One well-attested Roman board game is "Twelve Lines" (duodecim scripta), an early form or analogue of backgammon in which each player tried to advance his or her 15 pieces to the other side of a board with 36 squares (sometimes marked by short sayings or letters). Play was determined by two or three dice, which were rolled in a shaker known as a "tower."

A picture of a board may be found here.

This site outlines the rules of "Twelve Lines." I can't vouch for its accuracy, but the author seems to have done his homework and cites reputable sources.

Another popular Roman game was "the Game of Robbers" (ludus latrunculorum), a game broadly similar to checkers played on a large (usually 64 or 81 square) board. Each player seems to have controlled 20 stones, which they maneuvered to take their opponent's stones by trapping them between two of their own.

This site outlines the rules of "the Game of Robbers." As before, I can't vouch for its accuracy, but the author seems to have done his homework and cites reputable sources.

When playing dice, the Romans often used 6-sided dice of the familiar type, though 4-sided knuckle bones and other varieties of dice were sometimes substituted. Typically, 3 dice were rolled in a cup, and the highest throw (or sum of points over the course of a game) won. A triple 6 was a "Venus" throw; a triple 1 was a "dog" throw. Money was often staked on the outcome. In his Life of Augustus, for example, Suetonius quotes a letter of Augustus:

"I dined, dear Tiberius, with the same company; we had besides as guests Vinicius and the elder Silius. We gambled like old men during the meal both yesterday and to‑day; for when the dice were thrown, whoever turned up the dog or the six, put a denarius in the pool for each one of the dice, and the whole was taken by anyone who threw the Venus." (71.2)

Alright, thanks