Comment by Pinus
I once did it with 0.3R + 0.6G + 0.1B < 128, mostly because I could not be bothered to think deeper than that. It was certainly not perfect — there were obvious cases where the opposite choice of black or white for contrast would have been better — but it worked well enough for my purpose (making a label at least not unreadable regardless of background colour).
I implemented something where contrast matters a lot, so I am using more sophisticated algorithms, but yeah, there are cases where you could get away with less sophisticated ones. :D