The probability of your opponent holding a dominated (better kicker) Ace is not affected by the effective stack depth. 

There are effectively 2 cases you describe:

1. Villain min raise & calls a 3b jam with a dominating Ax

2. Villain calls our open shove with a dominating Ax

To work out the probability that villain holds a particular range, given a specified range you hold, you can use adjust the following example.

Hero holds a range of Ax7y, villain holds a dominating Ax approx 5.9% of the time from a starting range of any two cards:

PQL:

select 
count(InRange(villain,"AxKx-Ax8x,AxKy-Ax8y")) as dominated
from game="holdem",
hero = "Ax7y",
villain = "**"

For more information about propokertools poker query langage please see:

http://www.propokertools.com/pql

If you would like to flesh out the specific cases implicitly asked about please post more specifics about the required input ranges & your workings of attempting the problem. 

Cheers, 

cdon

FYI: This exercise is not really relevant to your net EV

You will only yield net EV in spots where you play your hand for more EV than your opponent would if your positions were reversed. 

Playing Ax is pretty straightforward in the situations you describe and it is unlikely you will be playing differently to your opponent in these spots. 

You sound pretty tilted. These spots shouldn't affect you at all because they happen all the time and even out over time due to both players typically playing the same way. That said, we've all been there (running into the worse side of a standard spot over and over again without any respite in a short period of time) and it can be really demotivating to keep playing. Suggest you take a break and do some fundamental analysis to reground your approach to the game in a rational framework. 

ok lets look at the 1st scenario

OOP hero 3 bet shoves Ax (why does hero seem to be facing stronger Ax)

while i like cdons answer i don't think its complete

if the Villain has a min raise % of less than 25% (we will consider it 15-25BB because below that many recreational players begin to open shove Ax) then this min raising range actually holds alot of Ax and Broadway we should also look at the fold to 3 bet of this villian, and infact not shoving but calling our weak Ax is probably the better play since @ a top 25% range is Ax and some Broadway hands we will be often dominated and probably called

V an aggressive min raiser we need to see how many times they folded to our Ax jam as well as that a large part of EV

also we should consider if we have a 3 bet shove of 25% polarized as the top 25% of hands then Villian calling @ 25bb calling should be A7s+ A8o+ 33+ and KQs and so when we are actually called we will be dominated often

but the place we are making +ev with our hands is when they fold to our Ax (low x) so u should also check how often u have shoved Ax OOP and see how many times u have been folded too especially against an opponent who min raises a high percentage but folds to 3 bets alot (then we can open our range quite wide)

2nd scenario

in position min raise / call 3 bet shove @25BB

we need to asses the villains 3 bet shove range if u think villain is 3 bet shoving all pocket pairs and all Ax then a large part of whether this is +ev or -ev depends on your calling range for that exact calling range we should only be calling 44+, A8s+, A9o+  so if you are calling a tight 3 bet shover with any Ax u are actually making the wrong play

if villians range now expands to 22+, A2s+, K9s+, QTs+, JTs, T9s, 98s, 87s, 76s, 65s, 54s, A2o+, KTo+, QJo

hero calling range should still only be 33+, A5s+, KJs+, A8o+

so u need to not just look at what hands have shown down but what u think the villians 3 bet shove range is and find the +ev call range

3rd scenario

call open shove (or open shove) we can look at both together we can look at villians open shove range and what our call range should be this can be reversed and "if" villian is calling our exact range correctly he should be dominating us, again its the folds that count alot to make a play +ev

again what do you think the villian is open shoving with ? if he is a tight with open shove lets say 22+, A2s+, A2o+

then our hero call range should be 44+, A9s+, ATo+ (effective stack does affect this but not that much this is 25BB effective)

which means if hero is calling Ax here he is making the incorrect play

and if u reverse the positions and hero open shoves 22+, A2s+, A2o+, and villain calls correctly with  44+, A9s+, ATo+, then again looking at only show down stats we will be dominated alot, we are not factoring in the amount of times they fold to our open shoves which adds ev back to hero

so all in all you need consider you calling ranges and the amount of times u have gotten a fold to your open shove or 3 bet shove to find if you are +ev or not

edit

and when a villain calls our open shoves even tighter then its more EV for the hero from folds and again hero will be dominated more when actually called but the folds count to hero ev alot, and if they cal to wide then they are going to bleed chips (same goes for hero if hero folds to much then ev gets added to villain etc)