 The analysis presupposes that, for any \(E\), there is exactly one such price — let’s call this your fair price for the bet on \(E\). This presupposition may fail. There may be no such price — you may refuse to bet on \(E\) at all (perhaps unless coerced, in which case your genuine opinion about \(E\) may not be revealed), or your selling price may differ from your buying price, as may occur if your probability for \(E\) is imprecise. There may be more than one fair price — you may find a range of such prices acceptable, as may also occur if your probability for \(E\) is imprecise. For now, however, let us waive these concerns, and turn to an important argument that uses the betting analysis purportedly to show that rational degrees of belief must conform to the probability calculus (with at least finite additivity).