I'm sorry, there's a mistake in the said reasoning. I don't have to reverse the inequality sign, but I do have to consider mismatches to make the inequality work, i.e,
num mismatches of (-30, 0) + number of mismatches (0,30) >= number of mismatches (-30, 30)
0.25 + 0.25 >= 0.5 (2 x 0.25) in...