After looking at the reasoning in that article I was about to credit myself with being unintentionally deep, but I'm pretty sure that when I posed the question I was assuming a fair coin for the sake of the problem. Doh. Thanks for the interesting link.

(It's really kind of embarrassing asking questions about simple probability amongst all the decision theories and Dutch books and priors and posteriors and inconceivably huge numbers. Only way to become less wrong, I suppose.)