Assuming only bb calls pot will be 4.5. You will cbet 2.25

Formula for a brekeven cbet is:

Size of the POT* (FOLD EQUITY) - Size of the BET(1-FE) = 0
4.5FE + 2.25FE = 2.25
6.75FE = 2.25
Fold equity required for breakeven cbet = 0.33 or 33%

Since you're losing 0.1087 you don't want a breakeven cbet but a profitable one so that becomes

4.5FE - 2.25(1-FE) = 0.11

Going through the steps as before I get 35%

But that's a huge simplification because in reality you're not trying to win money by cbetting but maximise your profits for every hand.

So even if a cbet is profitable with any hand because villain is folding more than 35% who's to say that checking back isn't even more profitable? There are no 0 equity hands and you will win sometimes after checking back so EV of check back is not 0.

I think there is some serious misunderstanding here.

"I'm trying to find out, how much villain needs to fold postflop to make a 0% equity hand profitable."
This is totally independent of preflop play.

If you cbet 50% on the flop, villain have to fold to cbet 33%.
example:
1$ cbet into 2$ pot = 1$/3$ = 33%.

Right?

Yes, there is some misunderstanding.

Because a cbet is profitable doesnt mean the hand is profitable.
I'm thinking about pre- and postflop, not just postflop.

"This is totally independent of preflop play"
Exactly. When you open, you will lose 2bb preflop and those 2bb i want in the equation.

I'm just using 0% equity hand as example.

Yes, there is some misunderstanding.

Because a cbet is profitable doesnt mean the hand is profitable.
I'm thinking about pre- and postflop, not just postflop.

"This is totally independent of preflop play"
Exactly. When you open, you will lose 2bb preflop and those 2bb i want in the equation.

I'm just using 0% equity hand as example.

For betting half pot , villain needs to fold 33% or more of the time given you have 0% when called.

No hand has ever 0% preflop against any other hand.

Yeah, it seems I described it pretty bad.

When hero opens 2x from BTN, he will lose money preflop by opening because BB and SB defend to wide to make a 0% equity hand profitable preflop.

So, then we lose money preflop, we need to win them back postflop, otherwise it wouldnt make sense to open the 0% equity hand.

Even tho the c-bet breakseven, the hand still lose money because of the preflop opening.

I think i understand the question now. You try to justify a loose open with ppls postlflop instead of their preflop tendencies. Well if villain folds to c-bets on any flop with a frequency of exactly 33%, you cannot raise trash and c-bet it all the time, you will lose your pre investment.
Lets say we make it 2bb from the btn and bb calls. There are now 4,5bb in the middle. You bet exactly 2.75 bb everytime, anytime (with 0% EQ and no double barell attempts). Now the longterm EV of the c-bet must be bigger than 2bb (our preflop investment).

Assume villain fold 50% on all flops. Now the EV becomes: -2.75bb*0.5 vs +4.5bb *0.5 = +2.75 bb so our overall profit would be .75 bb.

Now take into account that we will be 3bet sometimes in which cases we have to fold regardless and the times we have a mulitway pot and cannot make the assumption that both villain will fold x amount of times.