 In the subjective probability version, a gamble is an act (sometimes called as “Savage act”; Savage 1954) that assigns consequences to possible states of the world. Consider, for example, the act of cracking an extra egg into one’s omelet, when the egg may be rotten: if the egg is fresh, the consequence will be a large omelet, but if the egg is rotten, the consequence will be a ruined omelet. We can represent this act a as {extra egg is fresh, large omelet; extra egg is rotten, ruined omelet}, and we can represent the act of not cracking the extra egg as {extra egg is rotten or fresh, small omelet}. More generally, acts have the form \(g = \{E_1, x_1;\ldots; E_n, x_n\},\) where \(x_i \in\cX,\) \(E_i \subseteq \cS\) is an event (a subset of the state space), and \(x_i\) obtains when the true state of the world is in \(E_i.\) Again, acts needn’t be restricted to a finite set of consequences. In the subjective probability version, the individual has a probability function \(p\) that assigns to each \(E_i\) a number between 0 and 1 (inclusive), which represents her subjective probabilities, also called “degrees of belief” or “credences”. The probability function is additive in the sense that if \(E\) and \(F\) are mutually exclusive, then \(p(E v F) = p(E) + p(F).\) (For some of the discussion, it does not matter if we are talking about lotteries or acts, so I will use the variables A, B, C… to range over lotteries or acts.)