(Not a post about Juan Williams.) From the comments in a post from Jonathan Weinstein:

In fact, there is a simple procedure to simulate a (exactly) unbiased random coin from a biased one. Flip your coin twice (and repeat the procedure if you obtain the same outcome). Call “Heads” if you first got heads than tails, and “Tails” otherwise.

Check out the whole discussion to see how this relates to Ultimate Frisbee, the essential randomness of the last digit in any large integer, Mark Machina, and Fourier analysis over Abelian groups.