Can we ever fold this full house?

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Posted by posted in Low Stakes

Can we ever fold this full house?

Blinds: $0.02/$0.05 (5 Players) BB: $5.00 (Hero)
UTG: $4.72
CO: $1.25
BN: $6.95
SB: $2.38
no reads on button player. His sizing seems to be pretty low given the two limpers, but would not be making any assumptions probably.
Preflop ($0.07) Hero is BB with Q 9
UTG calls $0.05, CO checks, BN raises to $0.14, SB folds, Hero calls $0.09, UTG folds, CO folds
Flop ($0.40) 4 Q 4
Hero checks, BN bets $0.15, Hero calls $0.15
Turn ($0.70) 4 Q 4 4
Hero checks, BN bets $0.61, Hero calls $0.61
River ($1.92) 4 Q 4 4 6
Hero checks, BN bets $2.05, Hero
Pretty standard till the river. I would put him on KK,AA,A4s,AQ,KQ,QJ,QT and 0-5% bluffs. However, I am still more and more concerned with his river sizing. I am pretty sure that he is not playing all his Qx this way. Because it seems like he wants to get value from Qx. Actually I do think that he is more likely polarized to KK+ which kinda sucks, because now we need to find more bluffs in his range to justify calling here. On the other hand folding here might really exploitative.. buut imo it is highly assumptive to expect that someone would start exploiting us, given the fact that 95-100% players would snap call this river.
To summarize it, my main data point is the sizing on the turn and river as well. Up to 3/4 I think it is a good call since I expect much more split equity, but otherwise I think he is pretty polarized on a KK+ and most of the time he puts us on a Q - which most players would call, sooo based on this assumption I more inclined to folding this river.

Really happy to discuss your thoughts about this highly exploitative play:)

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