The paper considers the intricate web of conditions that made for the rise, from a suitable ground of constructive scepticism, of a mathematics of the probable, in the latter half of the seventeenth century, setting forth the theoretical elements for a new prudence and providence: this emergence is examined with reference to such traces as are extant and available to this day, of a quantification of probability, as effected in the fourteenth century. Central to this later mathematisation was the concept of value for the expectation in a risk situation, on the basic pattern of the wager in a game of chance. Jakob Bernoulli's approach thus becomes intelligible, when he set down, in the context of a projected general logic of the probable, the groundwork for a mathematics of the probable harking back to the problem-situation of probability evaluation.