Older dice are usually smaller than modern ones. Modern dice are about 3/4" and dice from the 1930s and 1940s are more likely to be 5/8" or less.

Most really old dice are cellulose nitrate and usually will have at least a hint of crystalization on the corners.

Modern dice, from the 1950s and later, are cellulose acetate. Cellulose acetate won't crystalize, and instead of cracking it shrinks or melts and gives off a vinegar-like odor.