Check-Raising AQo on the Flop OOP PFR three-way

My short answer is I dont think you lose a lot of value missing bluff/semibluff raises, the much higher value bluffs tend to be when someone shows weakness.

Theres a lot to say on a longer answer, but part of that answer is that MW, at least theoretically you oughta be range checking, and MP oughta be checking a lot as well, so raising MW with an uncapped range behind you would be rare.

I think if youre gonna be check raising, probably morso in HU pots

This.

And when you do check raise, you should probably do so linearly, that is, your strongest hands and hands with almost no equity. Only do this if you think they will call, though. Otherwise, call your entire range.

Thanks for that tip.

How would you answer my question if V2 folded pre, that is, heads up oop to the flop with AQo against a loose passive? What flops are you check raising, if any?

The short answer is if you are only checkraising monsters you are indisputably sacrificing piles of EV against the vast majority of players

I'm struggling to come up with any flops where I'm looking to c/r OOP in a 3-way pot with AQo.

Against a LP im check raising 0% of the time. Theoretically you also range check a bunch of boards to an IP caller, but thats because GTO plays a strong (but capped) range. Against LPs, that isnt the case. Any hand i hit im betting out, because LP dont bet often enough for CR to be valuable, id rather just bet my value.

If they check back flop, i delayed cbet and take it down ott or barrel and take it down otr, because they will be weak.

If they do bet, despite their range nor having a ton of air, im probably still calling with my weak hands including overs and gutshots and bdfds pretty wide, because they are only double barreling with really good hands, so if turn goes check check, i just bluff river with my air and scoop when they overfold hands like second or third pair or draws that missed.

So against LP im probably folding or check raising AQ damn near 0% of the time otf.

You don't need a monster to check raise. Especially at lower spr we can check raise with good top pair, overpairs etc and try to get the money in as fast as possible.

People play very face up. When they bet small it is a good time to make a thin check raise. Generally if you are the preflop raiser in a single raised and you have top top or better on a T high board or higher, generally that is going to be the best hand when you check and they bet small. If you can narrow their range to exclude hands like AK, then KQ is the nuts on a K high board and AQ is the nuts on an A high board. If they always 3b AQ, then KQ is the nuts on a Q high board, otherwise AQ is. Typically speaking, people don't check raise thin enough and they check raise bluff only with their very high equity hands like 8 out straight draws, flush draws, combo draws. They don't check raise enough with hands like guy shots or 2 overs and a bdsd, bdfd, or middle/bottom pair bdfd. On the other hand, live players tend to bet way too much when checked to. So check raising is very strong.

I can see a case for x-raising QTx or QJx boards for pure value with AQ against some loose-passives but probably not at a 150bb. In lower SPR spots (in your example the SPR is around 8), we can level a loose-passive into calling with Tx or Jx sometimes on the flop, since they might put you a fd or AK etc, whereas often if you x-call flop they xb a number of turns. You can still lead river against these players and get called by worse, but often the run-out makes such a value line more difficult.

Since LPs tend not to turn their weak pairs into bluffs, you might not get as much value from an x-c flop compared to an x-r. In this respect, I don't believe x-r bluffing a LP makes much sense, unless you have enough equity to barrel turn OOP (although according to the logic above LPs are checking back a lot of turns, so we can still just x-c flop and realise our equity often enough).

Theoretically, we should be x-raising enough to protect our OOP checking range. But this theory tends to be designed around players who will stab flop and barrel turn with air, which is not what a LP typically does, so against a LP we just exploit to the max and assume they stab only with weak value.

Short answer, yes, you're losing value if you only check raise monsters.

As the PFR, I'll check raise TPTK, 2P, sets, combo draws, NFD's, ISSD's + BDFD, pair + draws, etc, depending on the variables of the situation. As the PFC, I'll mix donking thick value with check raising for value or as a semi-bluff.

The frequency of our opportunitirs to make good flop check raises as the PFR goes up exponentially when we check range from OOP.