Hero (BTN): $113.10 (113.1 bb)
SB: $888.72 (888.7 bb)
BB: $97.16 (97.2 bb)
UTG: $181.04 (181 bb)
MP: $123.41 (123.4 bb)
CO: $149.01 (149 bb)

Preflop: Hero is BTN with K 9 A Q
2 folds, CO raises to $2.50, Hero raises to $9, 2 folds, CO calls $6.50

Flop: ($19.50) 4 7 5 (2 players)
CO checks
Hero ?

CO agressive player 40% open from CO
Bet or free card?
If we take free card what is our line on turn different cards both when villain checks or bets?

I do both at some frequency..probably betting more often though. vs aggressive players who will check raise /fold you here you can get it in.

If we check and he bets most turns we call ; occasionally we could fold on a pairing card and a large lead, for example (we could also float that)

if he doesn't donk here then its kind of hard spot, although your 3b renage from BTN may hit this board allowing you to c-bet , having to fold to a pot check raise is bad and its pretty good spot for him to CR with air aswell. I guesss you can check behind some of your 3b range which hit this board,

it ultimately depends on how he sees your BTN 3b range and his donk freq

Many things to think about in this spot. If you check behind he will assume that you cbet your NFD,,, ig he cr his own flush draw then you get folded out , so in vacuum I like check behind

if he doesn't cr wide then you can get away with 1/2 pot cbet as with known cards he will only connect this board about 30% (just guessing) of the time.

It is a lessor board to c bet with the 6 gap aswell, compared to say two gaps lower down. but it still should swing it for cbet alot.

Hand Optimized Count Base Count
6:40%!aa** 15573 (5.75%) 27080 (10.00%)
4:40%!aa** 8377 (3.09%) 18962 (7.00%)
5:40%!aa** 10923 (4.03%) 24076 (8.89%)
7:40%!aa** 13587 (5.02%) 29226 (10.80%)

I like betting than checking, but its pretty close. since villan is agressive, i would rather bet myself cause i wont be able to delayed cbet here too often...
but it all depends on your villans read and the reads that he has about you

If he c/r you evaluate with the villans profile - about folding or shoving; calling is pointless