the fractional obstacle problem in $\mathbb r^n$ with obstacle $\varphi\in c^\infty(\mathbb{r}^n)$ can be written as \[ \min\{(-\delta)^s u , u-\varphi\} = 0,\quad\textrm{in }\quad\mathbb{r}^n. \] the set $\{u = \varphi\} \subset \mathbb{r}^n$ is called the contact set, and its boundary is the free boundary, an unknown of the problem. the free boundary for the fractional obstacle problem can be divided between two subsets: regular points (around which the free boundary is smooth, and is $n-1$ dimensional) and degenerate points. the set of degenerate points, even for smooth obstacles, can be very large (for example, with infinite $\mathcal{h}^{n-1}$ measure). in a joint work with x. ros-oton we show, however, that generically solutions to the fractional obstacle problem have a lower dimensional degenerate set. that is, for almost every solution (in an appropriate sense), the set of degenerate points is lower dimensional.