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The conventional way to transfer a RGB image to gray is
Gray = 0.299R + 0.587G + 0.114*B,
which has 3 coefficients to control the final result.
However, I tried the 'black-and-white' filter in Ps and found out it has 6 separate controls. I set red and green channel to 0 but the gray result of yellow, the combination of red and green, remained the same. Therefore I infer this filter is not working in RGB channels. It should be working in HSV, where you can adjust the luminance of one color without affecting the others.
