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Hold on a sec. You're assuming this guy will just donk out with Ax here on the flop all the time? this is ridiculous he has almost every combo of Ax when he checks to us here.
You can stove a calling range here and see how you do vs it on the flop, unless we assume he'll call with stuff like any PP (Don't think we can quite do this simply based only on his preflop stats on this board) we aren't going to be doing all that well. Yes there are some draws, but that's a very small part of this guy's range and we're not actually that far ahead of flush draws anyway so we don't get super +EVness by betting vs them.
Since we've seen villain stab at pots in the past, our equity is going to be likely far better vs his turn leading range than vs his flop calling range. As the former will include Ax, draws, air and better Qx; while the latter will include Ax, draws, less better Qx, and most importantly a lot of air!
You have to be insane to want to bet 3 streets for value and shove river with 2nd pair, it's just so bad. Just to clarify are you doing that for value? if so, stove a range that he calls your river shove with and see what your equity's like.
So here's the bottom line. Regardless of whether or not we're slightly +EV vs villains calling range by betting this flop (which is in itself optimistic) if we cannot bet 3 streets for value and can get money into the pot with far more equity by taking an alternative line, we should take that line.
Here the idea is that checking the flop makes our equity way better when a turn bet goes in and hence we select a more profitable street to get money into the pot in a case where we cannot get 3 streets and lose very little by checking the flop and in fact stand to gain a fair bit.
I fear most of this post will go entirely over your head but try to have a think about these ranges and how they behave relative to our actions. Stop dwelling on half concepts and, as Sruviva would call it, "poker rhetoric"
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