Question
There are $2m$ members (where $m$ > 1) seated randomly around a circular table at the Olympic Members Party. All $2m$ people have unique numbered labels $0,1,\dots, 2x-1$, which represent how many people they know, the person with label $i$ knows exactly $i$ of the other $2x-1$ people at the table. These connections are one way, meaning that just because person $B$ knows person $A$, it does not imply person $A$ knows person $B$. Whats the expected proportion of people that know at least one of the people on either side of them.