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BTN v BB 3b pot spot, turn/river decision

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BTN v BB 3b pot spot, turn/river decision

Blinds: $0.50/$1.00 (6 Players) BN: $137.74 (Hero)
SB: $191.07
BB: $101.50
UTG: $134.10
MP: $231.67
CO: $100.00
Preflop ($1.50) Hero is BN with 9 K
3 folds, Hero raises to $2.00, SB folds, BB raises to $7.00, Hero calls $5.00
BB is a reg, his 3b on these positions is 10%. I'm not even sure if we should defend K9s here but I guess it's not as bad since we're in position.
Flop ($14.50) K 2 5
BB bets $9.00, Hero calls $9.00
Turn ($32.50) K 2 5 7
BB checks, Hero checks
So far in 3b pots he X/folded 2/6 times, X/raised 1/6 and X/called half of the time when missed a turn CB. Do we need to bet for protection here? We probably get called only by better KX combos and sometimes shoved on by Ahi FDs or flushes. Our range is now mostly flushes, KX, AsX and pp.
River ($32.50) K 2 5 7 8
BB bets $19.00, Hero calls $19.00
Assuming we don't bet turn with all of our K9s-KQs, KJ-KQ, all pp higher than 5 (excluding 77), do we need to defend this combo or it's fine to fold since it's the worst of our KX and it's hard to find worse value combos he bets here? What do we do with KxJs/KxQs? Can we turn some of our KX/pp combos into a bluff? We have 27% pot odds. We need 62,5% FE to break even on our bluff shove.

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