AA deep stack x Double card turn

Not sure about the best move but I would b/f.

Ok, if we bet what worst hands can as call ? Queen improved, flush draws gets there, gutshot, OESD and all pairs are folding here. I don't see much value of betting here.
So we are left with x/c or c/f:
what hands would value bet here ? Trip Queens, Flush and I would put in JJ and TT but these hands might check back. What hands would he semi bluff ? JT, KT. And if he is fishy player he could even bet with air on this turn.

So I would go with x/c by pot controlling and giving him a chance to bet worst.

We dont get much calls from worse hads, that is true. I just thought that there is plenty of other hands than completed flushes or Qx in villains range and we have to protect vs single club hands and other possible draws. I think villain wont necessarily bet his trip queens ott. If we x/c what do we do otr?

He should bet his queens as board is pretty wet. He could check back nut flush tho.

I would x/f river on clubs, K, 8, J. And by his bet sizing i would consider to call off.

You cannot bet turn. Just xc.

BB cold calls your 3b, his range is mostly TT-QQ, AQ-AK, might even have KK, because you are 151bb deep. So flop is clear bet, OTT you can't value bet

Board: 3♣9♣Q♦ Q♣
       Equity     Win     Tie
MP2    43.71%  43.71%   0.00% { AhAs }
MP3    56.29%  56.29%   0.00% { QQ, JdJc, JhJc, JsJc, AQs, AcKc, AQo, AdKc, AhKc, AsKc, AcKd, AcKh, AcKs }

Now let's see if you can x/c:

Board: 3♣9♣Q♦ Q♣
       Equity     Win     Tie
MP2    33.64%  33.64%   0.00% { AhAs }
MP3    66.36%  66.36%   0.00% { QQ, AQs, AcKc, AQo, AdKc, AhKc, AsKc, AcKd, AcKh, AcKs }

You can x/c OTT, of course he might not bet all his AK OTT, it depends on his aggression and if he is betting just a few AK here, you have to x/f.
I made a lot of assumptions about his pre flop cold calling range, but from my experience this is the range which will be very close to real calling range for reg in this spot.