Never take artefacts at face value, especially in archaeology. Broken gaming pieces may have been misnamed. They are flat discs, about 1 to 4 inches in diameter, made of clay. The Romans lacked the refinements of Japanese toilet technology, but even they found that hard to reach itch most irritating.
The remedy was the use of ceramic disks, dipped in vinegar. Imagine the mechanics: a good, abrasive rub. What other artefacts may have been mistaken for something else?