[tgv]

It's simpler: an ideal coin flip is simply assumed to be uniformly distributed, on the basis of there being two possible outcomes and no influence. Where the bias in reality comes from, doesn't matter.

This also happens to be the great divide between frequentists and Bayesians.

[kqr]

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.)