 It is natural to begin thinking about probabilities with a simple mathematical account that takes as its point of departure various games of chance involving cards, dice, or coins. Bettors have long noted that some outcomes are much more likely than others. In this context it is convenient to take the probability of a kind of outcome to be the ratio of such outcomes to all possible outcomes. Usually for reasons of symmetry in the physical set up, the possible outcomes are assumed to be equally likely. Where that assumption happens to be true or nearly so the empirical results of, say, a great many throws of a pair of dice tends to be close to what the simple mathematical account would suggest. Conversely, where the outcomes deviate from the expected ratios, bettors begin to suspect that the dice, coins, and cards (or the manipulations of them) are not all that they seem. The suspicion is that the outcomes are not equally likely and that the simple mathematical account does not apply.