While you're in a prime spot to 3b light or extend your value 3betting range (you kind of do both typically, like I'd 3b/call off midpairs but also 3b 68s A4s etc), Q8o won't play very well postflop and youre likely trying to learn to navigate these situations. Because of that, I'd probably just muck and choose something that plays better postflop. That's how I first got into the open/4bet shove game a few years ago when 5 million bets were being made preflop and you had players final tabling after getting in huge 80bb+ confrontations deep in the tournament with 83o vs 77 or something. I would open anything I thought would play well postflop (connectability), and if I were 3bet by a player in a spot I thought they'd likely to have air, I'd shove what would then play well vs a calling range. That's just how I sort of got into it. I didn't really do a lot of studying on this back then outside of looking at pokerstove and checking equities of my shoving vs their calling ranges.
Moving on, this is what villain sees- The big blind plays at most 20% of hands in this position (vpip+3b, though now that I think about it, vpip should include 3b, but for this example I'll assume it doesn't), meaning he folds 80% of the time. If you run similarly, you're folding around 80% of the time as well. That means combined, both you and the big blind are folding around 80%x80% = 64% of the time. If villain raises to 2bb, he's risking 2 to win 4.0625. If he sees a success rate higher than 2/4.0625 = 49.2% of the time, then he profits that difference. I just showed you how 20% defenses from the blinds results in 64% folds. 64-49.2= 14.8% That's huge! That's better than your equity on winning all ins preflop AK against QQ. (to most, that part is obvious, but bear with me (rawr)). This literally means he doesn't need cards. He can just put chips out there and he will make money. I like to think of it as a money button you push to print your dollars. So his range here should approach 100%, as opening every hand here is profitable, though its unlikely because most people aren't thinking that far.
All of the above has been known to anyone with a calculator and the patience for quite some time. Button opens are profitable as steals, who knew?! The next step is defending yourself from them so you don't get exploited. You 3bet or call with a certain range, and play from there. In this example, you 3b from .5bb to 5bb, risking 4.5bb to win 8.65625.
Your villain then sees a decision as (1bb+5bb+.65625bb+2bb)/3bb or risking 3bb to win 11.65625bb. If the hand ends here, he needs 25.7% equity to make a neutral ev call/fold. Because it's going postflop, and he likely believes he'll outplay you in position, he actually doesn't even need that much equity because it's unlikely you go to showdown everytime. If you're 3betting as wide (not implying all hands between Q8o and AA are being 3b, nor that you're 3betting them every time) as Q8o, then you're getting postflop with a lot of hands that don't connect, and his hand doesn't matter. You'll cbet and ck/fold. You'll ck/fold. You'll cbet and cbet and ck/fold. You could even cbet/ cbet/ cbet and fold to a shove.
(44+,A2s+,K2s+,Q5s+,J7s+,T7s+,97s+,87s,A4o+,KTo+,QTo+,JTo) Here's a 30% opening range.
(TT+,A7s+,K8s+,Q8s+,J9s+,A8o+,K8o+,Q8o+,J9o+) Here's a stab at your 3betting range. It's about 23%.
Coincidentally, those two ranges are actually about 50% against each other. If villain were to fold any part of his range vs any part of your range, he's making an average mistake of what I think is 25% He needs 25.7% equity to call, he has 50% equity, folds are bad. He can choose to split up his range (as pretty much everyone does, even button clickers) so that he defends with a certain part, 4bets with a certain part, and folds a certain part, in an effort to maximise ev, as opposed to simply not being exploited (folding the btn open would be an exploitable spot for either you or the bb). If suited Aces are in his defend range, then we can simply look at the ev of calling against your range with that hand individually. A4s vs that 23% 3b range has 49.42% equity.
Basically, to answer your first and most important question (in my mind), “Why?” well, this is why.
I just sat down and sort of rambled this all out, so I hope it's coherent and correct. If anyone has any questions about this, feel free to ask them in here. It might be best to message me on twitter, as I often forget to look back here. @jacob_sharktank