Always get in these spots with TT? Advice please

[seven-deuce]

Same Example (correct me if im wrong)

Pot is $3. Villain bets 2/3 pot which is $2. If hero calls the final pot will be $7

Made up of the $3 pot + $2 bet + $2 call = $7

Hero contributes $2 out of $7 (do we discount previous betting rounds because that money is no longer ours and belongs to the pot?)

So hero needs to win 2/7 showdowns to breakeven or win 29% of the time. Therefore if villain is bluffing more than 29% of the time calling is +EV?

Can we work out how much EV we stand to gain from this if we know a villain is bluffing on the river 40% of the time for example? (I'm aware we can never actually know this but just as an example)

So we should just call with a selection of our stronger hands with good showdown value vs a LAGGY villains range when we need to win 2/7 to breakeven as villain could be bluffing with the best hand on some occasions and calling too frequently would be -EV?

[Robb]

Do we discount previous betting rounds because that money is no longer ours and belongs to the pot?

For simplification, yes we do.

The actual answer is a bit deeper. Suppose you make 5 bet/call/fold decisions in a hand, starting with preflop. If each one is +EV or break even, then the next one can be made disregarding what has happened before. If you get to the river having a chosen a line that is at least break even at each stage, then the 2/7's win rate is enough to break even as well.

Since we don't know villain's range exactly at any given point, errors in reads or ranges can make any decision along the way -EV, and by extension we may be -EV on the river with our 2/7's expectation. In that case, however, it's not the river call that's flawed.