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.
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.)
Wait, didn't Ed Thorp argue for the exact opposite – if you have a super-person that can guarantee lack of bias, then you also have absolute Newtonian predictability on virtue of the mechanical perfectitude. The randomness must come from somewhere, and it comes from imperfections which also incidentally introduce bias.
Let's consider a spherical cow...