  Dark matter substructure can contribute significantly to local dark matter
searches and may provide a large uncertainty in the interpretation of those
experiments. For direct detection experiments, sub-halos give rise to an
additional dark matter component on top of the smooth dark matter distribution
of the host halo. In the case of dark matter capture in the Sun, sub-halo
encounters temporarily increase the number of captured particles. Even if the
encounter happened in the past, the number of dark matter particles captured by
the Sun can still be enhanced today compared to expectations from the host halo
as those enhancements decay over time. Using results from an analytical model
of the sub-halo population of a Milky Way-like galaxy, valid for sub-halo
masses between $10^{-5}\,M_\odot$ and $10^{11}\,M_\odot$, we assess the impact
of sub-halos on direct dark matter searches in a probabilistic way. We find
that the impact on direct detection can be sizable, with a probability of $\sim
10^{-3}$ to find an $\mathcal{O}(1)$ enhancement of the recoil rate. In the
case of the capture rate in the Sun, we find that $\mathcal{O}(1)$ enhancements
are very unlikely, with probability $\lesssim 10^{-5}$, and are even impossible
for some dark matter masses.
