  We introduce DRAKE, a numerical precision tool for predicting the dark matter
relic abundance also in situations where the standard assumption of kinetic
equilibrium during the freeze-out process may not be satisfied. DRAKE comes
with a set of three dedicated Boltzmann equation solvers that implement,
respectively, the traditionally adopted equation for the dark matter number
density, fluid-like equations that couple the evolution of number density and
velocity dispersion, and a full numerical evolution of the phase-space
distribution. We review the general motivation for these approaches and, for
illustration, highlight three concrete classes of models where kinetic and
chemical decoupling are intertwined in a way that quantitatively impacts the
relic density: i) dark matter annihilation via a narrow resonance, ii)
Sommerfeld-enhanced annihilation and iii) `forbidden' annihilation to final
states that are kinematically inaccessible at threshold. We discuss all these
cases in some detail, demonstrating that the commonly adopted, traditional
treatment can result in an estimate of the relic density that is wrong by up to
an order of magnitude. The public release of DRAKE, along with several examples
of how to calculate the relic density in concrete models, is provided at
drake.hepforge.org
