Statistical Science

Marie-France Bru and Bernard Bru on Dice Games and Contracts

Glenn Shafer

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Abstract

This note introduces Marie-France and Bernard Bru’s forthcoming book on the history of probability, especially its chapter on dice games, translated in this issue of Statistical Science, and its commentary on the history of fair price in the settlement of contracts.

As the Brus remind us, the traditions of counting chances in dice games and estimating fair price came together in the correspondence between Pascal and Fermat in 1654. To solve the problem of dividing the stakes in a prematurely halted game, Fermat used combinatorial principles that had been used for centuries to analyze dice games, while Pascal used principles that had been proposed in previous centuries by students of commercial arithmetic.

Article information

Source
Statist. Sci., Volume 33, Number 2 (2018), 277-284.

Dates
First available in Project Euclid: 3 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.ss/1525313146

Digital Object Identifier
doi:10.1214/17-STS639

Mathematical Reviews number (MathSciNet)
MR3797714

Zentralblatt MATH identifier
1397.62012

Keywords
Dice games emergence of probability De vetula expectation

Citation

Shafer, Glenn. Marie-France Bru and Bernard Bru on Dice Games and Contracts. Statist. Sci. 33 (2018), no. 2, 277--284. doi:10.1214/17-STS639. https://projecteuclid.org/euclid.ss/1525313146


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References

  • [1] Al-Kadi, I. A. Origins of cryptology: The Arab contributions. Cryptologia 16 97–126.
  • [2] Al Khalili, J. (2011). The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance. Penguin, New York.
  • [3] Al Kindi (2004). Al-Kindi’s Treatise on Cyptanalysis. KFCRIS & KACST, Riyadh. Book One of the Series on Arabic Origins of Cryptology.
  • [4] Bellhouse, D. R. (2000). De vetula: A medieval manuscript containing probability calculations. Int. Stat. Rev. 68 123–136.
  • [5] Bernoulli, J. (1713). Ars Conjectandi, Opus Posthumum. Accedit Tractatus de Seriebus Infinitis et Epistola Gallice Scripta de Ludo Pilae Reticularis. Impensis Thurnisiorum fratrum, Basel. French translation by Jean Peyroux, Paris, A. Blanchard, 1998. English translation with notes by Edith Dudley Sylla, Johns Hopkins University Press, Baltimore, MD, 2006.
  • [6] Bernoulli, J. (1969–1999). Die Werke Von Jakob Bernoulli. Birkhäuser, Basel. 6 volumes.
  • [7] Bru, B., Bru, M.-F. and Bienaymé, O. (1997). La statistique critiquée par le calcul des probabilités: Deux manuscrits inédits d’Irenée Jules Bienaymé. Rev. Histoire Math. 3 137–239.
  • [8] Bru, B., Bru, M.-F. and Chung, K. L. (1999). Borel et la martingale de Saint-Pétersbourg. Rev. Histoire Math. 5 181–247. Translated into English as “Borel and the Saint-Petersburg paradox” in Electronic Journal for History of Probability and Statistics, 5(1), 2009.
  • [9] Cardano, G. (1539). Practica arithmeticæ, & mensurandi singularis. Castellioneus, Milan.
  • [10] Coumet, E. (1965). Le problème des partis avant Pascal. Arch. Int. Hist. Sci. 18 245–272. Reprinted on pages 73–95 of Œuvres d’Ernest Coumet, volume 1, Presses universitaire de Franche-Comté, 2016.
  • [11] David, F. N. (1962). Games, Gods, and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era. Griffin, London.
  • [12] Edwards, A. W. F. (2002). Pascal’s Arithmetic Triangle: The Story of a Mathematical Idea, 2nd ed.
  • [13] Franci, R. (2002). Una soluzione esatta del problema delle parti in un manoscritto della prima metà del Quattrocento. Boll. Stor. Sci. Mat. XXII 253–266.
  • [14] Franklin, J. (2001). The Science of Conjecture: Evidence and Probability Before Pascal. Johns Hopkins Univ. Press, Baltimore, MD. Second edition 2015.
  • [15] Hacking, I. (1975). The Emergence of Probability. Cambridge Univ. Press, New York. Second edition 2006.
  • [16] Hald, A. (1990). A History of Probability and Statistics and Their Applications Before 1750. Wiley, New York.
  • [17] Høyrup, J. (2014). Fibonacci—Protagonist or witness? Who taught Catholic Christian Europe about Mediterranean commercial arithmetic? J. Transcult. Mediev. Stud. 1 219–247.
  • [18] Huygens, C. (1657). De Ratiociniis in Ludo Aleae. In Exercitationum Mathematicarum, Liber V (F. V. Schooten, ed.) 511–534. Elsevier, Leiden. The Dutch original, written in 1656, was published in Amsterdam in 1659 and reprinted along with a translation into French in Huygens’s Œuvres, volume 14, pages 1–91.
  • [19] Kendall, M. G. (1956). Studies in the history of probability and statistics: II. The beginnings of a probability calculus. Biometrika 43 1–14. Reprinted in Pearson and Kendall, Studies in the History of Statistics and Probability I: 19–34.
  • [20] Klopsch, P. (1967). Pseudo-Ovidius De Vetula: Untersuchung und Text. Brill, Leiden.
  • [21] Lacroix, S. F. (1816). Traité élémentaire du Calcul des Probabilités. Courcier, Paris. Second edition 1822.
  • [22] Laplace, P. S. (1814). Essai Philosophique sur les Probabilités, 1st ed. Courcier, Paris. The fifth and definitive edition appeared in 1825 and was reprinted in 1986 (Christian Bourgois, Paris) with a commentary by Bernard Bru. Multiple English translations have appeared.
  • [23] Lewis, D. L. (2008). God’s Crucible: Islam and the Making of Europe, 5701215. Norton, New York.
  • [24] Lubbock, J. W. and Drinkwater-Bethune, J. E. (1830). On Probability. Baldwin & Craddock, London.
  • [25] Meusnier, N. (2007). Le problème des partis bouge… de plus en plus. Electron. J. Hist. Probab. Stat. 3.
  • [26] Pacioli, L. (1494). Summa de arithmetica, geometria, proportioni et proportionalità. Paganino de Paganini, Venice.
  • [27] Pascal, B. (1665). Traité du Triangle Artimétique et Traités Connexes. Desprez, Paris.
  • [28] Robathan, D. M. (1968). The Pseudo-Ovidian De Vetula: Text, Introduction, and Notes. Hakkert, Amsterdam.
  • [29] Saliba, G. (2007). Islamic Science and the Making of the European Renaissance. MIT Press, Cambridge, MA.
  • [30] Schneider, I. (1985). Luca Pacioli und das Teilungsproblem: Hintergrund und Lösungsversuch. In Mathemata (M. Folkerts and U. Lindgren, eds.). Steiner, Wiesbaden and Stuttgart.
  • [31] Schneider, I., ed. (1988). Die Entwicklung der Wahrscheinlichkeitstheorie Von Den Anfängen Bis 1933: Einführungen und Texte. Wissenschaftliche Buchgesellschaft, Darmstadt.
  • [32] Schneider, I. (1988). The market place and games of chance in the fifteenth and sixteenth centuries. In Mathematics from Manuscript to Print, 13001600 (C. Hay, ed.) 220–235. Oxford.
  • [33] Shafer, G. and Vovk, V. (2001). Probability and Finance: It’s Only a Game! Wiley, New York.
  • [34] Shafer, G. and Vovk, V. (2006). The sources of Kolmogorov’s Grundbegriffe. Statist. Sci. 21 70–98.
  • [35] Shafer, G., Vovk, V. and Takemura, A. (2012). Lévy’s zero-one law in game-theoretic probability. J. Theoret. Probab. 25 1–24.
  • [36] Stigler, S. M. (2014). Soft question, hard answer: Jacob Bernoulli’s probability in historical context. Int. Stat. Rev. 82 1–16.
  • [37] Swan, E. J. (2000). Building the Global Market: A 4000 Year History of Derivatives. Kluwer Law International, The Hague.
  • [38] Sylla, E. (2003). Business ethics, commercial mathematics, and the origins of mathematical probability. Hist. Polit. Econ. 35 309–337.
  • [39] Tartaglia, N. (1556). General Trattato di Numeri e Misure. C. Troiano dei Navo, Venice.
  • [40] Todhunter, I. (1865). A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace. Macmillan, London.
  • [41] Toti Rigatelli, L. (1985). Il ‘problema delle parti’ in manoscritti del XIV e XV secolo. In Mathemata: Festschrift Für Helmuth Gericke (M. Folkerts and U. Lindgren, eds.) 229–236. Steiner, Stuttgart.