I'm not a business maaan

[rafiki]

I'm a business, man
so let me handle my business, daaaamn

15/30 Bellagio game

CO has been raising almost every orbit, and has shown that he's raising light. LAG city for sure, but I've yet to see him get massively out of line post flop. All fold to him, he pops it.

I look down at two black 6's in the sb and decide I want to play the hand alone against him. I've folded a ton of blinds to him, not this one. I raise, BB folds (super nit), and flop is

K56 rainbow

I check raise the flop, he goes 3. I call with the intention of banging on his head on the big streets

turn:

K56K, and the second king puts a red flush draw out. I check raise him again, he goes 3, I go 4, he calls. Nice I'm going to win this.

river

K56K2, no flush

I bet, raise, I 3, he 4's...

Does this have to be KK if he goes 6 ? Anyone not put one last raise in on the river ?