Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Apeiron

A Journal for Ancient Philosophy and Science

Ed. by Wildberg, Christian / Morison, Benjamin

Print + Online
See all formats and pricing
More options …
Ahead of print

Issues

Why Mathematical Probability Failed to Emerge from Ancient Gambling

Stephen Kidd
Published Online: 2019-01-26 | DOI: https://doi.org/10.1515/apeiron-2018-0045

Abstract

The emergence of mathematical probability has something to do with dice games: all the early discussions (Cardano, Galileo, Pascal) suggest as much. Although this has long been recognized, the problem is that gambling at dice has been a popular pastime since antiquity. Why, then, did gamblers wait until the sixteenth century ce to calculate the math of dicing? Many theories have been offerred, but there may be a simple solution: early-modern gamblers played different sorts of dice games than in antiquity. While ancients diced at communal risk, early-moderns diced at individualized risk. These individual wager-games, for example, the game “hazard”, incentivized solving questions like “how likely is it to roll a triple-six?”. Before the early modern period there was no gambling game to which working out mathematical probability would have brought an advantage.

Keywords: probability; ancient gambling; mathematical probability; ancient combinatorics

References

  • Basulto, J, J.A. Camùnez, and F.J. Ortega. 2006. “Azar Game in the Book of the Dice of Alfonso X the Learned. Its Relation with the Hazard Games of Montmort, Cotton, Hoyle, De Moivre and Jacob Bernoulli.” Mathématiques et sciences humaines 174 (2): 5–24.Google Scholar

  • Bellhouse, D.R. 2000. “De Vetula: A Medieval Manuscript Containing Probability Calculations.” International Statistical Review 68 (2): 123–36.CrossrefGoogle Scholar

  • Bellhouse, D.R. 2005. “Decoding Cardano’s Liber De Ludo Aleae.” Historia Mathematica 32: 180–202.CrossrefGoogle Scholar

  • Brunschvicg, L., P. Boutroux, and F. Gazier. 1914–25. Oeuvres de Blaise Pascal. Paris: Hachette.Google Scholar

  • Canettieri, P. 1996. Alfonso X el Sabio: Il libro dei giochi. Bologna: Cosmopoli.Google Scholar

  • Corominas, J., and J.A. Pascual. 1980–91. Diccionario crítico etimológico castellano e hispánico, vol. 6. Madrid: Gredos.Google Scholar

  • Cotton, C. 1674. The compleat gamester, or, Instructions how to play at billiards, trucks, bowls, and chess together with all manner of usual and most gentile games either on cards or dice. London: Brome.Google Scholar

  • Daston, L. 1988. Classical Probability in the Enlightenment. Princeton: Princeton University Press.Google Scholar

  • David, F.N. 1955. “Dicing and Gaming (A Note on the History of Probability).” Biometrika 42: 1–15.CrossrefGoogle Scholar

  • David, F.N. 1962. Games, Gods and Gambling. London: Griffin.Google Scholar

  • Eerkens, J.W. and A. de Voogt. 2018. “The Evolution of Cubic Dice: From the Roman Through Post-Medieval Period in the Netherlands.” Acta Archaeologica 88 (1): 163–73.Google Scholar

  • Eichmann, R., and J. DuVal. 1984. The French Fabliau B.N. Ms 837. Vol. 1. New York: Garland.Google Scholar

  • Ekert, A. 2008. “Complex and Unpredictable Cardano” submitted to arxiv.org on 6/3/08

  • Falk, H. 1986. Bruderschaft und Würfelspiel. Freiburg: Falk.Google Scholar

  • Finkel, I.L. 2007. “On the Rules for the Royal Game of Ur.” In Ancient Board Games in Perspective, I.L. Finkel (edited by), 16–32. London: The British Museum Press.Google Scholar

  • Fowler, D.H. 1999. The Mathematics of Plato’s Academy. A New Reconstruction, 2nd edn. Oxford: Clarendon Press.Google Scholar

  • Franklin, J. 2015[2001]. The Science of Conjecture: Evidence and Probability before Pascal. Baltimore: Johns Hopkins University Press.Google Scholar

  • Gerhard, K.I. 1875–90. Leibniz: Philosophische Schriften, Vol. 7. Berlin: Gerhard.Google Scholar

  • Gould, S.H. trans. 2016[1953]. Girolamo Cardano: The Book on Games of Chance. New York: Dover.Google Scholar

  • Graf, F. 2005. “Rolling the Dice for an Answer.” In Mantikê: Studies in Ancient Divination, S.I. Johnston, and P.T. Struck (edited by), 51–97. Leiden: Brill.Google Scholar

  • Hacking, I. 2007[1975]. The Emergence of Probability, 2nd edn. Cambridge: Cambridge University Press.Google Scholar

  • Handyside, P. 2015. The Old French William of Tyre. Leiden: Brill.Google Scholar

  • Harris, J.R. 1901. The Annotators of the Codex Bezae, with Some Notes on the Sortes Sanctorum. London: Clay.Google Scholar

  • Hoffmann, D. 1973. The Playing Card, an Illustrated History. Greenwich: New York Graphic Society.Google Scholar

  • Hollis, A.S. 2007. Fragments of Roman Poetry c. 60 B.C.-A.D. 20 Oxford: Oxford University Press.Google Scholar

  • Hoyle, E. 1754. An essay towards making the doctrine of chances easy to those who understand vulgar arithmetick only. London: Jolliff.Google Scholar

  • Husband, Timothy B. 2015. The World in Play: Luxury Cards 1430–1540. New York: The Metropolitan Museum of Art.Google Scholar

  • Ineichen, R. 1996. Würfel und Wahrscheinlichkeit. Heidelberg: Spektrum Akademischer Verlag.Google Scholar

  • Johnston, R.C., and D.D.R. Owen. 1957. Fabliaux. Oxford: Blackwell.Google Scholar

  • Katz, V.J. 2013. “Jewish Combinatorics.” In Combinatorics: Ancient & Modern, R. Wilson, and J.J. Watkins (edited by), 109–21. Oxford: Oxford University Press.Google Scholar

  • Kendall, M.G. 1956. “The Beginnings of a Probability Calculus.” Biometrika 43: 1–14.CrossrefGoogle Scholar

  • Kendall, M.G. 1957. “Studies in the History of Probability and Statistics. V. A Note on Playing Cards.” Biometrika 44 (1/2): 260–62.CrossrefGoogle Scholar

  • Kidd, S. 2017a. “How to Gamble in Greek: The Meaning of Kubeia.” Journal of Hellenic Studies 137: 119–34.CrossrefGoogle Scholar

  • Kidd, S. 2017b. “Greek Dicing, Astragaloi, and the ‘Euripides’ Throw.” Journal of Hellenic Studies 137: 112–18.CrossrefGoogle Scholar

  • Knuth, D.E. 2013. “Two Thousand Years of Combinatorics.” In Combinatorics: Ancient & Modern, R. Wilson, and J.J. Watkins (edited by), 3–37. Oxford: Oxford University Press.Google Scholar

  • Kopp, Peter F. 1973. “Die frühesten Spielkarten in der Schweiz.” Zeitschrift für Schweizerische Archäologie und Kunstgeschichte 30 (3–4): 130–45.Google Scholar

  • Kusuba, T., and K. Plofker. 2013. “Indian Combinatorics.” In Combinatorics: Ancient & Modern, R. Wilson, and J.J. Watkins (edited by), 41–62. Oxford: Oxford University Press.Google Scholar

  • Lamer, H. 1927. “Lusoria Tabula.” RE 13: 1900–2029.Google Scholar

  • Lanciani, R. 1892. “Gambling and Cheating in Ancient Rome.” North American Review 155 (428): 97–105.Google Scholar

  • Lloyd, E.K. 2013. “Enumeration (18–20th Centuries).” In Combinatorics: Ancient & Modern, R. Wilson, and J.J. Watkins (edited by), 285–307. Oxford: Oxford University Press.Google Scholar

  • Lo, A. 2000. “The Game of Leaves: An Inquiry into the Origin of Chinese Playing Cards.” Bulletin of the School of Oriental and African Studies, University of London 63 (3): 389–406.CrossrefGoogle Scholar

  • Lüders, H. 1907. “Das Würfelspiel im alten Indien.” Abhandlungen der Göttinger Gesellschaft der Wissenschaften: 1–75.Google Scholar

  • Martin Hernandez, R. 2014. “Two More Verses for the Homeromanteion (PGMVII).” ZPE 190: 97–98.Google Scholar

  • Mayer, L.A. 1973[1939]. In Mamluk Playing Cards, R. Ettinghausen, and O. Kurz (eds.). Leiden: Brill.Google Scholar

  • Mikhail, A. 2006. “Gambling.” In Medieval Islamic Civilization: An Encyclopedia. A-K, Vol. 1, J.W. Meri, and J.L. Bacharach (edited by), 275–76. New York: Routledge.Google Scholar

  • Montero Cartelle, E. 2013. Les Sortes sanctorum: Étude, édition critique et traduction. Paris: Classiques Garnier.Google Scholar

  • Montmort, A. de. 1713. Essay d’analyse sur les jeux de hasard. Paris: Quillau.Google Scholar

  • Morgan, M.G. 1975. “Three non-Roman Blood Sports.” CQ 25 (1): 117–22.CrossrefGoogle Scholar

  • Netz, R. 2009. Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic. Cambridge: Cambridge University Press.Google Scholar

  • Nollé, J. 2007. Kleinasiatische Losorakel: Astragal- und Alphabetschremologien der hochkaiserzeitlichen Orakelrenaissance. Munich: C.H. Beck.Google Scholar

  • Noomen, W., and N. van Den Boogard. 1983. Nouveau Recueil Complet Des Fabliaux (NRCF) Vol. 1. Assen: Van Gorcum.Google Scholar

  • Ore, Ø. 2017[1953]. Cardano: The Gambling Scholar. Princeton: Princeton University Press.Google Scholar

  • Purcell, N. 1995. “Literate Games: Roman Urban Society and the Game of Alea.” Past & Present 147: 3–37.CrossrefGoogle Scholar

  • Purcell, N. 2007. “Inscribed Imperial Roman Gaming-Boards.” In Ancient Board Games in Perspective, I.L. Finkel (edited by), 90–97. London: The British Museum Press.Google Scholar

  • Rabinovitch, N.L. 1973. Probability and Statistical Inference in Ancient and Medieval Jewish Literature. Toronto: University of Toronto Press.Google Scholar

  • Rosenthal, F. 1975. Gambling in Islam. Leiden: Brill.Google Scholar

  • Schädler, U. 2009. Das Buch der Spiele. Vienna and Berlin: LIT Verlag.Google Scholar

  • Schädler, U. 2012. Religions in Play: Games, Rituals, and Virtual Worlds. Zürich: Pano-Verlag: 23–47.Google Scholar

  • Schwartz, D.G. 2013[2006]. Roll the Bones: The History of Gambling, 2nd edn. Las Vegas: Casino.Google Scholar

  • Schwartz, J. 1998. “Gambling in Ancient Jewish Society and in the Graeco-Roman World.” In Jews in a Graeco-Roman World, M. Goodman (edited by), 145–66. Oxford: Oxford University Press.Google Scholar

  • Semrau, F. 1910. Würfel und Würfelspiel im alten Frankreich. Halle: Niemeyer.Google Scholar

  • Tait, W.J. 2007. “Were There Gamesters in Pharaonic Egypt.” In Ancient Board Games in Perspective, I.L. Finkel (edited by), 46–53. London: The British Museum Press.Google Scholar

  • Tamborini, M. 2006. Girolamo Cardano: Liber de Ludo Aleae. Milan: FrancoAngeli.Google Scholar

  • van Buitenen, J.A.B. (trans. and ed.) 1975. Mahabharata Book 2. The Book of the Assembly Hall (Sabhāparvan). Book 3. The Book of the Forest (Āranyakaparvan). Chicago: University of Chicago Press.Google Scholar

  • Whitmarsh, T. 2015. Battling the Gods: Atheism in the Ancient World. New York: Knopf.Google Scholar

  • Wilkinson, K.W. 2015. “A Greek Ancestor of the Sortes Sanctorum.” ZPE 196: 94–102.Google Scholar

About the article

Published Online: 2019-01-26


Citation Information: Apeiron, ISSN (Online) 2156-7093, ISSN (Print) 0003-6390, DOI: https://doi.org/10.1515/apeiron-2018-0045.

Export Citation

© 2019 Walter de Gruyter Inc., Boston/Berlin.Get Permission

Comments (0)

Please log in or register to comment.
Log in