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I'll try to expand on what badgers is saying. First off on the 4bet amount.. It's really poor. You min 4-bet.. Sure you wanted action with your KK, but make them pay if they want to play against your strong hands. He had already 3b and I'm sure that players at 5nl aren't 3betting light. If they do it they probably think their hand is golden no matter how bad it really is, so I'm betting he is willing to felt. Although I'm not sure I 4b here always, but it's fine. Just increase the amount to as badgers said to $1.8 or so.
Okay on the flop bet what badgers is saying is this.. When you make a bet you want to the bet to accomplish a few things. Namely...1) Better hands fold....2) Worse hands calls... 3) Protect your hand.... Your bet on the flop achieved neither of those. Let's look at each.
1) better hands fold - Okay, so by betting the flop what better hands fold. Let's name a few hands that are ahead of you and let's see if he folds them. He isn't folding an Ax. If he 3b preflop and called a 4b he isn't gonna fold if he hit his hand. Same goes for TT. That's obviously not folding. So no better hands are folding.
2) Worse hands call - What worse hands call your flop bet? Well there are cases when QQ,JJ, Tx, or worse (gutshot) call, this is usually rare, especially at microstakes. So when you bet usually hands like QQ, JJ, Tx, or KQ etc fold. And these are all hands we are ahead of and have them drawing rather thin. So no worse hands call (or very few do).
3) Protect our hand - This is a rainbow flop. Only a gutshot straight draw or 2pr draw out there, so not much protecting to do. Even if this had a flush draw I'm checking behind.
So we find that a bet here doesn't accomplish any of the things we need it to accomplish. Okay, so we don't bet. What does that do? Well for one hands like QQ, JJ, Tx, or total air, might think they are good on the turn due to the "weakness" you showed on the flop. So you can call a modest bet of the turn and re-evalute on the river, effectively inducing "bluffs" (or what your opponent's think is a v-bet).
So your play should have been to check behind on flop and evaluate on the turn. If he leads on the turn you can either toss it then or call a bet and see if he is willing to fire again on the river.
This is usually the play with KK on an Axx board. If you were oop here I would c/c flop, c/f turn I believe.
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