  We are examining a new kind of lattice gas that closely resembles modern
lattice Boltzmann methods. This new kind of lattice gas, that we call a Monte
Carlo Lattice Gas, has interesting properties that shed light on the origin of
the multi-relaxation time collision operator and it derives the equilibrium
distribution for entropic lattice Boltzmann. Furthermore these lattice gas
methods have Galilean invariant fluctuations given by a Poisson statistics,
giving further insight into the properties that we should expect for
fluctuating lattice Boltzmann methods.
