“The die is cast!” exclaimed Julius Caesar, as he crossed the Rubicon with his legions and sparked a civil war in his quest for absolute power. The metaphor was apt, because the Romans were big gamblers. And while ambitious leaders played with their own and their soldiers’ lives, the general populace preferred the less risky pastime of betting on dice throws at the local taberna.
But inquisitive modern minds have long been asking: why were most Roman dice so lopsided? Why did the builders of elaborately engineered aqueducts and monumental amphitheaters frequently fail to make perfectly cubic dice, producing game pieces that were either visibly squashed, elongated or just irregular?
Experts have often interpreted this design bug as a form of cheating, an attempt to manipulate the shape of the die to increase the probability of throwing certain numbers. But a new study suggests this was not the case. Instead, the janky qualities of these ancient dice were linked to the way Romans viewed the world and the role fate and the gods played in it, says the study published in June in the journal Archaeological and Anthropological Sciences.
The research was conducted by archaeologist Jelmer Eerkens, a professor of anthropology at University of California Davies, and Alex de Voogt, a professor at the department of economics and business of Drew University. The two studied a sample of 28 dice from the Roman period found in the Netherlands and then conducted an experiment asking unknowing students to reproduce similar game pieces, to understand whether the placement of the pips was influenced by a desire to cheat – more on that later.
Luck be a matrona tonight
Previous research had already shown that about 80 to 90 percent of Roman dice were visibly asymmetrical: that is, one of their sides differed in size by at least 5 percent from the others. By comparison, this only occurs in around half of later dice from the medieval and post-medieval ages, Eerkens and de Voogt note.
The visible irregularities were similarly present in 24 of the 28 Roman dice, which included artifacts made of clay, metal and bone, that the two archaeologists studied.
The choice of taking a sample from the Netherlands was made because in Roman times that region was split in two, with the border of the Roman Empire running along the River Rhine. This allowed the researchers to examine both Roman dice and pieces that were made by the Frisii, a local Germanic tribe that lived north of the border, to check for any cultural differences (there didn’t seem to be any).
There did seem to be a pattern to the irregular dice, in that many had the one and six placed on the larger opposing surfaces of the dice. Probability studies have shown that asymmetry affects the odds of a throw. There is a mathematical formula to calculate this, but suffice it to say that the bigger the difference between die sides, the greater the chances are of rolling a number placed on the larger surfaces.
If, on a perfect cube, there is a 1 in 6 chance of rolling any number, for the Roman game pieces the odds of getting a number on the larger side could be up to 1 in 2.4, depending on how asymmetrical the die was.
The fact that the asymmetry often seems to favor specific throws, namely a one or a six, could support the theory that the Romans (and their immediate neighbors) were not above intentionally cheating to get Lady Luck on their side.
After all, dice had an important part in Roman society. They were used in board games, similar to today’s backgammon, gambling and divination activities, Eerkens says. So there could be a lot on the line in a single roll of a die: from a life’s savings to a soothsayer’s reputation as an accurate predictor of the future.
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Guinea pigs in the class
To check whether the Romans intentionally created their dice to cheat, Eerkens and de Voogt left the study of ancient artifacts and designed a clever little experiment, enlisting what they call “naïve dicemakers.” They asked 23 psychology majors to place pips on reproductions of asymmetrical Roman dice.
The logic was that these students – who would not be gambling with the dice and were oblivious to the purpose of the experiment – had no incentive to purposely create unfair game pieces. If the students placed numbers randomly on the irregular surfaces then we could assume the Romans had a specific intent in favoring certain throws, whereas if these “naïve” modern dicemakers repeated the patterns found in the ancient artifacts then we would have to conclude that some other cultural or psychological mechanism was at work.
And lo and behold, most of the students placed the one and six on the largest surfaces of the asymmetrical dice, especially when they were told ahead of time to use the so-called “sevens” configuration. This means placing the numbers so that two opposing sides of the die always sum up to seven (one and six, two and five, etc.). This is the way numbers on most Roman and modern western dice are placed, the researchers note.
The fact that, like the ancient Romans, modern students involuntarily created dice that favor rolling a one or a six suggests that this is the result of a “production bias” rather than an attempt at gaining an advantage, Eerkens and de Voogt posit.
The most frequent explanation the students gave for their design choice was that it felt natural to start placing numbers from the largest side or to reserve the most space for the six, which requires the highest number of pips, the researchers report.
This suggests that the reason why Romans made such lopsided dice was quite simple and not sneaky at all: they just didn’t care. Dice were made in different sizes and materials, which could also often influence shape, and as long as the artifact could roll it didn’t matter if it wasn’t a perfect cube.
This also gives us precious insight into the way the Romans believed the world worked, the researchers say. Ancient texts show the Romans didn’t quite grasp the concept of probability and its mathematical rules. Instead, they believed that random events, like the throw of a die, were governed by fate and the favor of gods such as Fortuna, the personification of luck, and other supernatural beings, Eerkens explains. (This, by the way, is not too different from the superstitions of many modern-day casino-goers).
“Knowing that, it makes sense that Romans probably did not think that die shape mattered, because even with a non-cubic die all sides can still be thrown,” he says. “Today we would say that, yes, each side can be thrown but with unequal probabilities - however, most people in Roman times probably would not understand that way of thinking.”
Still, there were some ancient authors, like Cicero, who scoffed at the idea that gods controlled every aspect of human life. The first-century B.C.E. philosopher and statesman even used dice rolling as an example to express some rudimentary understanding of probability and question whether throws were really determined by divine beings, Eerkens notes. But Cicero was an intellectual, writing about philosophy in scholarly treaties that most Romans could not read or would have been unaware of, the archaeologist adds.
It is no coincidence that during the Middle Ages and the Early Modern era irregular dice became rarer as probability theory began to reach a more mainstream audience, particularly through the work of 17th century French mathematician Blaise Pascal, Eerkens says.
Back in Roman times, it is still possible that some experienced gamblers realized that die shape somehow affected throws, he acknowledges. They certainly could have taken advantage of this to manipulate their soothsaying or gambling activities, but this was most likely not common knowledge, Eerkens adds.
Understanding why Roman dice were so frequently asymmetrical is not just about figuring out ancient gambling methods. Artifacts like dice are common throughout history, from ancient Egypt and Mesopotamia until today, and looking at the subtle changes in these seemingly unchanging objects can tell us a lot about past civilizations, Eerkens tells Haaretz.
“We can connect to these ancient cultures because we still use dice and recognize them,” he says. ”But we can also see how thinking and understanding about the world has changed through little hints from these ancient objects.”