Even simpler than that, actually. There's no requirement for any distribution at all. (And I would argue strongly against a uniform prior, but that is a separat

Even simpler than that, actually. There's no requirement for any distribution at all. (And I would argue strongly against a uniform prior, but that is a separate discussion.) What's necessary to guess 50 % on the first toss is simply (a) complete ignorance about the bias, whatever it is, and (b) the hypothesis that the bias is just as likely to be negative as positive (i.e. a symmetric prior.)