I have 88 and villain has AQo. I openraise to 3bb, he 3 bets to 10.5bb and I 4 bet shove. Both blinds folded. We are both 100bb deep. The pot is now 112bb.

What is our EV if he calls and what is our EV if he folds ?

When you 4 bet, the pot had his 10.5bb , your 3bb, and the 1.5bb from the blinds.

Your equity if he calls is about 55%
Your equity if he folds is 100% (albeit of a smaller pot)

EV is calculated as the weighted average of all possible out comes. It is basically the sum of the value of the outcome, multiplied by the liklihood of the outcome.

You don't really calculate EV by saying what is the EV if he calls and what is the EV if he folds. that does not really help inform the decision. You want to estimate the liklihood of each outcome, then use that to calculate EV. If EV is positive, then it is a profitable action.

Let's say in your above case that estimate that if you 4bet shove, that the villain folds 50% of the time. That means, 50% of the time, you win 15bb.

Of the 50% of the time he calls, you win 55% of the time. That means (50%)*(55%) of the time, you win 104.5bb.

Of the 50% of the time he calls, you lose 45% of the time. that means (50%)*(45%) of the time, you lose 97 bb(the amount of your shove)

You don't consider any prior action when evaluating your decision, That 3bb you already bet is gone and is now irrelevant to your decison making.

using the numbers above, you calculate your EV as

EV=7.5+28.7375-21.825=14.4125

Which means that this is a profitable play. if you did this play 1000 times, you would profit an average of 14.125 bb per play.

You're jamming 97bb. That is your risk.
The potential reward is the 15bb in the middle (when he folds) or your equity share of the final pot (201.5bb) (when he calls).

The expected value when he folds is 15bb. That's simple. You just win the pot.

The EV when he calls is slightly more complicated and there are a few ways of calculating it. When he calls, you have just over 55% equity, so 55% of the time, you're going to win (1.5 + 100 + 3) = 104.5bb and 45% of the time you'll lose $97
This can be simplified as (55% * 104.5) + (45% * -97) = 57.48 - 43.65 = 13.83

So the EV when he calls is $13.83.

Now you have to assign the probability of each option. Let's call his folding frequency F.
If F% = how often he folds to the shove, the total EV of the jam is
[F% * (15)] + [(100-F%)*13.83]

e.g. if he folds 20% of the time, the total EV is (20% * 15) + (80% * 13.83) = 3 + 11.1 = 14bb.

It's clearly a profitable play because - since you're a favourite even when villain calls - you make money whether he calls or folds.

It might be interesting to flip it round and see what your EV is when you have AQ and get it in as an underdog. The EV of getting called would then be (45% * 104.5) + (55% * -97), which is slightly negative, but not enough to make the play a losing shove unless he calls extremely often. (You don't need much fold equity for slightly losing "flips" to be long-term profitable).

Thank u so much guys !