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Couple random thoughts (no conclusions).
The thing about dry flops is that they're not dangerous - should we bet when it's not dangerous? It's probably either a way ahead / way behind situation with us being way ahead and there are a lot of second best hands the opponent can improve to that will pay us off later. Also the opponent is an aggro-donk. It's not unlikely we can merely check to him and let him take himself to value town.
On the flop we have a sweet SPR. He has $126 behind and the pot is $42. For people new to planning bets around commitment consider this: If you bet pot now, it'll be 3 times pot on the next street - and then you bet another 3 times pot and have gotten everything in on two streets. A simple 'reality check' rule of thumb is to take the stack behind, divide it by 4, check if it's below the current pot - if it is you CAN get all in on two bets if you fire out pot sized bets. The smaller it is, the easier it is to get all-in.
In the present case we have exactly 3 times the pot behind, which can be bet in many ways - one pot sized bet and one 2/3 pot sized bet for example - but preferably probably something in between. If we bet $32 we'll have $94 behind and build a pot of $106 - this could be enough to get a shove called on the turn. Often bets on earlier streets are called more with curiousity - also they are smaller amounts and carry implied odds. Both these suggest that we could maybe go as high as $36 for a $114 pot and $90 behind which is even more callable when we shove. Counter to that is received wisdom that wet flops take big bets and dry flops take small bets. This bet sizing hint is just one of course, where bet sizing around stack sizes and commitment decisions is another, and arguably a more important one.
I think to come up with a good play here (extracting value) we probably have to consider what our opponents range is. He opened the button small (wide range), then called a small/standard 3bet which considerably narrows his range. He's in position, so he may have done this with a number of speculative hands, expecting us to play premiums. He could be sitting on a premium himself, or something like a T9s. He could have a pocket pair between TT and QQ, but he almost certainly does not have KQ or any other top pair hand that will stack off easily except if he has AK too.
This suggests to me that if we bet hard on the flop with the plan to shove the turn he will likely either outright fold the flop, or fold the turn when he sees that we're shoving. On the other hand if we show weakness he might be willing to fire a steal bet off himself even if he has nothing. That's money we would not otherwise have won.
Alternative plan 1) Callable bets - the slower betting plan. $20 makes a $82 pot with $106 behind. $40 on the turn makes a $162 pot with $66 behind. This might enable us to get the villain to cross the commitment threshold without registering it until it's too late - or it might put us in a position where we're putting in our biggest bets when we're already beat.
Alternative plan 2) Check/call flop if he bets small, check/raise flop if he bets big. If check/call, check/call turn and if he doesn't bet just shove river. Anyway - we're still planning to commit our stack we're just thinking about how to make sure the opponent puts his stack in.
Worth noting is that people who sit down and play this aggro will often just leave the table when they stack off - so balancing ranges as Splenda mentioned is probably not a key concern. It might even help us image wise if other players observe us if they think we'd actually play this way against them.
If I thought some of the above in this situation I'd probably check and let the villain take himself to valuetown.
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