 Modern notions of probability are quantitative (Hájek 2011). They underlie the representation of probabilities by real (initially: fractional) numbers from the interval between 0 and 1. On this basis, a probability calculus with its own mathematical rules (the Kolmogorov axioms) has  arisen.[1]  The present mathematics of probability marks the end-point of a development which began in the middle of the seventeenth century with the calculation of chances in games of fortune by Pascal, Fermat, and Huygens. These early calculations were considerably refined in the eighteenth century by the Bernoullis, Montmort, De Moivre, Laplace, Bayes, and others (Daston 1988; Hacking 2006; Hald 2003). Modern conceptualizations of probability emerged at the same time. They evolved around the ideas of a ratio of possibilities, a relative frequency of events, a degree of belief, or a degree of confirmation.