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Simple C-Bet Question 10NL on A-high Board

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Simple C-Bet Question 10NL on A-high Board

Blinds: $0.05/$0.10 (6 Players) BN: $19.00
SB: $10.00
BB: $13.86
UTG: $10.91
MP: $13.74
CO: $10.24 (Hero)
Preflop ($0.15) Hero is CO with K Q
2 folds, Hero raises to $0.25, 2 folds, BB calls $0.15
Flop ($0.61) 3 8 A
BB checks, Hero checks
Turn ($0.61) 3 8 A 3
BB checks, Hero checks
River ($0.61) 3 8 A 3 Q
BB checks, Hero bets $0.32, BB folds
Final Pot CO wins $0.58
Rake is $0.03

I have probably a simple question whether to cbet this hand or not but I am never quite sure with these A-high flops when I have K-high or a middle PP.

When I give the BB a tight calling range then Flopzilla says he has "no made hand" 45-50%. I guess with no made hand most people at 10NL don't continue on this board.

So a 40-50% cbet should be profitable here, right?

However, we have SDV so checking is an option. But what is your experience in realizing the SDV in such spots? Can we call a Turn when checked?

If I have some reads that Villain is passive then I normally check and try to get to show down, but what do you do here without reads?

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