I'd bet the flop.
It's true that as (opponent check raise frequency) increases, (the profitability of betting draws) decreases. However, some draws are so strong that it would take a very high opponent check raise frequency to make checking have an ev higher than betting.
If we change our hand to K
J
, it would likely take an unrealistically high opponent check raise frequency to make checking here have an ev higher than betting.
If we look at the list of available draws in our button range:
straight+flush combo draws
Naked Ace high flush draws (like A7dd)
Naked King high flush draws
etc etc down the line(this is a long list of draws)
We reach a point (undefined) where ev check = ev bet. We should bet every draw that is stronger than this, and check every draw that is weaker than this, naturally. Yes this implies that I don't use mixed strategies in multiway pots as default.
Considering that we have relatively many strong hands in our flop betting range(we are on the button, after all), I would think that our betting range should have relatively many draws in it as these draws are supported by strong hands, if compared with other situations vs both blinds.
If you're not betting A7dd here, what draws are you betting? A8dd? A9dd? Surely the combo broadway + flush draw hands are bets(I would bet these hands from any position vs both blinds). I would think that (utg draw betting range) differs from (btn draw betting range) quite drastically given such preflop action. In other words, if Jd9d is a ldo bet, then I believe that the next best draws (A9dd, A8dd, A7dd) must be quite profitable as well provided that we have a logically structured preflop range that provides us with many available draws.