H1 is well played in my opinion. 3 bet pot with the As on the board leaves very little value combos. We'll get shown sets and some occasional flushes but I'm also defending TPTK here.
H2 I'm still 4 betting BTN vs BB since we've seen him squeeze before and we don't have a large sample of hands on him. It's kind of gross to put in 30 BB then fold to the jam but if we have him on a tight enough range I'd rather 4B/fold then flat and hope to hit the flop. Not sure how aggressive V is post but if we are floating a cbet on most flops with 2 over cards then we are putting in more than the 30 BB anyways. As played the 3/4 cbet then check turn line is very strange. I've seen this both be a 3B that missed and tried one street to get a fold and a trap. The board is fairly dry and we have a pot sized bet left so I don't mind the turn check. Could get tricky if a Q, J, T hit the river but other than that I'd be ok with calling it off or betting for value if checked to twice. As far as sizing I think it's V dependent as well. Given the turn checked through I can go either way with 1/3 or even less or jamming. After V checks twice it's rare he has a monster on this run out. We can't bet fold though if he was running some elaborate trap it worked. I actually like the small river bet to try and get crying calls from AQ type hands. You mention getting value from hands like JT by betting turn but if we have his 3B range that wide we should be 4 betting. It becomes really tough to play a consistent line against a range that isn't nailed down so the answer of what to do on the turn seems to have changed only after we got the result and realized we could have gotten more value. I think it's fine to go with our read and then learn after the hand for next time rather than switching gears mid hand.
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