Just a quick sanity check,

Imagine this scenario:
6-max online cash game, everyone's 100bb deep.

UTG opens 3x, folds around to Hero on the BB and we have AKo.
Do we:
1) flat to not inflate the potsize OOP and play passive?
2) flat because we don't want to want to flat OOP against UTG's 4 bet range postflop.
3) or 3 bet because it's going to be harder to realize our equity post-flop and we have blockers.
4) or 3 bet and play aggressive as we'll have the range advantage as he'll be capped at JJ and AQ.

Additonally,

What if it was AKs or more than 100bb deep?

3-betting and calling should both have very similar EV, so are both viable imo.
If you have reads/stats on how villain plays (i.e. how tight he opens and how he reacts to 3-bets) that can sway your decision one way or the other. I usually 3-bet, despite having a relatively low 3-bet percentage in this particular spot. (AK helps balance QQ+, but you can also 3-bet some other big Ax/Kx).
P.S. I'm even more likely to 3-bet AKs. I can't remember the last time I flatted that against anyone.

And if we get 4 bet against a competent reg, I'm assuming we're going to have to maybe fold???

What's your particular reasoning to 3 betting in that spot if you don't mind me asking?

Sent from my SM-N900T using Tapatalk

As standard:

5) Flat, so that you keep some control over the size of the pot, disguise your own range slightly, and keep his range as wide as possible

It depends on sizing (of both the open and the 4-bet), but yeah I usually sigh-fold to a 4-bet.
I think the reasons for 3-betting in the first place have already been mentioned. Blockers/instant fold equity, equity vs hands that call, balance etc etc.
The GTO solution is probably to use mixed strategies for almost all the hands in the top left of a hand matrix. (TT+/AJs+/AQ+/KQs). i.e. sometimes 3-bet AKo and sometimes flat, do the same with QQ, AQs etc. You just have to have a strategy that isn't too unbalanced, such that you've got some "good" hands in both your 3-betting range and your flatting range, and you've always got some hands that 3-bet/fold to help balance the monsters that don't fold to a 4-bet.
Board coverage also comes into it. It can be quite nice to flat AK sometimes, because you want to be able to flop TPTK in single-raised pots as well as 3-bet pots.

I see, and I assume, the hands further from the top left corner would be a less frequent 3 bet yes?

Thank you for the tremendous help in understanding, I forgot about mixed strategies.

3bet nits and flat LAGs. Sounds counterintuitive but you don't want the LAG to fold his AQ, AJ and even weaker aces. Vice versa you don't want to run in the nits AA and KK, and its much better to get that information preflop. 3betting an UTG-raise from the blinds looks incredibly strong and you'll probably get them to fold hands as strong as 99 or TT. If you get called you can narrow their range in most cases to TT-QQ, and AK. If they 4betting you, you can easily fold. Sometimes they will flat your 3bet with AA and KK but that happens very rarely.

LAGs are not going to fold often enough, that's why we call them loose. We do not worry about that when we hit a nutty hand.

In that special case (3bet from BB vs UTG) they're going to fold Ax-AQ probably more than 50% of the time, unless your image justifies a call or raise.

What are the opening range and the 4b/3b-flatting ranges in this special case?

Yes. It's probably fine to 3-bet the occasional A5s, A4s, (the ace blocker is important) but it's going to be less good to 3-bet something like 98s, because when you do get called, you want to have decent equity (at least one overcard) against hands like TT/99/KQs.

Opening Range UTG for LAG somewhere between
11%: 22+, ATs+, KQs, AJo+, KQo
and
15%: 22+, ATs+, KJs+, QJs, JTs, T9s, 98s, 87s, 76s, 65s, ATo+, KJo+

4B: JJ+,AK, and sometime 4bet bluffing with worse Ax and maybe few SC
3BC: 88-TT,AQs,(AJs) and few SC like JTs,T9s,98s

I don't expect too much calls with any other Aces, which are a significant part of his range (~4%). I know its not a standard line not to 3bet a LAGs UTG-open with AKo, but you get more value from dominated Ax hands and you earn a lot more respect for your BB calls later. On the other hand I would never call with AKs.

Is 11 % LAG?

What do you think given your ranges (15 %) can BB 3b ATC with instaprofit (and 3BC ATC will have some equity)? If it is close is that a sign of "LAGness"?

Also (anyone?) is it better to have 18.5 BB and AK vs 88-TT,AQs,(AJs) and few SC like JTs,T9s,98s or 6.5 BB and AK vs 22+, ATs+, KJs+, QJs, JTs, T9s, 98s, 87s, 76s, 65s, ATo+, KJo+?

As I said it is between 11 and 15%. UTG is not where you define your playing style the most, but you're right 11% is not standard LAG. It is more of a bottom line where LAG starts.

If UTG-LAG is never adjusting to our 3betting frequeny, then yes. I know you want me to say that my UTG LAG folds too often vs. my BB 3Bet and equity wise you're right, it is +EV. But my point was that it is imo more +EV not to 3Bet him with AKo. One drawback in 3Betting with AKo vs. UTG-LAG open is, you have to 5B/shove to his 4B more often. He will frequently 4bet bluff you with a weaker Ace and you will hate it to either fold the best hand or run into his nuts. When you got the same 4bet from a nit you know he is almost never polarizing and you have an easy fold. Imo flatting AKo vs LAG-UTG makes your life easier...

Best,
fairy

Heh, I think you are right And usually LAGs are bad in folding enough.

Weird. I'm a nit and I open 16% by default, but my range contains many hands (mostly Axs) not listed, and doesn't include 55-22.

Playing against someone with a tighter range (e.g. EP in full ring) AKo presumably becomes more of a flat than a 3-bet, because villain doesn't have as many dominated hands to start with. (I haven't really studied full ring, but I imagine the BB 3-bet frequency vs UTG in that format is extremely low).

You open 16% UTG? What's your op range otb? 16% seems a little bit too wide for me UTG. Don't get me wrong, I just didn't expect that of a nit...

The only mistake we can do with AK here is fold pre or 3b/fold. Personaly prefer call on BB and surely 3betting rather lag than a nit.

Based on the OP, I assume the UTG example is for 6-max, not full ring. 16% seems fairly inline to me.