The formula for the entropy s of the accessible volume of the phase space for frictionless hard spheres is combined with the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state for polydisperse three-dimensional packings to obtain an analytical expression for s as a function of packing density φ. Polydisperse hard-sphere packings with log-normal, Gaussian, and Pareto particle diameter distributions are generated to estimate their ideal glass transition densities φg. The accessible entropy s at φg is almost the same for all investigated particle diameter distributions. We denote this entropy as sg and can predict φg for an arbitrary particle diameter distribution through an equation s(φ) = sg. If the BMCSL equation of state is used for s(φ), then φg is found to depend only on the first three moments of a particle diameter distribution.