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flush on river 3 way pot after calling a raise on turn

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flush on river 3 way pot after calling a raise on turn

Blinds: $0.05/$0.10 (6 Players) SB: $8.24
BB: $11.53 (Hero)
UTG: $8.53
MP: $12.90
CO: $24.57
BN: $9.92
Preflop ($0.15) Hero is BB with T Q
2 folds, CO raises to $0.20, BN calls $0.20, SB calls $0.15, Hero calls $0.10
Flop ($0.80) 3 8 7
SB bets $0.40, Hero calls $0.40, CO calls $0.40, BN folds
Turn ($2.00) 3 8 7 2
SB bets $0.70, Hero calls $0.70, CO raises to $2.10, SB calls $1.40, Hero calls $1.40
River ($8.30) 3 8 7 2 J
SB checks, Hero checks, CO checks

CU is 43/28 over 76 hands / 9.3 agg factor / 55% bet river (6/11) / 55% att to steal
SB is 56/37 over 43 hands

is betting river better than checking and hoping CU bet when flush hits?

i decided to just check cause after CU raise turn i thought that he would almost always bet river.... i cheked on his river betting % and assumed that there was a good chance he would stab to go steal or maybe even for value with 2 pairs or a set.... which he didnt... my plan was to check raise shove river... but since it diddnt went the way i planned i want to know if maybe jsut betting like 5-6$ on river would do the job

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