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OK. You have top two pair. You have an opponent who may easily have you beat with a set or a straight, or may have what he thinks is a good draw - there are TWO possible flush draws out (clubs and spades) and three broadway cards, meaning any hand with a queen or jack in it has an inside straight draw as well. Would this guy possibly call a flop bet and then raise the turn with something like Kc Qc, Kc Jc, Jc 9c (close to his actual holdings)?
Lots of players will min-raise a good draw, but few of those same players will raise again if you three bet with a strong hand. They'll generally just call and hope to hit. That's a piece of information. The same guy with a set or made straight though is going to keep raising you. He's already shown strength with the first raise; he's not backing down with you firing at him.
So if you raise the turn and he raises you back, you may call (if it's a cheap raise) or push (if you think he's bluffing, or overvaluing AT) or even fold. Hard laydown, but possible. But if you raise the turn and he just calls, you can peg him for a draw. Then what are you looking out for on the river? Spades maybe, but really you're looking at clubs, queens, and jacks. If none of these cards hits and he pushes, it's an easy call because you have him on a draw and it wasn't satisfied. Also, there's a significant chance the river will go down differently, in any case. If a blank comes on the river after he just called your three-bet on the turn, and you bet again on the river, he's probably folding, not bluffing. Or better yet if you make him for the draw you can then check to him, he probably will bluff as he did here, and you can call with confidence.
What's bothersome about this hand, and I'm assuming is the reason you posted it, is that it's hard to read him for anything specific. There's a wide range of hands he could have. To me, another raise on the turn (and his reaction to it) will narrow his possible holdings significantly. Then you can be a lot more confident in your river action. It might well end the exact same way, but you won't be as bothered calling. And if a club, queen, or jack comes down and he makes a big bet (which probably would NOT be a push), you can read it for a value bet and not pay him off.
There's one more reason to raise the turn, which is that you're probably ahead of him and you have an equity edge, whether he's drawing or just has a second best hand. It's never a bad thing to get more money in the pot when you're ahead, especially on a draw-heavy board. Ignore the fact that on this hand, this particular guy ended up pushing on the river. A lot of players will play a hand this way with similar cards (hitting a club draw and a straight draw on the turn) but then check behind on the river, or fold if you bet. In other words if they miss, they're not going to give you any more money. So why not get more of their money in the pot when he's still drawing? It so happens that this gentleman gave you all his chips, which was kind of him, but a generic online opponent - especially one you don't have a read on as being very aggro - may not be so accomodating. I almost never slowplay a hand like this unless I have a very compelling reason to do so (i.e. a read that says 1. my opponent is way behind, and 2. has a decent chance of pulling a huge bluff on the river if he misses his draw).
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