The Yule-Nielsen effect, also called optical dot gain, has often been modeled based on convolutions between halftone dot patterns and a point spread function PSF characteristic of the paper. An alternative approach to modeling the Yule-Nielsen effect employs probability functions that describe the fraction of reflected light emerging between halftone dots and under dots. The probability model is shown to fit experimental data on the Yule-Nielsen effect for a variety of different types of halftone geometries, including both AM and FM halftones. The particular form of the functions is shown to be dependent on the halftone geometry, but all forms examined contained a parameter ω, which is a quantitative index of the magnitude of the Yule-Nielsen effect. The ω parameter in all cases was shown to be related exponentially to the MTF constant k_p of the paper.