For an explanation of what Bulgarian Solitaire is, look here.
I have worked out the full graphs for $1 \leq \text{number of cards} \leq 13$ in the past, and all of them had just one root loop...except for $8$ cards. In that case, there are two root loops, one of which is $(4,2,2) \to (3,3,1,1)$ (which is also the entire subgraph for that loop). So, here we have a loop of size $2$ and a loop of size $4$. Unlike my previous question, I have no good intuition as to why this is the case.
Which numbers have multiple root loops? How many do they have?