This is just an example hand. So let's say the BTN is a nit 3betting only 3% of his hands aka JJ+, AK.

We know really precisely his range and our equity is 33.3%. We are getting
3.25-to-1 odds (I hope I calculated correctly haven't done this in years actually). So we basically can set mine here always profitably and play fit or fold?

If our opponent would have a larger range our equity is better and I always play fit or fold. Even if we have worse equity now, our information about his holding compensates for it, or does it? Say he would only raise AA, we would definately call this with the worst possible equity, say we would play live and see his holdings, right?

However with 3% we can never be quite sure about holding the best hand with a set on a K6x board for example when compared to opponent only raising AA.

I'm getting a bit confused here on what is the main factor when determining our decision here.

Bonus points for explaning the same situation when holding 67s.

Oh and actually 3.25-to-1 with 33% EQ is an -EV move, sorry about that.. But the point is that does it turn into a positive play with our information?

Versus a nit who 3bet less than 5%, you call call too set mine. (you XC the flop then XR turn could be a good line). If you miss, you check-fold the flop. It will be tough for him to fold his monster hand and you will win a 100BB stack. A good opponent knows, that with TPTK and a SPR around 4 in 3bet-pot, he is commited.

With 67s, forget. Only 2 or 3% of chance to getting a monster compared to 11% for a set!