What makes you think we're ahead? What worse hands does villain call with if we check/raise the flop?
It is the dynamic of this hand;
2 important factors, the first is that it is a short handed table, and villains stats are unreliable and then it is button vs blind, that gives credence to the very real possibility that we are ahead. The button baggage I mention before is very real, it is almost mandatory that the button open an unopened hand, he is usually considered weak if he doesn't.
Villain here (button) will be playing a large range including a lot of hands that have us beat at this point. My point is that we can not let him have the free bet here. Villain may have the monster, we can't know for sure ever, but to offer him the hand by simply checking the flop is wrong.
We don't really need any math here, we are very likely good here most of the time. We need info, and we get none by checking.
Re-look at the hand, and ask yourself this;
If we check the flop, is there any way we are gonna call a bet?
-Slow play 9's with an ace on board? Really?
-Come along for value? Really?
-C/R ? Really?
As for the C/R We get the same info cheaper by betting out. Whether villain calls or raises.