some EV calc. help. Mojo?

I don't understand how "3-bet is premium" works as a stat but I'm skeptical of its usefulness.

Anyway if you assume he's folding exactly 50% of the time and having QQ+ AK the rest of the time (equity of 36.1%), the EV is as follows:

Outcome 1: He folds
Probability: 0.5
EV magnitude: +18.5bb
Product: +(0.5)*(18.5)

Outcome 2: He calls, we win
Probability: 0.5*0.364
EV magnitude: +105.5bb minus rake
Product: +(0.5)*(0.364)*(105.5 - rake)

Outcome 3: He calls, we lose
Probability: 0.5*(1-0.364)
EV magnitude: -96bb
Product: -(0.5)*(1-0.364)*(96)

Then you sum the outcomes:

EV = X = (0.5)*(18.5) + (0.5)*(0.364)*(105.5 - rake) - (0.5)*(1-0.364)*(96)

At your stakes I have no clue what the rake would be, I'll assume 3bb. Just note that the rake does matter quite a bit if the shove is marginal.

Plug 3 for rake and use www.wolframalpha.com solver:

X = -2.62bb

Now, we can use a variable to find the breakeven point for how often he would need to fold for the shove to be profitable. We set EV equal to zero and the 50% fold frequency equal to X, while setting the 50% call frequency to 1 minus x.

0 = (X)*(18.5) + (1-X)*(0.364)*(105.5 - 3) - (1-X)*(1-0.364)*(96)

X = 56.2%