The probabilistic formula provided by Hauptman and Giacovazzo for estimating three-phase invariants when anomalous scatterers are present is revisited. Its main defects are: (a) it is absolutely resistant to any attempt at interpreting it in terms of parameters accessible via the experiment; (b) its calculation is time consuming and requires computing resources. A distribution based on interpretable estimates of the parameters is proposed. The role of the old and the new expressions in the single-wavelength anomalous diffraction (SAD) techniques is discussed, and compared with the role of analogous formulas estimating triplet invariants from isomorphous diffraction data.