The final stage of a relativistic heavy-ion collision is a hadron gas. Final-state interactions therein distort the $p_T$ spectrum of particles coming from the phase transition upon cooling the quark-gluon plasma.
Using recent state-of-the-art parameterizations of pion interactions we provide theoretical computations of the pionic depth of the gas: how likely is it that a given pion rescatters in it (we find a high probability around $p_T=0.5$ GeV at midrapidity, corresponding to the formation of the $\rho$ resonance), a comparison of the collision and Bjorken expansion rates, and how many pions make it through without interacting as a function of $p_T$. This is in the range 10-24% and the main result of the contribution.