Wagers were probably also involved, as it happens; one of the historical sets found at Ur included a number of small clay balls that have been theorised to have been used like casino chips.
Irving FInkel, the man who decoded the rules of the game, also thinks it may have been used as a form of fortune-telling.
(I've not played the game as I have my own physical Ur set that I made, but it looks authentic. Might try it out later.)