Well yeah I didn't mean to say it would be -EV I just mean when would you actually use this "theory" if you were sitting down at a cash game and always had 100BB on you?

But since you feel that's irrelevant let's just ponder the question some more...

It's independent of villains decision making. I can't see how or why but ok, that means that we can't assign him a range since we aren't allowed to use his thought process.

So we shove x BBs and if villain folds we win 1BB.
If he calls we're risking x BB to win x BB (neglecting rake) and so we win ( QQ vs villain's range ) % of the time and lose the other times.

How can we not include villain's decision making?

The less BB we have, the more inclined villain will be to call . If we start making our stack bigger and bigger the villain will call less and less. Eventually when chip stack gets high enough villain will only call with AA.

So:

1226 combinations, we hold 1.
1219 times we win 1 BB ( or is it 1.5 since our SB counts as dead money?)
6 times (When he has AA) we risk x bb with 18.45% equity.

6x * 0.8155 = 1219 x 1.5
x ~ 373.7BB

That is the definitive number of BBs where it is DEFINITELY -EV to shove since we know that AA is calling if he has common sense.

If we add KK to his calling range then obv that number gets approx halved.

Clar

*edited for clarity*