Probability distribution of similarity estimates for the uniformly random sequence null model – e.g. experimental values deviating from this model would indicate real homology, as in Fig. 4. The dark lines represent the numerical solution for the bi-directional over-determination, P3 (Equation 11), for different dimensionalities, n, identified by numbers in the plot. The gray lines represent the numerical solution for the same values of n, for the uni-directional over-determination, P1 (Equation 9). The solution for the dimensionality of the two stanzas, n = log2(19) = 4.25, is highlighted by a thick line, for both P3 (thick dark line) and P1 (thick gray line).