AK 3-bet hits K on flop vs nit

[Oct0puz]

I think I played this hand really bad. Comments on all streets.

SB ($187.37)
Hero ($100)
EP ($126.1)
Button ($156.2)

EP is 19/6/0.55 over 45 hands. Button is 60/17/0.9. No other reads.

Preflop: Hero is BB with A[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img]
EP raises $4, Button calls $4, Hero raises to $16, <font color="#666666">1 fold</font>, EP calls $12, Button calls $12,

Flop: K[img]/images/graemlins/club.gif[/img], 2[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/spade.gif[/img] ($46.0)
<font color="#CC3333">Hero bets $22</font>, EP calls $22, <font color="#666666">1 fold</font>,

Turn: J[img]/images/graemlins/club.gif[/img] ($90.0)
Hero checks, <font color="#CC3333">EP bets $41</font>, Hero raises to $62, EP calls $21,

On the flop I didn't think Villain would call with many worse hands, thats' why I bet pretty small. HU I propably would have checked. But now when I think about I should have bet bigger, because my main target should be the button. Should I have bet more or maybe even checked?

On the turn I just didn't think there was any value in betting so I checked. Then when he bet I just thought "Screw it. I have TPTK in a 3-bet pot, all-in I'm getting 2.5:1". Fold here?

[ejay]

3b more pf, lead bigger on the flop. You are just try to be too tricky when there really isnt much need, they will call you with worse kings and maybe worse pp and they will fold anything else no matter if you bet 1/2 or full pot

[Oct0puz]

What about turn?