[paragraft]

It's a fairly well studied area, deriving unbiased randomness from a consistently biased source eg http://web.eecs.umich.edu/~qstout/abs/AnnProb84.html

The simplest approach I know of is to extract a random bit repeatedly until it transitions from 0 to 1 or 1 to 0, and then use the second result. 50/50 split, regardless of any (constant) bias in the generator.