generally boosting the probability values computed for most systems. In general, however, there is a strong correlation between the probabilities at both pericenters, so our conclusions seem only weakly dependent on the assumption of first infall.

The increase in probability is most notable in the cases of Dra 2 and Hy II, whose probabilities jump from $\sim 0.01$ and $0.01$ in a first pericenter passage to $0.50$, and $0.16$, respectively, when considering the second pericentric passage. The jump in probability is even more remarkable when including velocities, reaching $0.47$ in the case of Dra 2 at second pericenter, more than for the SMC.

The reason for this, in the case of Dra 2, is that it sits at the very far edge of the “trailing arm” of the tidal stream. Although its distance and velocity are consistent with an LMC association, at first infall there are only a few particles at that sky location and its probability is quite low. When the Clouds are in a second passage, several particles accumulate near the apocenter of the LMCa orbit, not far from where Dra 2 is, increasing substantially its probability of association. Similarly, Hy II is at the tip of the 