Throwin’ Bones: Astragali – Ancient Games and Probability

astragalus 3
Goat Astragali. November 3rd, 2017.

Probability has been a part of human consciousness since ancient times. Dice inspired Pascal in creating a formalized theory of probability. How did dice come about?

Modern dice are actually derived from the talus or knucklebone from a wide variety of animals, known as the astragalus. Astragali were most commonly used for gambling. Fate was often attributed to spiritual or supernatural forces, leading to the use of astragali in divination rituals and burial rites (Gilmour, 1997). It has been suggested that astragali may have been used as a primitive form of currency (Holmgren, 2004a).

Astragali used for these purposes have been discovered from arge deer, fallow deer, roe deer, whitetail deer, cattle, goats, pigs, ibex (a type of wild goat) and chamoix (a goat-antelope) (Poplin, 1984, as cited by Gilmour). Imitiation astragali have been discovered made of bronze, glass, silver, ivory, and limestone (Poplin, 1984). Prevalent modifications included cut marks, polishing, creating holes, which were filled with lead, copper, iron, or bronze (Gilmour). Astragali have been found across many cultures, throughout the Arabian Peninsula, Greece, Rome, Egypt, Iraq, Iran, Israel, Jordan, Lebanon, Palestinian territories, Syria, Turkey, Cyprus, Bulgaria, Spain, and even Mongolia (Gilmour, 1997, Freeman, 1989). Astragali have also been found in North America and South America, used by many Native American tribes (Koerper, 2004). The earliest known astragali are originally from 2000-1500 B.C (Gilmour).

Scattering the astragali could potentially result in one of six sides facing up. However, unlike modern cubic dice, the sides were not equally likely. Landing vertically was quite rare since the edges are rounded, and is nearly impossible on dirt or uneven ground. The typical roll might include one of four sides, colloquially known in some cultures as the camel, horse, goat, or sheep. The wide side, a sheep or goat, is about three times as likely as the narrow side, the donkey or camel, which was considered a better roll (Koerper). Usually dice were rolled in multiples, and achieving the same result with several astragali was considered lucky. A roll of four astralagi resulting in four different sides was also lucky, a probability of 0.0384 to be exact (Freeman, 1989). Another game originating in modernday Turkey and also present in Mongolia involved throwing a heavier astragalus, such as a cow talus bone or one that has been made heaver at lead, at others, in an attempt to flip the other bones (Holmgren, 2004). Eventually, astragali were grinded and polished on each side which increased the possibility of a more randomized result (Foster, 1986, as cited by Gilmour). Games and a desire to beat fate led to the widespread use of astragali, and over time, our current understanding of probability.

 

References

Freeman, G. (1989). The Tactics of Liar Dice. Journal of the Royal Statistical Society. Series C (Applied Statistics), 38(3), 507-516. doi:10.2307/2347737

Gilmour, G. H. (1997). The Nature and Function of Astragalus Bones from Archaeological Contexts in the Levant and Eastern Mediterranean. Oxford Journal of Archaeology, 16(2), 167-175.

Holmgren, R. (2004). Money on the hoof: The astragalus bone – religion, gaming and primitive money

Koerper, H. C. (2004). Additional notes on Astragalus bones. Pacific Coast Archaeological Society Quarterly, 40(2)

Poplin, F. (1984). Contribution, oste´o-arche´ologique a`la conaissance des astragales de L’Antre corycien. In L’Antre corycien, II. Bulletin de Corresponance Helle´nique, Supplement IX, 381–393.