Hi,

I've tried to search for this but all fold equity threads I have found involve a player going all in. I think i am overthinking this and have got myself confused.

I want to know the missing part of this equation:

Preflop, we raise 10bb into a pot of 4.5bb, and get folds 65% of the time.

When villain folds, we make + 2.925bb

Villain re-raises to irrelevant size 10% of the time and we always fold.

When we fold, we make - 1bb

Villain calls 25% of the time. How many bb does our hand need to make postflop in order to make our first raise profitable?

You language is a little inaccurate. You do not win 2.925 when he folds. You in 4.5 when he folds, which happens 65% of the time. So your fold equity component of your EV is 2.925

Let's assume, for the sake of simplicity, that action is on the river (implied odds and so forth make this type of calculation exceedingly difficult preflop). There are four outcomes. You bet, he folds. You bet, he raises, and you fold. You bet, he calls, and you win. You bet, he calls, and you lose.

W% is the percentage of times you win on the river

EV is going to be the sum of the likelihood of these outcomes times the value of these outcomes. In this example
EV=.65(4.5) - .1 (10) + .25*W%*(4.5+10) - .25*(1-W%)*(10)

So, for this to be a profitable play, EV must be greater than zero. Solving for W%, you would get that you must win at least 9% of the time to break even at showdown.

The reason why we cannot do this calculation preflop is that the outcome tree branches at each decision point, leading to more outcomes whose values have to be calculated, and leading to pot values that may make the values being calculated preflop largely irrelevant.

The short answer to your question is that you cannot lose more than 1.925 BB in post flop action, on average, for this play to be profitable. But this information is largely unusable.