Aha, very nice. This is generalizable too: to get a fair dN from a randomization source with any number of unfair outcomes, do sets of N randomizations until you get a set that's exactly 1 of something and N-1 of something else, and the position of the unique one gives the ultimate result. (This requires N > 2, since for N=2 you can't tell which was the 1-of and which was the N-1.)