Dice Games: Not always played with 6-sided cubes

• Yahtzee

When most people think of dice, they generally picture a six-sided white cube sporting one to six black dots on each side. But this has not always been the predominant dice template.

Ancient dice were often made of stick, shell or seed and most were two-sided, often with one flat side and one rounded side, like a shelled peanut. Sometimes the two sides were decorated with paint or carvings to further differentiate them. Two-sided dice were widely used by ancient peoples across the globe, from the Aztecs to Native Polynesians. Some modern cultures, like the Navajo Nation, still use them for traditional games.

Astragals, also known as knucklebones, are fascinating objects in their own right. As their colloquial name suggests, knucklebones are literal bones taken from the back ankle of a sheep, goat, deer, horse or other large, hoofed mammal. They have been used as four-sided dice since at least the fifth century B.C.E. by numerous civilizations, including Indigenous Americans, ancient Greeks and ancient Egyptians, who prized them so highly that they were sometimes buried with their favorite astragals. In Roman antiquity, each of the four sides was given a name corresponding to its shape: the belly, the hole, the ear and the vulture.

Tossing knucklebones is not a truly random process. Two of the sides — the belly and the hole — are much broader than the other two and are therefore more likely to come up. Ancient Romans assigned points accordingly. The broad sides were worth 3 and 4 points, while the ear and the vulture were worth 6 and 1 points, respectively. "They were aware of this different probability," says Schaedler, "So, good luck comes very rarely, but bad luck comes also very rarely."

"Dice changed over time from natural objects, such as shells and sticks or astragals, to manufactured objects," says Anne-Elizabeth Dunn-Vaturi, a researcher at the Metropolitan Museum of Art.

Today, plastic or metal versions of knucklebones are popular in some parts of Europe. But none of these dice resemble anything you'd find in a Vegas casino. So the question is: Where and why did dice become cubes?

Dice and their forerunners are the oldest gaming implements known to man. Sophocles reported that dice were invented by the legendary Greek Palamedes during the siege of Troy, whereas Herodotus maintained that they were invented by the Lydians in the days of King Atys. Both “inventions” have been discredited by numerous archaeological finds demonstrating that dice were used in many earlier societies.

The precursors of dice were magical devices that primitive people used for the casting of lots to divine the future. The probable immediate forerunners of dice were knucklebones (astragals: the anklebones of sheep, buffalo, or other animals), sometimes with markings on the four faces. Such objects are still used in some parts of the world.

In later Greek and Roman times, most dice were made of bone and ivory; others were of bronze, agate, rock crystal, onyx, jet, alabaster, marble, amber, porcelain, and other materials. Cubical dice with markings practically equivalent to those of modern dice have been found in Chinese excavations from 600 BCE and in Egyptian tombs dating from 2000 BCE. The first written records of dice are found in the ancient Sanskrit epic the Mahabharata, composed in India more than 2,000 years ago. Pyramidal dice (with four sides) are as old as cubical ones; such dice were found with the so-called Royal Game of Ur, one of the oldest complete board games ever discovered, dating back to Sumer in the 3rd millennium BCE. Another variation of dice is teetotums (a type of spinning top).

It was not until the 16th century that dice games were subjected to mathematical analysis—by Italians Girolamo Cardano and Galileo, among others—and the concepts of randomness and probability were conceived (see probability and statistics). Until then the prevalent attitude had been that dice and similar objects fell the way they did because of the indirect action of gods or supernatural forces.

• Yahtzee