Live 1-3, $500 Cap, Florida

Bttn straddles $6 and is $300 eff
Hero raise BB 8-Max to $22 AcKs $750 eff
Player on direct left cold calls $750 eff
Bttn defends

player on left is a recreational who is def capable of folding top pair against alot of action, and will flat kinda wide pre. all offsuit broadways, all pairs, all suited connectors and gappers, maybe even stuff like T9o or 98o or Q9o etc. He used to be a huge whale but after getting stacked repeatedly by me seems to have realized he can't bluff me like crazy/run me over. Still prob calls too light tho

Bttn is a splashy side recreational who seems to be kind of thinking, but def no solid theory understanding. Think will call down too light in general too with top pair, especially when the SPR gets lowered like this.

Flop JhTd4c
Pot = $60
Checks around

Turn 5c
I open action with a $40 bet, intending to follow thru on the river when a C comes in if I only face a call from one of them. Think vs the 2 check back ranges, they often do not contain Jx in range, and are capped at Tx and weak stuff that fold to a turn bet. Against Tx we have our outs, plus I can bluff club rivers to make up for any lack in turn fold equity we may have.

BUT what I am wondering after thinking about this hand, is what do we do when we don't turn a "flush draw" turn. Like say the turn is a rainbow, now what do we do with a hand like AK. Could we still profitably stab turn to give up river? Likely alot of Txin their ranges, and they also prob stab alot of their equity when check too(say KQ, Q9o etc)

I think it's prob not profitable to stab turn with out the ability to confidently follow thru on a good river like when we have the nut blocker. And it's live so after we check flop and go bet bet, I think these guys will just be like "you no have Jx or better cuz you check flop, so I call any Tx". I guess maybe it's a spot we just super underbluff unless we have reason to think we can actually make them fold some stuff?

Curious how other people may be approaching this situation. And how you may approach it from the get go on the flop.