[converted_hand][hand_history]Poker Stars, $0.01/$0.02 No Limit Hold'em Cash, 6 Players
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Hero (SB): $4.12 (206 bb)
BB: $3.20 (160 bb)
UTG: $3.17 (158.5 bb)
MP: $3.23 (161.5 bb)
CO: $2 (100 bb)
BTN: $3.30 (165 bb)

Preflop: Hero is SB with K K
UTG folds, MP raises to $0.06, 2 folds, Hero raises to $0.24, BB folds, MP calls $0.18

Flop: ($0.50) 9 8 3 (2 players)
Hero bets $0.16, MP calls $0.16

Turn: ($0.82) T (2 players)
Hero checks, MP checks

River: ($0.82) 4 (2 players)
Hero checks, MP bets $1.16, Hero calls $1.16

My assumption was that villian is fish, i checked him and he played one table.
I have a pretty narrow 3b range SBvsMP so i decided to bet 1/3 with all my range here (is it ok? or better to use bigger sizing and split my range on bet & check?). OTT i decided to pot control. I don't know how should i play OTR, i was thinking about blocking bet and about x/call, but i didn't expect such sizing. I tanked almost all my TB and called, perhaps it's terrible call. My thoughts were that all his sets/straights he would bet on turn, so OTR he polarised himself to a flush/bluff, i was thinking that he can bluff with Ad or turn into a bluff some crap. Is is better to call such bet with Kd? Or i needed just to fold my hand here?

Vs a fish just barrel turn or as played bet river smallish (folding to a raise on both streets). As played river call or fold both seem fine should be very close.

If we fire second barrel on turn, which sizing to pick?

~0.5

I'd bet the flop a bit bigger with the board being marginally coordinated - maybe something like 50% pot. If you're concerned about too narrow a 3-betting range in this spot maybe look to opening up your range pre-flop a bit more: ATs,JTs,QJs,KJs,AQo kind of thing.

There's definitely worse he'll call you with on the flop so I'd definitely fire the flop close to 100% of the time with KK. His calling range equity increase on the the turn but you're still ahead of a range which includes JJ-77,AQs,ATs-A8s,QTs+,JTs,T9s. So I'm definitely firing again probably 50% to 70% pot.

Usually bet the turn, but when villain checks back, I think he has SDV (hands like JTs or A9s) and you should blockbet the river for thin value (fold to a raise). He's hardly ever checking back the turn with a naked FD. Some fish will make a stupid check back with the nuts though.
As played, probably sigh-fold this combo, but call with the Kd, as you said.

Why are you using a balanced sizing post flop vs a muppet. As played bet turn big. You're playing like a nitfish.
Fish generally underbluff and call to often, why check river as played.

You may go bigger pre and in all streets as you are deep.
Bet agr and reevaluate to any raise

River is a very clear value bet and I don't even think it's thin or needs a block sizing.

They don't bluff enough, they don't value bet thinly enough, he had a opportunity to bluff turn and either chose not to or didn't need to. Check-call river is massively -EV at your stake regardless of colour of your Kings.

I think flop should be bigger

b/f river

Yeah my bad. What sizing would you use on flop/turn 66-80% ?

How much bigger pre? I made 12bb vs 3bb open, something around 15bb?