Gambling with Etruscan dice: A tale of numbers and letters

The graphical and linguistic interpretation of the first six Etruscan numerals has long been confronted with the ambiguous assignment of the words huth and sa to either 4 or 6. Here, we show how the systematic combinatorial analysis of the numerals appearing on ancient southern Etrurian dice dated from the eighth to the third centuries BC, together with the careful comparison of the results with the only two existing dice carrying the alphabetical translations of the numerals conserved at the Biblioth\ue8que Nationale de France, Paris, finally allows unambiguous mathematical resolution of the linguistic riddle, allowing the firm attribution of the numeral 6 to the graphical value huth and 4 to sa. Combinatorial analysis of the numerals distribution on the six faces of the die shows that only two of the 15 possible numerical combinations were actually in use in southern Etruria, and that during the fifth century BC there was a marked shift from the typical (1\u20132, 3\u20134, 5\u20136) combination used in the early seventh- to fifth-century BC dice to the (1\u20136, 2\u20135, 3\u20134) combination used at later times and still largely adopted today. The largest body of archaeometric data on dice specimens from Etruria is presented, based on macroscopic examination, X-ray diffraction, DRIFT spectroscopy and density measurements