Definition:
The ludi were public Roman games started before 220 B.C. as annual communal games to give thanks to the gods. During the Republic, the entertainment provided at the games was chariot races (ludi circenses) or theatrical performances (ludi scaenici). Tradition says that Tarquin the Elder started the ludi circenses and that he made the plans for the Circus Maximus where they were held. The games were known as ludi Romani or the great games from 366. Three years later the first ludi scaenici were introduced.
During the Roman Empire, the ludi included gladiatorial combats or beast hunts.
Source: Sport and Spectacle in the Ancient World, by Donald Kyle; p.257.
Examples:
Examples of the Roman games are the Ludi Romani, Ludi Megalenses, Ludi Saeculares, Ludi Apollinares, Ludi Capitolini, Ludi Florales, Ludi Plebeii, Ludi Victoriae Caesaris, Ludi Taurei quinquennales, and Ludi Victoriae Sullae.
Chariot races and theatrical events, part of the public entertainment of the ludi were held in the circus.