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What you need to do is plan your hands.
First, 3x vs 4x. Nothing wrong with 3x. What you need to do (for deception - not a big issue at 2NL but the principle holds) is to be consistent in your raise size. So if you raise 3x with this hand you should be raising 3x here with any hand that you raise. (Except if you make adjustments to this specific player and with this stats and at 2nl you probably can, but different story)
Opponent is 85bb deep. If you raise to 4bb flop pot is 8bb with 81bb behind. If you raise to 3bb flop pot is 6bb with 82bb behind. If you were playing a suited connector type hand you would prefer a 3bb raise over a 4bb raise. If you were playing a TPTK type hand (like AQ) you would prefer a 4bb (or even 5 or 6bb) raise over a 3bb raise. The question is - what range are you playing in this situation? If the range you play has more of the hands that require a 4bb raise you should raise 4bb. If the range you play has more of the hands that require a 3bb raise you should raise 3bb.
The fact that you come here saying that you should have raised more pre means that you do not have a plan for the hand when you decide to put money in preflop. Why are you putting money in preflop without a clear idea of how that is a prudent investment of your hard-earned cash?
A7o is a hand that flops crap. Any hand can flop quads, trips, two pair and that this hand can also flop these things just goes to show that it can't flop much better. If you hit an ace you would normally have to worry about being outkicked. If you hit a 7 there will typically be cards on the board better than 7. Why are you building a pot at all? Are you trying to punish him for completing the small blind? How about punishing him when you have the tools to do so? Preflop if he folds more than 67% of the time when he completes the small blind feel free to raise trash on the BB, but if he's just going to call, don't raise him with trash but rather check behind and just raise him with hands that have potential.
Or at least only raise him if you know his tendencies well enough to know how often you can bluff him off his hand profitably after the flop, because relying on flopping good with A7o is not a good plan.
Flop happens to give you TP. Good, you now have a weak-to-medium strength hand. The pair on the flop is both a blessing and a curse. It is a blessing because it makes it more likely that you can split with other aces rather than be outkicked. Like if you are up against A8 and any card higher than an 8 comes you'll be splitting. It's a blessing because with A65 there would be 6 combos of sets that crush you where as with AJJ only one pocket pair (outside AA) improves. It's a curse because while pocket pairs are certainly in his range, so are a lot of random jacks. Like AJ/KJ/QJ/JT/J9. While there are only two jacks left to make combos with that's still 36 or so combos.
So, the paired board here is more a curse than a blessing.
A cbet is not unreasonable. Checking behind is also not unreasonable. What hands are he checking with? Most of them really. If he's missed he wants to check/fold and maybe also with his pairs under J. With a weak ace he wants to check/call. With any J he wants to check/raise.
If you do decide to bet you should size your bet appropriately for the flop. This flop is scary-looking, but also relatively dry. By this I mean that there are no hands possible that have 8+ out draws. The best possible draw is a gutshot with a backdoor flush draw - on a paired board this might not even be a draw to the nuts. A big flop bet is mostly justified by needing to price out draws. You don't need to price out draws. If you want to bet, betting small is not offlimits. Now think about his continuation range.
Scenario 1: Continuation range of Jx, Ax, KK, QQ
Ahead of 12 combos
Splitting with approximately A9- maximum 62 combos - probably more like 15ish as some of the worse aces may not have been limped or may not have called the raise
Behind approximately 60 combos - presumably all AT or better aces have called.
So in scenario 1 you are really not betting for value. You are betting to pick up the dead money when he folds the majority of his range and whatever equity you have against his continuation range is likely to end up being very little as you'll either check down to showdown and maybe win part of the pot or fold to opponent aggression before showdown because you're behind.
Scenario 2: continuation range 22+, Ax, Jx
Ahead of 66 combos
Splitting with maybe 15ish combos
Behind 60ish combos
The idea of betting for value is stronger here. If we could bet for value there would be an argument for making a bigger rather than a smaller bet, but even in this best-case scenario for your hand the bigger bet is not a clear correct decision. You might argue that since the Jx hands will likely c/r you could bet for value and if the opponent then calls you can rule out Jx and continue betting for value. In the event that you see a showdown against a weaker hand I suggest that the way to keep the opponents range the widest is to bet no more than 2/3 pot on the flop, check the turn and bet 1/2 pot on the river. If he calls 22/33 type hands on the flop, this way he may also call the river.
My flop plan here is to bet 1/2 psb and then only put any more money in if I improve (a 7 does not improve me as it is counterfeited by the JJ on the board) or if I strongly feel that my opponent has continued with pairs below J that are willing to pay a little more on a later street. In that case I will consider a small value bet on the river. Bluffing (beyond the cbet) is not part of my plan.
Checking behind the flop and doing a delayed cbet on the turn is more likely to get weaker pairs to call, so if you think he is reluctant to call with 22 on the flop but would be willing to call 22 on a blank turn - check behind the flop. Yours is not a hand that wants a big pot, so pot controlling one street is not a bad idea.
As played, fold. He has a jack. Or to put it differently - the range of hands with which he check/raises contains so many Jx hands that you cannot profitably call hoping that his time he's holding one of the few bluffs in his check/raising range.
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