re: Poker & 50NL FR TPTK in 3 bet pot w/wet board
Your base theory puts you in a lose/lose situation. You are saying if you hit TPTK and bet it is guaranteed they will fold lesser hands, i.e. you lose. However, if they call they must have a better hand, i.e. you lose.
I think the hand is pretty straight forward. It is a case of each player worried the other has a monster (unless villain of course truly does have a monster).
Follow villains thought process. Your stiff reraise instantly narrows your hand range to JJ+ or AK. His call puts him roughly in the same hand range ball park. Flop comes so as the villain I check to the raiser regardless of what I hit.
When you check behind villain rules out you holding AA or AK. Villain is not going to consider that you are having some weird poker epiphany going on in your head that is placing you in a lose lose scenario. If I'm villain your check makes me pretty confident you hold JJ and the two overs on the flop scared you or you hit a monster flop.
So on the turn if I'm villain and you showed weakness postflop why don't I lead out? I know you don't have AA or AK so whatever I hold that was good enough to call a stiff reraise must be good. But I still don't lead out. I'm either scared you are slowplaying a set or I'm the one with the set. You bet $7.50 and I call. As villain I now consider including AQ and KQ in your stiff reraise range. So I have you on AQ,KQ,KK,QQ,JJ. So as villain what do I have? Possibly I hold AQ, KQ, KK, QQ, or playing AA scared. When I hold AK I usually rule out my opponent holding AA or KK (not that it can't or hasn't happened), so lets say villains range is AQ,KQ,QQ.
J hits on the river. Based on the raise pflop and your check post flop this is a card I didn't want to see. I think there is a strong chance you hold JJ and I am still highly confident you don't hold AK. I thought my AQ or KQ was good here, but with a J hitting I may have just lost the hand. So I check...this kinda of rules out villain holding QQ unless he plays really that scared.
So what should you do on the river? Check, because at this point there is really only one hand you can realistically get value from, AQ. Going with your lose/lose philosophy if villain holds AQ and you bet they will most likely think long and hard and then think you must have being slowplaying a monster or you hit your set on the river and they fold, so you get no value. And if villain has KQ or was slowplaying even a bigger hand you lose either way.