[Fallen Hero]

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TT min-bets the flop, gets called. check check on turn. you value bet the river after being checked to, he looks you up about 50% of the time

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FYP, and you just won a massive $3 pot. Calling that minbet is effectively checking behind on that flop.

If TT min bets and you raise, TT is probably calling. Turn Check/check, river check/call, you just won an extra $4 bucks (double the pot).

Edit re. TT calling the flop raise: in my experience, a min bet means absolutely nothing more than a check. Villain checked the flop. If he raises TT (unlikely) then you fold, shucks, we just folded the best hand on a [censored] flop. move on, [censored] happens.

If AQ min bets and you raise, he is either 3betting (easy fold) or smooth calling and leading turn (easy fold). If a queen doesnt bet the turn, make a note on the stupid donkey and move on.

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if you're folding TT 50% of the time on the river you'll lose a LOT of pots, that's not my experience at all. And it's also not very commum to see TT calling on that flop (and imagine it isn't TT, rather 66, do you still think he calls?).

Specifics apart (we could invent situations all day to prove our points) raising purely for information is BAD.