bad runout, 8 high vs fish, still bluff?

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bad runout, 8 high vs fish, still bluff?

Blinds: $0.10/$0.25 (6 Players) BN: $45.97
SB: $59.99
BB: $25.00
UTG: $25.00
MP: $29.76
CO: $37.19 (Hero)
villain unknown, 40/5 over 8 hands
Preflop ($0.35) Hero is CO with 8 7
2 folds, Hero raises to $0.62, BN calls $0.62, 2 folds
Flop ($1.59) K 6 T
Hero bets $1.18, BN calls $1.18
Turn ($3.95) K 6 T 2
Hero bets $2.94, BN calls $2.94
River ($9.83) K 6 T 2 K
Hero bets $3.09

I'm interested in how you go about river spot like these. Normally I just x/lose but feel like with 8 high we might have some FE from higher diamonds, AQ, AJ, QJ, 6x although the latter is rare and somewhat optimistic. Combinatorics-wise he shouldn't have a ton of Kx but I doubt he ever thinks about folding Tx. Does putting out a small bet just to fold out better highcard hands and few pairs therefore make any sense or do you think that's still just not profitable?

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