[Shillx]

When we raise the turn, the pot will be about 30 SB if you assume that the manaic calls and the CO folds. If getting that AK to fold nets us 7% more equity, then the raise buys us 30*.07 = 2.1 SB of the pot. Of course he also loses on every bet that goes in, so by coldcalling he is losing ~2.7 SB on that street should he have 8% equity. So he would be making a bigger mistake by coldcalling then folding (though it might not benefit us).

Let's say that you are playing a hand where you have 40% equity, Player A has 30% equity and Player B has 30% equity. If you bet, Player B will always fold and the pot is right now 9 BB (before you either check or bet 1 BB). Is he making a good fold? Are you making a good bet?

We all know that he is making a bad fold, but you may or may not be making a good bet. If you have 70% equity and player A has 30% after he folds, then the bet was good. If you still have 40% and player A has 60%, then the bet sucks. Just because the dude with AK has 8% equity doesn't mean that it all goes to our aces when he folds. So it is tough to evaluate the EV of knocking him out of this pot. Him coldcalling could very well benefit us more (and the math on it is very close). Assume we have 50% equity if he coldcalls.

Pot Equity from a cold call = 34 sb*.5 - 4 = 13 sb
EV fold = 30 sb*.57 - 17 sb = + 0.1 sb

So in that case, it really doesn't matter if he calls or folds. I'll make more comments about your post in bit, but there a lot of points in your reply that need to be addressed.

Edited