Hey OZ, welcome to RIO keep posting hands mate you in the right place!

Preflop I like your play, three betting linear here not calling much unless I had a reason; fish behind or low three bettors and than id be trying to sneak some PP's etc into that calling range. With no info I like simplifying and playing three bet or fold here.
Very good board for IP, who might slightly push equity vs a wider linear 3 bet range range.
Im thinking maybe just check range and have a very agro CR?
Im sure optimal play has us CBing a weird merged range x% of the time and checking x% of the with a nutty CR range, favoring BDFD overcards as bluffs in both CB/CR lines .
But I think this flop is interesting going to take a look at it closer and come back later :D
dk

OOP cbet strat

SB cbets 70% of the time at equillibrium with the following assumptions:
- SB 10% 3bet range (see above)
- CO 11% calling range
- Only the 35% betsize option

OOP is pushing only 51% equity because IP has many more 9x than him. But you can still push the mixed strats towards pure bets with only 2.3% EV loss.

Equillibrium
Range bet

The hands that want to check are the suited hands without BDFD and AJo/KQo with a non BDFD suit (in this case a spade). Another option is to cbet everything apart from those suited hands. The check range will be a very small portion of your range so you shouldnt care about it being all trash. There is a slight EV gain when you do that

Check spades

I checked in my DB if people are really defending K9s-J9s vs 3bets in position from the CO. From my 50z DB alias, people open 27% hands and fold 56,5%. which means they defend (with a call or 4bet) with 43,5 % x 27% = 11,7% of hands. This is what I think 11,7% hands mean in this spot: CO defense vs 3bet IP

So IP probably doesnt have all K9s-J9s at nl10. If thats the case, then OOP EV jumps to 102.6. Now OOP is pushing 52% equity, and betting range (now betting range for the bigger sizing - I compared EVs and not a single hand prefers to bet 1/3) loses 2.8% EV. Check/folding spades also improves EV a little bit: check spades/ bet 60% otherwise

PS: I ran a sim at first with two OOP bet sizes, 35 and 60 and then only 35. OOP prefers the bigger sizing and it lost EV when I removed the 60% size.

Conclusions:
1) The board is close to neutral, favoring OOP a little bit because of QQ+. The fact that IP has more 9x affects things significantly. So when making a postflop decision its importante to understand what our opponents preflop range looks like.

2) OOP can cbet range for 1/3 or 60% with not a big EV loss.

3) Check/folding the hands with very poor equity (spades) and betting the rest improves EV.

4) 60% is almost always prefered over 1/3

OOP can probably cbet range here

My inital thought expressed above comes from the significant amount of study I've been doing in SB vs BTN 3BP. I haven't done any significant work in SB vs CO though. In this scenario, SB pushes 55% equity, signifcantly more than SB vs CO. SB vs BTN @ 962r

I thought it was relevant to bring the context of SB vs BTN, because it has been helpful for me in order to understand similar spots.

Still I think cbetting would be a better option. I don't know why I have called without position and only backdoor FD and overcards but it's a spew IMO.

Its not the end of the world to check/call this hand but the prefered action is indeed to cbet

Nice work saulo my equity assumption was a little off

Thank you Saulo and others for great analysis :)