Gonna differ with griffey on this one (edit: he may have meant "entire betting range" which if so you can disregard). I think that you'll potentially make a good bit more money with your air if you check back some of it here with some decent hands to balance.
I would check back some air that can turn strong second pair hands vs bb's calling range, stuff like J9, as I don't think betting and turning a 9/J would be worth much, we'd win at sd some but our hand will usually be too weak to call a river bet once we check back turn.
I'd also check back weak kings and QQ/JJ on this board with a relatively high frequency. All in all I'd probably check more air than pairs, but I think BB will give you a lot of credit for sd value and check his air ott a huge amount of the time, and you can make a delayed cbet that is significantly more profitable than a flop cbet would have been.
That said, I think betting stuff like 65/A3 on the flop is pretty standard. I could go either way on betting 33, I think there are strong merits for and against.
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