QQ flop comes a k

[Gnome123]

Most of this sounds great in situations where we need to worry about being exploited. This is such a specific case that you don't need to worry about balancing and should just take the highest EV play as if its in a vacuum. Worrying about balance here is like worrying about balance when you flop quads.

To be fair, what the optimal play happens to be depends on a bunch of stuff OP doesn't provide us (player tendencies, position, etc.). I'm sure your assumptions about this opponent are different than mine.

Any math guys care to share how often this specific situation comes up?

Edit: I'm absolutely willing to concede that in any number of specific situations c/c, c/f, and bet are all correct on the flop.