OK Ejay it is a bit tenuous hence the ?
I was thinking of doing the round(s) when it comes to visiting/travelling. With regards to dancing and singing it's when everyone stands in a circle and dances withe each person. Harrhy makes the reference to round robin when everybody in the groups plays against each other.
Sorry but that was all I could think of. If you've got a decent dictionary it might be a little more help.
Andy