Astragali: some observations on the anatomy of different mammalian species and their performance as 4-sided dice when thrown onto different surfaces in the form of either the original bone or 3-D printed models of them

Duggan, Eddie, Bell, Duncan and Taylor, Danielle (2015) Astragali: some observations on the anatomy of different mammalian species and their performance as 4-sided dice when thrown onto different surfaces in the form of either the original bone or 3-D printed models of them. In: XVIII Annual International Board Game Studies Colloquium, 15–18 April 2015, Swiss Museum of Games, La Tour-de-Peilz, Switzerland.

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Abstract

Introduction
The astragulus, or talus, is one of the mammalian ankle bones. It has been used both in the ancient world and classical times as a 4-sided dice or randomisation mechanism for games and divination. The usual animal species from which the bones have been taken are those of the sheep, goat or deer i.e. even-toed ungulate artiodactyls. The Ancients also made anatomically correct astraguli out of carved ivory, precious metals and stones as well as lead, bronze etc. Reviewing the literature the evidence on which claims were made as to the relative chances of each of the astragal’s four surfaces appearing upper most when thrown were poor and the claims made were often on the basis of as little as 100 throws.

Materials, Methods
We dissected out 20 astraguli from mutton hocks and clean and dried them. These were X-ray CT scanned as were 5 fossil deer astraguli and those of several other mammalian species. The CT scan files were then used to make STL files from which life-sized 3-D model astraguli were produced in PLA using an inexpensive 3-D printer costind under £500 (Xiamen Datian Electronics, China admin@ediecs.com ). The sheep bone astraguli and both hollow and solid 3-D printed models were then tested for their performance as dice in series of at least 500 throws onto either a wooden table and/or a thick carpet.

Results and discussion
The 3-D printed model astragals behaved very similarly to the bone originals. We suggest such 3-D replicas can be used with confidence.The results show that the chances suggested by David(1962) of throwing either of the two wide surfaces (4/10) and either of the narrow surfaces (1/10) are broadly correct only when compared with our own results for astraguli thrown onto a carpet (n=2000). The results (n=3000) when the astraguli were thrown onto a smooth wooden table showed small but statistically significant difference from the throws onto the carpet surface. The two narrow sides in particular coming up significantly less frequently (p<0.001) on the wooden surface than the carpet surface.

We are currently designing a computer programme to allow us to compare minor differences in astragal dimensions and the coefficient of friction of the surface onto which they are thrown because much larger numbers of throws will be require to confidently state any differences observed are statistically significan

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: games, dice, 3D printing
Subjects: D History General and Old World > D History (General) > D051 Ancient History
D History General and Old World > DE The Mediterranean Region. The Greco-Roman World
G Geography. Anthropology. Recreation > GT Manners and customs
G Geography. Anthropology. Recreation > GV Recreation Leisure
H Social Sciences > HA Statistics
Depositing User: Eddie Duggan
Date Deposited: 06 Feb 2020 09:55
Last Modified: 06 Feb 2020 09:55
URI: http://oars.uos.ac.uk/id/eprint/1156

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