Implied risk neutral probabilities, betting odds and prediction markets.

We show that the well known equivalence between the "fundamental theorem of asset pricing" and the "dutch book argument" consists, in reality, of two parts: the first concerning the existence of a risk free investment, and the second the possibility of arbitrages. We argument that the "implied probabilities" of an odds system may be used to rate the bookmaker's fairness, and briefly discuss the significance of the same probabilities as defined by the prices in the prediction markets.