A Coin-Tossing Conundrum

It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be independent of the usual hypotheses governing probability, as well as whether this hypothesis might be assumed as a result of the Principle of Indifference. Also discussed are ways to implement or circumvent the hypothesis.