I think his range is pretty small so we can just list his possible hands and see the best way to extract from them.
KK- You stack him everytime (unless he hits a 1-outter). Money is going in the middle regardless so its irrelevant.
AK- Same as above.
QQ- He HATES this flop and will probably fold to any normal sized CB. Checking and betting the turn and river probably does better against QQ. Alternatively, messing with his head and betting ridiculously small here seems reasonable. Can he really fold for 50 cents? Why would you bet so little? Any doubt you put in his mind or excuse you give him to call adds lots of value to your hand.
Another benefit to checking, you give him the 4% shot of spiking an underset. All of the above applies to JJ and probably TT as well.
Of course it should be noted that checking back this flop looks super scary and will still probably fold his QQ on the turn, but I can't see it folding out QQ more often than a normal sized CB. If he's the kind of guy who can't fold QQ here ever because "you might have JJ" then he's almost certainly not the type to have a change of heart and fold the turn because you checked the flop, after all "he might be checking because he has JJ!"
Small PPs: Was probably just setmining and will fold to any bet. I still think checking does better here overall due to the aforementioned 4%.
AQ: Depends on how good he is but he should know that he's not beating anything you'd put the rest of your stack in with. I think betting flop and turn will blow out most decent players who have any sort of hand reading ability. Chk/Bet/shove or Bet/Chk/shove are better lines vs AQ imo.
Suited broadways/random junk: Is it possible he would have a hand like QJs here? Seems very unlikely to me but thats really the only sort of hand that poses any threat whatsoever to you, and I don't think its out often enough to alter our play. Obv the best line vs this type of hand is pot-bet/shove, Checking the flop vs this sort of hand would hurt.
Overall: Checking, or betting farcically small seems to do the best against his whole range, despite the fact that it does run the slight risk of letting an uncharacteristically played broadway/suitedconn holding get there. Yeah, checking this flop back vs QJ
is pretty horrible, but on balance I think its worth the risk.
- If you do decide to bet the flop I don't think there is any reason to bet more than 1/2 the pot. For some reason I feel like a CB of just about 1/2 pot or even slightly less is viewed as weakness by a lot of players, but 2/3 to full pot is seen as very scary, especially in 3-bet pots.
- If you check the flop, as I think you should, and the turn comes a club or a 3rd broadway card, over bet the pot if he checks it again, like $15. If you bet the flop, I don't think you should bet any non
/broadway turns because they will fold out AQ or AJs too often whereas you may get the rest of their stack if you check the turn.
TLDR, I don't know how this happened.