I think this lost a bit of context?

Anyhow from a pure math perspective the size of the raise doesn't matter, its all relative to effective stacks.

Some players 3bet large with AA/KK and small with everything else, so then its just a read on an individual and you cannot generalise.

I think it's very game-specific. The question is whether there's a lot of 3-betting. I've run into several players at the 100s where I think AK is a push if you get re-raised (don't have a sufficient read with regard to betting quantities).

At the 50s on Stars (admittedly insufficient sample size as of yet), I've never seen the $10 3-bet on anything but QQ+. As long as that read holds, I'm folding it.

With the more passive re-raise, I think I'm calling for the moment--although with a read that it's a loose 3-bettor, I think you can just push it.

There's apparently some sort of 2+2 discussion about frequent 3-betting. My impression is that it hasn't made it down to the 50 level but that some at the 100s are familiar with it. In any case, vs. a potentially light re-raiser, I do think AK is a push with full stacks. Vs. a tight re-raiser and a big re-raise, I don't see the point of continuing with the hand.

So, specifically to sham: I agree completely that against players who 3-bet a lot, AK isn't a fold. But the hypothesis is that for a specific game, there just aren't a lot of big re-raises, and when the exception occurs, you should believe it (as several of my lost stacks clearly illustrate) rather than assuming they're making a play--at least pending evidence to the contrary.

.might be off topic
but dont forget card removal

if you hold AK there's only 3 AA and 3 KK combos but there's 6 QQ. So if villain is only calling a shove with KK+ and is 3betting with JJ+, AK (which is a very tight range) and you have AK and action was lets say

you bet 5 bb
vill raises to 15 bb (this could be JJ+, AK right)
you shove

you can always shove and be winning because the 6 combos that beat you, 3KK, 3 AA, are much more unlikely than JJ, AK, QQ which he folds and thus take the money home.

i'll look into the maths maybe...