At 11bb in MP, A8o is borderline but I’d lean towards a fold. At 10bb it is profitable to shove but even then it is the weakest offsuit Ace that I’d consider shoving. I’d say it’s a clear shove in the HJ at <=12bb (and marginal but okay even at 15bb) but one extra player behind you makes a big difference.

As a general rule, I fold my weakest profitable shoves at tables that are tighter/more passive than average. Conversely, I’ll shove slightly wider at tables that are tough/aggro, especially if I’m almost never getting to RFI in later positions. So I’d be shoving at a particularly tough table, but I think it’s slightly better to fold as your standard move.

Debatable, but I see your point. I’m playing now so can’t really dive deeper into my (potentially flawed) reasoning but I’ll come back to this.

On looser tables I’d want to shove tighter than Nash, fold equity is what makes weaker parts of Nash ranges profitable. That’s an important part of PKO strategy, especially once your bounty gets larger. You end up wanting to shove way less middling to low cards (eg. T8s,87s) but still shove almost the same number of high card hands.

To the question of whether to shove tighter or looser on soft tables vs. tough tables. I can see decent arguments in either direction. I fully agree that on weaker tables (ie. overly tight to shoves, not splashy/loose) our shove is more profitable in isolation. My reasoning for the opposite line of thinking is that we won’t get nearly as many profitable shoving opportunities on strong tables, and probably need to shove fairly close to Nash if we’re using a push/fold strategy. I often prefer passing on shoves that are < +0.25bb but start going thinner if I’m rarely getting RFI opportunities.

I will absolutely shove wider than nash in CO or later positions if blinds are nitty, but it starts getting harder to exploit those tendencies with more players behind. 

At 11bb, A8o is a barely profitable shove in the Lojack vs Nash calling ranges (0.17bb), worse than all of KJo (0.18), A2s (0.19), K9s (0.19), and T9s (0.27), which are still borderline shoves.

At 14bb, A8o has similar value (0.19bb) in the Hijack. Even at 9bb, it is less profitable from UTG+2 (0.15bb).

That’s probably a little too tight, even if the blinds aren’t going up next hand. In my charts, KQo is winning 0.31bb shoving 10bb from UTG+1.

It’s slightly worse than all of the suited broadways (QTs is the weakest at 0.34bb) but better than hands like A8s (0.25bb), 44 (0.22bb), T9s (0.18bb), K9s (0.14bb), and A9o (- 0.02bb).

I should correct something from my earlier post. I usually want edges >= 0.25bb when shoving 13+bb (at 12bb I stop using a min-raise range and only push/fold), but this is not only wanting to make sure my edge is large enough. Because I’m min-raising the top of my ranges, I become exploitable if I shove the bottom parts of Nash ranges since my overall shoving range will be too weak.

If you’re only push/folding, you’re able to take thinner edges and probably don’t want to pass on anything that’s at least 0.15bb profitable at <=15bb.

At <=10bb I’d want to take any shove that’s winning at least 0.05bb.

On my charts that is 33+,A7s+,A5s,ATo+,K9s+,KJo+,Q9s+,J9s+,T9s. If you want to play a bit tighter, the worst of those hands are KJo(0.06), 33(0.09), and Q9s(0.11).