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Q is definitely in his range, AQ, KQ, QJ, QQ(!), but so are KK, AA, AK, TT, maybe 99, A8, A3 (unlikely, but, it's 10NL). 33 is unlikely, because there's only one way to make it and bottom set on the flop will likely donk into you. He could have a nutly hand like QQ or 88 and check twice to induce a bluff from you. I'm not sure what percent of the time he's not showing up with at least a queen.
If you think that % is >10 and he won't shove the river, you can probably call and try to see a cheap showdown. This is what you'd call a polarized range. You are either way ahead or way behind. You have no more than 2 outs if you're at all behind, and if he's got AK, he has as many as 6 outs to catch up.
In these situations, you typically want to get to showdown cheap, because you have showdown value. If he has air, he'll likely try to make showdown expensive (rep the Q or the 3 and hope to fold out your JJ- or AK-type hands) or give up after this checkraise. If you call the checkraise and he's giving up, he'll check the river unless he hits big. If he's pitbulling this pot, you're going to face a big bet on the river with what may very well be 78s.
The pot is already 31BBs (or 62bbs), so it's worth fighting for. At 31/24, this villain may well be the type to fight hard for pots and take it down a lot of times with worse.
I'm guessing you folded and are questioning how good a laydown it was. Or you called and folded to a river shove (this would be my guess).
If I decided this guy was bluffing, I'd call with the intention of calling a river shove if I'm not scared of him improving (AK and A8 are likely bluffing hands here, though he may be c/ring A8 for value to "find out where he is"). If I'd like to just end the hand and not let him hit his 2-6 outer, I can reraise AI here, but he's calling pretty much 100%, since he has 70%+ of his stack in the pot already.
In fact, since he just C/Red 50% of his stack, I'm thinking this is more likely to be for value than as a bluff. But, he may be betting for value with A8 or 55+, not putting you on a made hand, since you checked the flop.
So, in conclusion, I'm apt to fold here a fair amount of the time (~60%?), and reraise all in the rest. I don't cold call here often if ever, unless I really want to make sure he stays in the hand, and this board is dangerous enough for me not to want to encourage that.
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