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i would've pushed the river... he could have just as easily had two pair or an under-set.
It sucks that he had KK, you got two outed. The thing you have to learn is to put your opponents on a range of hands. Most of the time you cannot put someone on a single hand, or even 3 different possible hands. So you have to think to yourself, "if i were in his shoes, and i were him (eg loose aggressive, tight aggressive, loose passive, etc.) what hands would i do this with?"
In this specific situation, he raises you $24 on the river. Against an unknown, i'd put him on 45, 66, 33, JJ, K7, K6, K3, KJ, well a lot of hands. basically a lot of two pair hands, some undersets, a straight, an overset, and also possibly a missed flush draw bluff (never rule out bluffing). I actually wouldn't put him on KK because he didn't reraise preflop.
So really, if you look at this play objectively, without results, you should go all in.
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