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BvB oop w/ middle Set

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BvB oop w/ middle Set

Blinds: $0.10/$0.25 (6 Players) BN: $27.70
SB: $32.42 (Hero)
BB: $54.42
UTG: $71.92
MP: $29.98
CO: $13.44
Preflop ($0.35) Hero is SB with 8 8
4 folds, Hero raises to $0.75, BB calls $0.50
Flop ($1.50) 8 K 5
Hero bets $0.90, BB raises to $3.03, Hero calls $2.13
K-high semi-connected Flop, the plan is to c-bet roughly 40-50% of my hands here oop BvB. I choose to use one sizing ~60% pot as default.
Villain raises Flop and we have basically nuts as KK most likely 3bets pre. FD is out many possible straight draws or gutters and population tends to not value raise thin enough --> I assume this board is overbluffed when flopraised. That is why I only call (to keep (semi-)bluffs in with the plan to x/shove many turns for value.)
1st Question: With given datapoints, do we want to have a 3-betting range otf?
As there are quite a few bad turn cards, especially for a bit weaker hands like 55, K8?
Turn ($7.56) 8 K 5 4
Hero checks, BB bets $5.56, Hero calls $5.56
4d is kinda a bad turn card. Villain might think it is a blank (due to it being a low card) and gives up some low equity bluffs because he does not see enough FE.
Additionally, 76 gets there, which Villain is very possible to have in all its variations with his line. That is why I do not x/shove for value. Ingame I was unsure if Villain folds two pair vs. my shove. Now off table, I think best line could be x/shove as Villain might call most of his two pairs.
River ($18.68) 8 K 5 4 3
Hero checks, BB checks
spade hits OTR. I go for x/decide, probably x/fold.
What do you think about leading 1/3 pot and folding vs shove?
Final Pot SB wins and shows three of a kind, Eights.
SB wins $17.84
Rake is $0.84

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