Hi busisi,

Preflop seems standard.  When you flop a set with QQ it's usually gonna be a top set, so AQQ$ss is usually a playable hand on the button, whether it's suited to the A or not.

On flop I agree with you that HJ probably doesn't have a strong piece, and that we don't know what SB's range looks like.  If this were a HU pot, I think we have an easy c-bet for value and some protection.  In this 3-way pot where we have no idea about SB's range though, except that he probably doesn't have a lot of AA (still possible though) because he didn't 3bet pre, we have to think about upsides and downsides of betting. 

If we are betting here, that would be for value/protection.  Bluffing with our hand would be silly, because no better hands will fold.  That said, what worse hands can he call with?

- Pair + worse draw than yours, like you mentioned

- Nothing else, really

So we are looking to get called by hands like JT98, AT9, etc. that have anywhere from 30 to 45% equity, roughly speaking.  And that's fine.  We are slightly ahead of his range on this flop too (58% vs his $fi20!$3b6o range).  There isn't anything wrong with betting.

Now the next question is, what should we do if he check raises?  This can be a tricky question at the beginning, but you can get better with some practice.  Things we have to look at are:

- How often can he x/r for value?  And are we ahead of his x/r range?  If so, we have an easy 3bet for value (or we can slowplay too, sometimes).

- If we aren't ahead of his x/r range, do we have enough equity to stack off on flop?  If not, do we have enough equity/implied odds to flat and see the turn?

- If not, we might have to fold.  How much equity are we throwing away, then?  Could we have done better by just checking back flop?

This is something you can try to answer by yourself, but in my opinion, this is a hand that I wouldn't mind c-betting on flop, but would hate to get check raised on.  Against his value range, we have very few, if at all, clean outs.  Against Ax + Add (NFD) we are drawing very slim, plus a HUGE reverse implied odds; against AA we might have some outs but we don't know if they are clean or not.  That said, this is a hand that I either bet/fold-and-hate-my-life or bet/call-and-hate-my-life, or just check back and play turn in position with.  Sure, we can bet and just get called or get a fold, but his x/f range probably doesn't have all that much equity anyway, and when he calls, there are few turn cards that we can value bet on.  That said, I prefer checking back.

Now you might argue that we are "missing value" from his JT98 type of hands when we check back.  That's true, we missed that one bet on flop.  However, JT98 doesn't have a lot of outs to improve on turn anyway.  He needs J or T/9/8 of non-diamonds to dodge our flush, and that's just about ~8 cards.  And even if he hits, say, 9 of clubs on turn and has the nuts, we still have a decent redraw and are in position with deep stacks, so it's not like he can make a ton of money from us anyway.

Another benefit of checking back in this spot is, we will gain a lot more info on villain's range when the turn comes.  If flush or boat comes on turn, we get to see if they probe bet or not.  Also, we have QQ blocker and can rep a straight if the turn comes K or T.  Say, the turn is T, he leads and we raise - there isn't much he can do about it with his 2p/sets or even a straight, other than just calling or bluff catching again on the river, or just folding right away.  Especially, if SB has a strong hand, he will most likely bet out on the turn because he would be afraid that turn gets checked again.  So if they both check to you again on turn, you can now bet for value/protection, only against weaker ranges this time.  That's some valuable information you gained, by checking back flop.

As played, I think we can either fold or call, and jamming seems a very costly mistake.  I probably just fold and move on, because like I said, we can suffer from reverse implied odds even when we improve on turn, and when we don't, we probably have to fold anyway.