This paper will explain why probability was for so long defined in terms of equally possible cases. The definition is usually attributed to Laplace. It preceded him by a century and survived him by another two. How could so monstrous a definition have survived three hundred articulate years? The trouble with the definition seems obvious enough. One could quote from a score of eminent critics. Here, for example, is Reichenbach discussing attempts to use a principle of indifference: Some authors present the argument in a disguise provided by the concept of equipossibility: cases that satisfy the principle of "no reason to the contrary" are said to be equipossible and therefore equiprobable. This addition certainly does not improve the argument, even if it originates with a mathematician as eminent as Laplace, since it obviously represents a vicious circle. Equipossible is equivalent to equiprobable [35, P. 3531Even workers who, in our century, have defended equipossibility have done so because they have philosophical views about the impossibility of producing non-circular definitions. Thus Borel, to whom all probabilists owe so much, maintained that such circles were not vicious. It is an error of logicians, he thought, to try to produce a non-circular definition of probability [8, p. 16]. Reichenbach does not explain why equipossibility had such a successful career. The explanation has two parts. First we require an understanding of concepts of possibility. Second, we must show how those concepts solved or concealed problems about probability that still plague us. We shall show by analysis of four generations of theorists that equipossibility theories were central to the evolution of our concepts of probability.