74o Bet or Check Raise?

I'd probably bet 40 for the sizing progression lolz.

These spots are always weird to me because if I bluff they seem to always call Qx and if I value bet quads they seem to always fold Qx.

As said in a recent thread, you are supposed to bet a smaller size when you don't have many bluffs and I think it's likely that most of your worst hands are flushes here so maybe 40 is about correct.
But I don't see him raising ever, and he might just shrug call all Qx for 80 or even 120.

It depends on your image and how much you think V will be willing to call with Qx. If V hit his flush, you probably aren't getting much if anything, so I would focus on Qx.

If we were bluffing and V turned QJ face up, how much would we need to bet to bluff him off? I wouldn't even try it. So we can absolutely go chunky. For a normal person, that might mean something like $150.

If you have a reputation for occasionally betting huge OTR and have been caught with nothing or showed a few bluffs, now we can go for $400. If you have a really nice crazy image, jam. The larger you bet, the more rarely you need to be called, and most people are going to have a really hard time folding a Q here. If he does fold a Q here face up, then you know you can bluff the river like crazy in the future.

I would only consider a small bet if I was certain that V was going to raise a lot, but so many players will just call in this spot thinking that worse will never call them. I don't get it, but I've seen it. If V was a good aggressive player who is going to bet all their Qx and maybe turn some flushes into a bluff or might even seek value with TT, then I would bet small or even check to induce. But if we have to do the work, $150 minimum, AI maximum, depending on how aggro your image is and how fed up with your constant raising V is. If I were brand new to the table with no image, I think $200-$300 is the range.

My guess is that V has a much smaller range that Yami is expecting, and I wouldn't be shocked if H mainly had flushes and 4x (even QxJc seems dubious from H and 66 more likely).

Throwing something into GTOw that is not that close but maybe gives an idea:

GTOwiz 9max 100bb:
V as LJ opens 2bb
folds to H in BB who calls (no 74o, but 74s calls)

H bets 33% flop (96.3% check overall, and not for off that for 74s) and 50% turn

H now shoves a small amount of 4x (with 53s/42s bluffs), but mixes check with all of them apart from...
Q4s 100% checks
A4s 100% shoves
T4s ~90% shoves

...again, all ranges are tiny due to flop deviation.

V has TTc (and JJ with more JJc) but checks behind (incl. JJ) pure.
Even KQ mostly check behind.
AQ is about 50% check / 50% bet.
QJs/QTs is about the same as AQ, and it's also bluffing AJo/ATo/JTs/T9s

If H shoves then V folds AA/KK a lot (and the calls are 0% EV) AQs/KQs fold pure. Only real value calls are QQ/66/A4s.

It wasn't a raised pot - everyone limped. It GTO world, this position would never happen and everyone's range is a ton wider than they will ever be in a solver. We are well out of solverland the minute V limps.

So what is V calling with OTF? He is calling any Qx he played preflop. Which probably includes Q9s-KQs (some people might even open limp AQs, don't get it but I've seen it). And let's assume QTo-KQo. That's a lot of Qx combos that could reasonably be in a limping range.

Is V calling $20 into $33 with QTo in position? I'd say "yes". Most humans are going to do that on this board. Is he going to raise KQs? Not necessarily. So that is 39 Qx combos going to the turn and no real reason to believe a "passive" V is raising with them often.

What else is V calling flop with? Some FDs, but is V calling every FD? The board is paired. If V limped with 78cc, is he calling? Some will, many won't. A2-AJcc certainly calling, A2-AJss... maybe? K8-KJcc sure, and if V is calling wide we can throw in K9-KJss for the backdoors. So that is 26 FD/BDFD combos calling. Is V calling with Jx and lower FDs? Let's give him a couple like 56cc and JTcc because maybe V is going for the longshot runner runner SF to get a BBJ. Maybe two other random FDs/BDFDs. So 28 combos total.

Is V calling with pps? We can discount QQ, KK, AA. So lets assume he is limping with 22-JJ. 55-JJ might call one barrel but probably not always, should raise but V is "passive", so lets assume V calls 55+ when he has a pp with a club. 21 combos.

So 88 combos going to the turn 39 Qx, 28 FD/BDFD, 21 pps floating getting to the turn.

The turn removes a ton of these. Yes, we only bet 40% pot, but what is calling?

Well is V folding QT to a 40% PSB? Almost never.

Is V raising with KQ? I wouldn't expect a "passive" V to raise KQ here frequently.

So substantially all of V's Qx would also call the turn.

All the BDFDs fold. So we have A2-AJcc and K8-KJcc and JTcc. A6cc and 56cc no longer exist. So 14 combos of flushes probably continue. Is V raising sometimes? Certainly. I think Ax FD raise here somewhat frequently, even from a passive player. Let's assume Ax flush gets raised half the time and everything else calls. So when V calls, we now have 9 combos of flushes.

The pps? Is V still calling? Well we gave him pps with a club, so 66 is out, 55 certainly folds a lot. So we have 77-JJ with a club. Some of those fold. I think continuing with 10 combos is probably generous.

So going to the river, V has 39 combos of Qx that might play this way. 9 combos of flushes, and 10ish combos of pps. You might argue with some of the assumptions above, but clearly V has a ton more Qx combos, mostly focused on those double broadway Qs which people will limp both the suited and unsuited variety, and all of which would likely play this way post flop. I think V rarely shows up here with KK/AA those that limped were looking to trap and would have raised flop. Maybe you have a super slowplayed QQ rarely.

GTO is never getting to that range, but V isn't playing GTO so we shouldn't gear our betting range towards a GTO V's range, which never gets here. V will sometimes have a flush, and sometimes have a pp below Q, but roughly 2/3rds of the time V has Qx.

We'd have to bet tiny to get value from flushes - is V calling even $40 with an Ax flush? Probably not.

Is V calling a $40 bet with a pp below a Q? More likely, but hardly guaranteed.

Even against a small bet, I think V makes a "hero fold" with some frequency. But, because the math is so lopsided, lets assume that V calls $40 100% of the time with every flush and every pp and of course every Qx.

So we have V calling 100% of the time when we bet $40. So we win $173 100% of the time.

What happens if we bet larger?
Let's bet $150. Is V folding Qx against $150 when he just rivered a boat? I'd say almost never. Passive players who limp in to see cheap hands are not folding for $150 when they river a strong boat. But let's pretend that somehow V finds a hero fold 25% of the time and never hero calls with the nut flush or JJ. We guess that V has 39 combos of Qx, so let's say he calls with 29 of them. That would be 29/58 total combos that get to the river. Or 50%.

50% of the time we win the $133 in the pot because V folds.
50% of the time, we win $283 when V calls.

That is $66.50 + $141.50 = $208

Even though V goes from folding 0% to folding 50%, we make a larger profit betting larger. In fact, with a $150 bet, V would have to fold approximately 75% of the time before we are better off betting $40.

As we ramp up the sizes, the amount we need to be called decreases. If we are betting $400, we only need V to call about 10% of the time to match a $40 bet.

90% we win $133 in pot when V folds.
10% of the time we win $533 when V calls.

$120 + $53 = $173

We are betting with zero risk of losing, so now we need to figure out the largest number V would call with Qx a reasonable chunk of the time. If V thinks we are drunk and a loose maniac, we can jam. If V thinks we are tight responsible players coloring inside the lines, I think $150 gets paid almost always by Qx. I don't think its worth trying to price in the flushes, at the expense of letting Qx off cheap. V has a ton of Qx here. To the extent that 1% of the time V has QQ and has been trapping us the whole time, then when we bet chunky he still jams and we win the lotto today. Whether we go for $150, $250, $300, or $400 greatly depends on how V perceives us. I would not expect a V who limped pre to suddenly wake up with solver discipline when he rivers a boat. He is going to pay off a very chunky bet.

Grunch:

What a luck box!

PRE - obviously check.

FLOP - I love the bet. I'd love it more if it was bigger.

We can get called by a ton of PP's, flush draws, and QX. Might as well pot it before things get weird on future streets.

TURN - Honestly think I'd just check now, to see what V does. If he checks back, we can go for thin value on the river. If he bets, we can flat call, as long as he doesn't go crazy with his sizing.

RIVER - OMG.

If our read is that V is tight-passive, I think I might 2x pot it.

I mean...it's a limped pot. We'll never have AA/KK/QQ here. We're not leading out on the flop with 66 if we didn't raise pre. Any pair is a boat, and V can have a ton of 55-99 that thinks we're FOS when we go bet-bet-bet.

These sorts of extreme boards give most players fits. No one studies spots like these. He's just going to check back with a turned flush, and he'll probably check back a lot of PP's that would have a hard time folding after we take this bet-bet-bet line when the nuts change on every street. He might even check back QX sometimes.

He called a big bet on the flop, and a smallish bet on the turn. Pray he has QX and thinks we're just trying to bluff him off a chop. I can almost hear him say, "Well, if you got it, you got it...a 4 is good, I call."

Result: Hero bets 220 and V calls after a few seconds. Perhaps there was more value to be had with a larger bet or a check raise.

I think it's a good bet if you don't have a lot of history with V. Sure, you want to find that point where V goes "Ugh" and tanks for a good long bit before calling, but that is a hard line to find in real time. The check raise/blocker bet to induce is probably optimal if V is going to bet out, but if they don't those plays are a disaster. So absent knowing V well, I think $220 was a very reasonable option.

I think you played it fine, and got max value, or close to it.

I'd have bet bigger on flop and river, but I'd also have checked the turn. Plenty of ways to get to the same end point.

Out of curiosity, I ran a solve on pio with this spot. Gave it an option for a pot-sized turn (the solver greatly preferred your bet size), and gave it the option to bet 20%, 200% or 400% pot on the river. For the ranges, I gave H everything except JJ+, KQs+ and AQo+. All of which I think it is safe to assume you raise pre.

For V, I gave 22+, 56s+, 79s+ Q9s+, K9s+, A2s+ AJo+, KQo. I think that is a reasonable limping range and I kept AA/KK in there because sometimes Vs have the nutty idea of limp/raising with those.

OTF: H bets 10%, with 7c4x specifically, H should have checked 80% while without a club 74o was roughly 50/50 bet/check. Presumably because with the c we are less worried about charging FDs.

V was supposed to continue 65% OTF, all calling (raises were 0.02%). With hands very similar to what I outlined above, mainly any pair, FD or BDFD.

OTT: I provided a $30 and $73 (PSB) sizing. Solver selected PSB only 7% of the time with hands that primarily included a 4 (without 7c), Q6 for two pair, and Ax with a club. But all those hands are mixing sizes and the smaller size is preferred in all cases except bluffs like 56hh (I used 4h as the second suit OTF).

With the $30 bet, V is supposed to call 2/3rds of the time, raise 13% of the time and fold the rest. All quite intuitive, raises include nut flushes, sets and some bluffs like 77. Qx biased towards calling with only Q9 folding about 25% of the time. Most of the folding range are the BDFD hands that whiffed.

OTR: This is where it gets interesting - solver bets 4x pot 42% of the time and checks 57% of the time. It completely avoided the other size options. H should bet huge with most 4x except Q4 which checks over 80% of the time, and A4o with Ah rarely checks. All other 4x took the big bet 100%. The only other value betting this big is Q6. Then a bunch of random bluffs, T2, 82, 82, 78, etc. Basically, the solver is checking back most Ax/Kx/Jx trash, and is betting huge with all the low trash that took this route.

V is supposed to call only 17%. Even many Qx fold. For example, KQ is 100% fold and many of the other Qx is mixing about 40%ish folds. AQ is 100% call, and obviously QQ/66 are 100% call. AA without a club is calling, AA with club is folding. KsKd is mostly calling the rest of KK is over 80% folding. The solver is bluffcatching with 88 and 77.

So the bottom line is that it looks like the solver prefers to bet 4x pot and with that bet V is supposed to fold Qx about 40% of the time. So the question we need to answer, is faced with a 4x pot bet, is V going to overfold or over call? That probably comes back around to our image and V's nittiness. Obviously that's subjective, but I trust the solver's math is much more precise than mine in calculating the 4x bet ($520) is best if V is going to fold Qx about 40% of the time.