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2NL 3 barrels and push was right?

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Posted by posted in Low Stakes

2NL 3 barrels and push was right?

Blinds: $0.01/$0.02 (9 Players) MP+2: $3.98
CO: $6.91
BN: $3.54
SB: $1.61
BB: $0.92
UTG: $1.98 (Hero)
UTG+1: $2.33
MP: $16.50
MP+1: $2.14
Preflop ($0.03) Hero is UTG with 7 7
Hero raises to $0.06, UTG+1 folds, MP calls $0.06, MP+1 folds, MP+2 calls $0.06, CO folds, BN calls $0.06, SB calls $0.05, BB calls $0.04
Flop ($0.36) 4 4 5
SB checks, BB checks, Hero bets $0.27, MP calls $0.27, MP+2 folds, BN folds, SB folds, BB folds
Turn ($0.90) 4 4 5 8
Hero bets $0.48, MP calls $0.48
River ($1.86) 4 4 5 8 T
Hero bets $1.17 and is all in, MP calls $1.17
Final Pot UTG lost and shows two pair, Sevens and Fours.
MP wins and shows a full house, Tens full of Fours.
MP wins $4.05
Rake is $0.15

This guy in MP is a fish with 55/30, bet 96 and 3bet 16 stats. he entered many pots with garbage. as i checked equity calc i was ahead with about 70% equity vs his range all three streets(considering his range constant). Is my play here ok or should i be more careful?
How does his range change on every street?

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