A question I was asked about how I played a certain hand in the "Low Content" forum kept my up last night trying to figure out if I can ever make a defenite determination on whether pushing AK pre-flop is + or -EV.

Here are the definites:
1 - You have AK either in LP or the Blinds.
2 - Someone has raised and nobody has called the raise.
3 - There are either no limpers or limpers are not tricky (AA/KK) and will not call the raise. (Hard to say for certain, but for this example it is easier to make this assumption.)

If we know the following, can we figure out EV?
1 - Raiser's PFR%
2 - Raiser's normal PFR bet size (of course if he makes a larger than standard PFR we may be able to determine that he has AA or KK and this would be even easier, but let's say that all of his raises are the same amount).
3 - Raiser's Fold% when raise is facing a push. (This is the toughest one to figure out.)
4 - How many BB you and opponent have in stack.

*My math may be far off so I would not have a problem with someone double checking and correcting. Actually that's what I'm hoping for.

Example 1:
I have AK in CO w/ 90BB. PFR has me covered. There is one BB posting in LP who folds and raiser is UTG.
1 - Raiser has 11.76 PFR%
If we know that you are dealt AA or KK 9% of the time then we can determine % of times someone is raising with AA/KK. If raiser has PFR of 11.76% can we safely say that he has AA/KK about 7.6% of the time he raises.
Again, this is an estimate, but we'll say that PFR wins 80% of these hands.
So 80% of time we lose 90BB and 20% of the time we win 90BB when he has AA/KK or 6.08% of time we lose 90BB (-5.472BB) and 1.52% of time we win 90BB (+1.368BB) overall.(I'll discount blinds as part of the rake - again not an exact.)
Expected profit: -4.104BB when he has AA/KK.

2 - We know raiser's standard raise (which we will say he makes every time) and we can estimate how often he will fold (tough to acurately estimate).
(a)Standard PFR is 9BB
(b)He will fold 30% of the time to push
If he raises to 9BB and then folds 30% of the time we will win 10BB 30% of the time (leaving SB and dead Blind as rake and counting BB as won).
Expected profit: +3 BB when he folds 30% of time (If he folds more often this number grows).

3 - If we estimate that he will call with AK 3.24% of time (just to make numbers even), call with any 2 non-paired cards below AK 5% of the time (cause he's an idiot), call with any PP 40% of time, and call with a hand that AK has dominated (AQ, AJ, even KQ) 10% of the time then the following is fairly accurate.
(a) We win 0BB when he calls with AK
(b) We win 2.215BB when he calls with any 2 non-paired below AK. (assuming 2/1 fav)
(c) We lose (3.6BB) when he calls with any PP (assuming 55/45 dog)
(d) We win 4.5BB when he calls with any hand we dominate (assuming 3/1 fav)

If we add all of the numbers together we see that we
Lose 4.104BB 11.76% of the time (-.48BB)
Win 3BB 30% of the time (+.9BB)
Win 0BB 3.24% of time (0BB)
Win 2.21BB 5% of time (+.11BB)
Lose 3.6BB 40% of time (-1.44BB)
Win 4.5BB 10% of time (+.45BB)

Our EV in this situation is -.46BB if we add all the numbers together. Have I figured this out correctly? Somehow I don't think I have this absolutely right.

But if I can get this correct and everything stays the same, but the stack sizes are different and the fold% rises, can we find situations where this is a profitable move?

Again, I haven't seen a math book in 13 years since college Calculus freshman year (and I barely remember that), so any help or corrections would be appreciated.