The class of acylindrically hyperbolic groups, which are groups that admit a certain type of non-elementary action on a hyperbolic space, contains many interesting groups such as non-exceptional mapping class groups, $\operatorname{Out}(\mathbb F_n)$ for $n>1$, many CAT$(0)$ groups, and many fundamental groups of $3$--manifolds. We show that under mild hypotheses, an acylindrically hyperbolically group satisfies a strong ping-pong condition, called property $P_{naive}$, which, roughly speaking, allows one to construct many free subgroups in such a group. I will describe this property and discuss various consequences of it. This is joint work with Francois Dahmani.