False alarm probability (FAP) in variability studies in g-LSST. The results are presented as a function of the MBHB properties, grouped according to the used template. We used a total N_R = 10⁵ light curves for each MBHB, and each distribution encloses a total of N_det, g × 10⁵ entries. The coloured regions represent the total distribution while the horizontal segments locate the 25th, 50th, and 75th quantiles of each distribution. In all the distributions, the peak at FAP = 10⁻¹² corresponds to cases where we find FAP values equal to 0.