Monte Carlo simulation used to estimate the SIDM cross sections required to account for the DM cores of UFDs. The cross sections depend on a number of poorly constrained parameters (the parameters in Eq. (10)). The Monte Carlo simulations allow us to propagate their uncertainties on σ_H/m/β_age (the gray histogram) and, via Eq. (9), on the cross section σ/m. The blue histogram represents the distribution assuming the UFDs are in the process of forming the core, whereas the green histogram assumes that DM is evolving into the core-collapse phase. The vertical dashed lines mark the 2.3% and 97.7% percentiles used to constrain the range of viable cross sections given in Eq. (11). See the main text for further details.