Biased Coins

I've come to quite like Richard Wiseman's Friday puzzles - though sometimes the answer's obvious and sometimes it's a rather infuriating trick question. This recent one, on how to choose randomly with a biased coin, is of course right up my street. Richard's answer was posted here. Clever, but I (and others) think that this was cleverer than needed, given the set up of the question. I explain why in my comment here. I think epistemic randomness is sufficient here, so only one toss is needed.