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NL2- Tough spot with KK

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NL2- Tough spot with KK

Blinds: $0.01/$0.02 (7 Players) MP: $3.07
UTG+1: $1.95
CO: $2.14
BN: $2.00
SB: $2.00 (Hero)
BB: $2.67
UTG: $1.95
Preflop ($0.03) Hero is SB with K K
5 folds, Hero raises to $0.06, BB calls $0.04
Stats: 3bet: 4.2, cbet: 72%. fold to cbet: 58%, fold to steal: 79%, vpip/pfr is 18/11. Over 1200 hands for 9max

How often do you think villain defends here when he has such a high fold vs steal? I've no idea what range he would have here. I've made a rough assumption that they flat 15% and also they 3bet: JJ+ and AQ+. Their 3bet is close to 4% and combined with flat range gives him a total defence of 19%.
Flop ($0.12) 8 3 9
Hero bets $0.09, BB calls $0.09
Do you think that villain almost always raises their sets and 2pairs here? The board is very wet. I would never just call here. What do you think is the best play here for the villain?
Turn ($0.30) 8 3 9 7
Hero checks, BB bets $0.08, Hero calls $0.08
River ($0.46) 8 3 9 7 4
Hero checks, BB bets $0.50, Hero calls $0.50
I think here if it's ok to call then it is close to a breakeven call.

I've made some assuptions on what villain could have:

#Run1: They bet for value their straights(JTs and 65s, did not include JTo here since I assumed they folded pre but I may be wrong), 2p(97s, 87s) and TT, A9s, K9s. Could also bluff some stuff but I did not include that. Vs this range we have 45% equity. A clear call.

#Run2- The only difference from before is that he checks now TopPairs, but still bets TT though. We have 33% equity.

#Run3- They call on the flop low pocket pairs(77-44, 22) and so they might appear here with stuff like 77 which they hit on the turn. If they did that and the rest of the range was like Run2 then here we have about 29% equity.

-All those runs did not include any bluffing they might do.

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