Tivoli

Webster's Dictionary

(n.) A game resembling bagatelle, played on a special oblong board or table (Tivoli board / table), which has a curved upper end, a set of numbered compartments at the lower end, side alleys, and the surface studded with pins and sometimes furnished with numbered depressions or cups.

The Nuttall Encyclopedia

A town of Italy, known to the ancients as Tibur, beautifully situated on the Teverone, 18 m. E. of Rome; was much resorted to by the wealthy Roman citizens, and is celebrated by Horace; is full of interesting remains.