Abstract: If the dark matter has a sufficiently large elastic self-interaction, energy transported by scatterings can lead to gravitational collapse in the core of dark matter halos. Quantitatively following the collapse (in principle) requires solving the 6-dimensional collisional Boltzmann equation, a formidable challenge. Here, I present the code KiSS-SIDM (Kinetic, Spherically Symmetric Self-Interacting Dark Matter), which handles the collision term via the Direct Simulation Monte Carlo algorithm, and simplifies the dynamics by assuming spherical symmetry. The efficiency of the code enables exploration of parameter space on a laptop. Yet, in contrast to the commonly adopted "conducting fluid" model, the code requires no calibration parameters. Further, the high accuracy of the code enables simulating deeper into the collapse than traditional N-body methods. In this regime, we find that non-equilibrium effects alter the evolution compared to the predictions of the fluid model.