn is still pushing equity because the advantage that his overpairs (by which I mean to refer to an overpair that fears very few overcards; distinct from say "mid pair") have against the air/gutter+unders/etc is very nearly as large as bb's advantage with his 2x. And btn has a lot more more overpairs than bb has more 2x.

And if btn's pushing equity, doesn't he get to bet? Theoretically, I mean. If a 2bb cbet induces a check-pot half the time, isn't that a good thing? And if bb has such a high xr frequency, isn't he kind of dead in the water when he check calls (maybe he never check calls)?

Stopping here because I'm tired and I'm going to start spewing forth a whole bunch of..stuff.

Well, I read Brians questions and thought they were good. I read his answers and thought they were good. Thus no reply and just clicked the Like button.