How dice play became fairer over 2,000 years

In Roman times, many dice were visibly lopsided, unlike today's perfect cubes. And in early medieval times, dice were often "unbalanced" in the arrangement of numbers, where the one appears opposite two, three opposite four, and five opposite six, said the study published in the journal Acta Archaeologica.

All that began to change around 1450 A.D., when dice makers and players seemingly figured out that form affected function, explained Jelmer Eerkens, Professor at the University of California, Davis, and the lead author of the study.

"A new worldview was emerging – the Renaissance. People like Galileo and Blaise Pascal were developing ideas about chance and probability, and we know from written records in some cases they were actually consulting with gamblers," he said.

"We think users of dice also adopted new ideas about fairness, and chance or probability in games," Eerkens said. Dice are not common finds in archaeological sites. They are typically found in garbage, domestic areas, or cemeteries, and frequently are recovered as lone objects in a site, Eerkens said. Many are not accurately dated.

After looking at hundreds of dice in dozens of museums and archaeological depots across the Netherlands,the researchers were able to assemble and analyse a set of 110 carefully dated, cube-shaped dice. The researchers found that dice made before 400 A.D., or in Roman times, were highly variable in shape, size, material and configuration of numbers.

The study also showed that dice were very rare between 400 A.D. and 1100 A.D., corresponding to the so called "Dark Ages".

When dice reappeared around 1100 A.D. they were predominantly in the "primes" configuration, where opposite numbers tally to prime numbers (one-two; three-four; five-six), a numbering style that was also popular in ancient Mesopotamia and Egypt.

Around 1450 A.D., the numbering system quickly changed to "sevens" where opposite sides add up to seven (six-one; five-two; three-four), the researchers found. Dice also became highly standardised in shape, which could partly be a byproduct of mass production.

"Standardising the attributes of a dice, like symmetry and the arrangement of numbers, may have been one method to decrease likelihood that an unscrupulous player had manipulated the dice to change the odds of a particular roll," Eerkens said.