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I don't think that there are some completely unavoidable -EV plays, but there are some situations where you might decide to make a slightly -EV play preflop in exchange for the possibility of a much bigger +EV play post flop.
An example would be where you're on the button w/67 and decide to call an UTG preflop raise of 3bb when no-one else has entered the pot and you've seen him get KK cracked. It's -EV because the 67 is way behind the normal UTG PFR range, but your read tells you that if you hit the flush or straight postflop then you've got a good chance of stacking him which would be a big +EV.
These moves mostly depend on your reads and your postflop ability, which should be much better than your opponent's ability if you're deciding to make a move like this. Normally you want to avoid these types of fancy plays at 2nl. Just play ABC poker and value bet the crap out of someone who can't release TPTK, or in your case: second set with a completed flush showing.
As for the hand: You want to try to give him a range based on his previous actions and narrow it down street by street.
PF - If the villain's as loose a caller as you suggest then there are a lot more hands in his range than just AK or KQ. Pre his range is probably more like 55 - TT (maybe 22+ if he's that loose), 67s+, 78o+, Ax, and most broadways that you don't have blockers on. You'd think that he'd 3bet pre with QQ+.
OTF - if I did the math correctly the pot was about $0.15 and you overbet it to $0.30? If that's the case then the vilain made a really bad call against the odds for his NFD. He was only getting a bit over 4:1 implied and 2.5:1 expressed. I'd make a note about this tendency and remember to try to not pay off their implied odds when the villain's betting patterns are saying that they completed the flush. The other side of that coin is that a lot of players are becoming suspicious of large bets such as overbets and shoves, which could have been the trigger to get him to draw against the odds.
OTT - The flop c-bet has become so common that a lot of players are floating to the turn to see how the aggressor continues, because it's common for a flopped set to step on the gas on the turn and a missed flop to give up. Your check signals that your hand is weak, that the flop was a missed c-bet and/or you want to see a cheap showdown. All of which makes your river bet look like a bluff.
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