Let $(a_n)$ be a lacunary sequence and let $G_N(x)$ denote the maximal gap of the finite orbit ${a_1x,\ldots,a_Nx}\subset\mathbb T$. The maximal gap is equivalent to the finite-time covering radius of the orbit and may be viewed as a deterministic analogue of the classical random covering problem. I will present almost-sure asymptotics for $G_N(x)$ with respect to Lebesgue measure. In particular, we show that $G_N(x)$ has the optimal order $(\log N)/N$. This is joint work with Yuval Peres.