How empty are the voids?

We find an analytical solution for the minimal matter density of a void, its central density. It turns out that the voids are not so empty: most of the voids have the central underdensity Δc ~ -50% (which means that the matter density in their centers is only two times lower than in the Universe on average). For small voids (of radius R₀ 5-10~{Mpc}), the underdensity can be significantly greater, but the number of voids decreases rapidly with increasing of |Δc| over $50%$, and voids with Δc < -80% are practically absent. The large voids (R₀≥ 40~{Mpc}) always have |Δc| < 50%.