On a hyperbolic surface, a closed geodesic is said to be simple if it does not intersect itself, and a multi-geodesic is a disjoint union of simple closed geodesics. In this talk, I will explain how to pick a random multi-geodesic, and present an attempt to answer the following question: what is the shape of a random multi-geodesic on a hyperbolic surface of large genus? We will see that it looks like a random permutation, and in particular, the average lengths of its first three largest connected components are approximately, 75.8%, 17.1%, and 4.9%, respectively, of the total length. This talk is aimed at non-specialists (but specialists are welcome too!).