  When applied to compute the density jump of a shock, the standard
magnetohydrodynamic (MHD) formalism assumes, 1) that all the upstream material
passes downstream, together with the momentum and energy it carries, and 2)
that pressures are isotropic. In a collisionless shock, shock accelerated
particles going back and forth around the front can invalid the first
assumption. In addition, an external magnetic field can sustain stable pressure
anisotropies, invaliding the second assumption. It is therefore unclear whether
the density jump of a collisionless shock fulfils the MHD jump or not.
  Here we try to clarify this issue. A literature review is conducted on 68
articles dealing with Particle-In-Cell simulations of collisionless shocks. We
analyze the factors triggering departure from the MHD density jump and quantify
their influence on $\Delta_{RH}$, the relative departure from the
Rankine-Hugoniot jump. For small departures we propose $\Delta_{RH} = +
\mathcal{O}(10^{-1-3.7\kappa})t^\kappa - \sigma \mathcal{O}(1)$ where $t$ is
the timescale of the simulation, $\sigma$ the magnetization parameter and
$\kappa$ a constant of order unity. The first term stems from the energy
leakage into accelerated particle. The second term stems from the downstream
anisotropy triggered by the field (assuming an isotropic upstream). This
relation allows to assess to which extent a collisionless shock fulfils the RH
density jump.
  In the strong field limit and for parallel shocks, the departure caused by
the field saturates at a finite, negative, value. For perpendicular shocks, the
departure goes to zero at small and high $\sigma$'s so that we find here a
departure window. The results obtained have to be checked against full 3D
simulations.
