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NL Holdem 0.25(BB)
UTG ($25)
HJ ($25)
CO ($25.14)
HERO ($53.39)
SB ($20.89)
BB ($29.94)

Dealt to Hero: X X

UTG Folds, HJ Folds, CO Folds, HERO Raises To $0.50, SB Folds, BB Raises To $2, HERO Calls $1.50

Hero SPR on Flop: [6.81 effective]
Flop ($4.10): J K 6
BB Bets $1.20 (Rem. Stack: $26.74), HERO Calls $1.20 (Rem. Stack: $50.19)

Turn ($6.50): J K 6 2
BB Bets $4.14 (Rem. Stack: $22.60), HERO Calls $4.14 (Rem. Stack: $46.05)

River ($14.78): J K 6 2 5
BB Checks, HERO Bets $46.05 (allin)

So many (literally) choices...

AdQ/T. Doubt you have to worry about the 43 str. There aren't really any Qdx choices, other than AxQd, which I think would be good to block AQdd, which is the most likely Axdd hand, other than AK of course.

Edit: maybe TdTx, since it blocks ATdd. That may be too targeted to be worth it though (same with AxQd).

ATo folds PF. AQo should be folding turn

You have to call some of these to have bluffs otr. ATo is a call in my ranges, but they are not specifically for high rake.

Without checking solver

Given KQdd raises flop and we fold most Ax FDs, we're not going to have too many flushes by the river so we're repping A6dd, KTdd, K9dd, QTdd, Q9dd, 86dd, 76dd, 64dd, 34dd (9 combos) and slowplayed sets (6 combos). So at 1:2 we're looking for around 7 bluffs.

We have AJhh, A6hh to block sets, athough villain would possibly fire those on the river so the blocker factor isn't that strong. Tricky. I think solver would possibly call with at least some of those AQ-AT hands as bailas said although I have some of those as 4bet pre. Other than that we might have to dig into weakest heart draws that would've called twice like 75hh and 54hh.

I think you are right and we do need to bluff heart draws here since we have nothing else really.

I'd X back AJhh since it has some SDV. AQhh might be too strong as well.

Weaker FD's make the most sense to me or some weak Axhh

I revert the question and ask what are our valuebets on R that take bet, bet, shove line

It is a tough one as most of your potential bluffs will either have SD, block some of villain's fold range, or will be unprofitable to call Ott.

Ideally, you'd have some AdQx or AxQd, but as you say, not great turn calls. Dunno how many Kx and Jx offsuit combos you have, but for example, AdJx would play like this, and make a pretty good bluffing candidate. You could take the SD value, but any hands worse than yours are folding river, and you have to expect to be folding out some better hands, just not too many. And you block the nut flush, AA, AK, and KJ. Not sure whether you call AJo pre though. I'd only bluff that if I felt villain was likely to overfold, because otherwise you're not folding out any better hands really.

So effectively, you're stuck bluffing heart draws. So I think you have to look at those villain is least likely to have. I reckon that the lower cards are less likely overall, as is the Ahxh, because it is the most likely to want to check the turn. So, I think here I'd probably want to bluff the club and spade QTs (as they block KQ, which I think might call), as well as some small to mid Ahxh. The more you feel villain will be folding, the more you can look to include some Jx with a diamond. No point in bluffing that if you're not getting folds from K9, KT or KQ though I reckon.