Six-sided dice from Roman times are common at archaeological sites throughout Europe. While the shape of some dice approximates true cubes, many are visibly non-cubic, i.e. asymmetrical or slanted, and favor certain rolls, especially the numbers 1 and 6.
These objects appeal to us today because in Western culture six-sided dice are highly symmetrical, and because we expect the die to roll cleanly, in which each side has the same probability of being thrown. Three main explanations have been offered to explain the presence of highly asymmetric forms in Roman times.
The first explanation assumes that the asymmetry of the dice was intentional and had a function in Roman society. One interpretation is that the dice were purposely asymmetrical in shape so as to favor particular throws that were important in divinatory practices or in games of chance. In a sense, these dice could be considered cheatersas they helped the owner/user better predict casts, even though all casts were still possible.
A second explanation suggests that the asymmetry was still intentional, but that cultural transmission factors mainly explain the presence of asymmetric forms. For example, some suggest that the highly elongated cuboid or diamond-shaped dice of pre-Roman Iron Age cultures may have influenced dice-making from the Roman period in southern Britain, and dice have also been attested Pre-Roman asymmetrical patterns for Etruria. In this sense, asymmetrical dice were consciously part of the Roman cultural repertoire, but functioned to provoke a feeling of nostalgia or cultural affiliation with older, non-Roman cultures.
The third explanation suggests that the production of the asymmetry of the Roman dice was largely unintentional. Asymmetrical dice are considered by some to be unintended by-products of the types of raw materials used to make the dice. The long bone of animals, in particular, was a popular medium for dice, and could have placed restrictions on the size and shape of the die. Although plausible, this argument does not explain why the longer sides were not tapered to match the shorter sides, nor why dice made from other materials, such as clay and metal, with no obvious shape limitations, also They are usually asymmetric. On the other hand, some interpret the asymmetrical dice as the result of the lack of skill of the dice makers, who could not, or did not care, to carefully control the morphology of the object. Both interpretations suggest that users did not view conformance to a cubic shape as instrumental to the die’s function.
According to a study by Jelmer W. Eerkens of the University of California Davis and Alex de Voogt of Drew University, it is not clear if this asymmetry was intentional and corresponds to dice used in specific games or activities, if it is dices cheaters or if they are simply part of the continuous variation in the shape and configuration of the dice.
To explore this question, the researchers examined the shape distribution of 28 well-dated Roman-era dice from the present-day Netherlands. The results show that the asymmetry of the Roman die varies continuously from the true cube to the parallelepiped, where the long side is more than 50% longer than the short side.
They then carried out replication experiments to examine how manufacturers configured the dots on the faces in a variety of ways. The results show a production bias, in which manufacturers place the 6 on the larger face of the die, not to favor certain rolls, but due to space limitations and/or the order in which they place the dots.
In general, researchers consider asymmetrical Roman dice as part of a single but highly variable category of artifacts, not as distinct types. This extreme variation was acceptable because the manufacturers and users understood the results of the rolls as a product of fate, rather than chance or probability.
Dice should not be considered “chance devices” in a mathematical sense, as we understand them today. Instead, we should view Roman-era dice in a cultural sense as representing a belief in fate, and a material connection to the gods who controlled that fate. Since mathematics and probability theory are unable to predict the outcome of an individual toss, such a belief would not necessarily be altered or challenged by a die that was closer to, or even visually indistinguishable from, a true cube. Our findings are valid on both sides of the Roman border, beyond the borders of cultural groups, indicating that ideas about dice design and function were likely similar among Germanic, Etruscan, and Roman societies.
Conformity to an actual symmetrical cube was not perceived as essential to the function of the die, and asymmetrical shapes were simply tolerated as part of the acceptable range of shape variation.
Eerkens, J. W., de Voogt, A.. Why are Roman-period dice asymmetrical? An experimental and quantitative approach. Archaeol Anthropol Sci 14, 134 (2022). doi.org/10.1007/s12520-022-01599-y