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A Note on the History of the Gambler`s Ruin Problem
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 Title & Authors
A Note on the History of the Gambler`s Ruin Problem
Song, Seongjoo; Song, Jongwoo;
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 Abstract
This paper deals with the history of one of the well-known and historically important problems in probability, "Gambler`s ruin". This problem was first solved by Pascal and Fermat and published by Huygens in 1657. It was studied and extended by many probabilists in early years and thus, it became an important problem in probability history, introducing many new concepts. We would like to introduce the problem in detail to readers and share the ideas on how new problems are developed, relating to old problems.
 Keywords
Gambler`s ruin;Huygens` fifth problem;
 Language
English
 Cited by
 References
1.
Ampere, A.-M. (1802). Considerations sur la Theorie mathematique du Jeu, Lyon Chez les freres Perisse.

2.
Bernoulli, J. (1713). Ars Conjectandi, Thurnisius, Basilea. Reprinted in Editions Culture et Civilisation, Bruxelles, 1968, and in Die Werke von Jakob Bernoulli, 3, Birkhauser, Basel, 1975.

3.
Edwards, A. W. F. (1987). Pascal's Arithmetical Triangle, Griffin, London.

4.
Feller, W. (1970). An Introduction to Probability Theory and Its Applications, 3rd Ed., Wiley.

5.
Fieller, E. C. (1931). The duration of play, Biometrika, 22, 377-404. crossref(new window)

6.
Hald, A. (1990). A History of Probability and Statistics and Their Applications before 1750, Wiley.

7.
Hofmann, J. R. (1995). Andre-Marie Ampere: Enlightenment and Electrodynamics, Cambridge University Press.

8.
Huygens, C. (1657). De Ratiociniis in Ludo Aleae, printed in Exercitationum Mathematicarum by F. van Schooten, Elsevirii, Leiden. Reprinted in Oeuvres, 14, (1920).

9.
Moivre, A. de (1711). De Mensura Sortis, seu, de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus, Philosophical Transactions, 27, 213-264.

10.
Moivre, A. de (1718). The Doctrine of Chances: or, A Method of Calculating the Probability of Events in Play, Pearson, London.

11.
Moivre, A. de (1738). The Doctrine of Chances, second edition, Woodfall, London.

12.
Moivre, A. de (1756). The Doctrine of Chances, third edition, Millar, London.

13.
Montmort, P. R. de (1713). Essay d'Analyse sur les Jeux de Hazard, Seconde Edition. Revue et augmentee de plusieurs Lettre. Quillau, Paris.

14.
Ore, O. (1960). Pascal and the intervention of probability theory. American Mathematical Monthly, 67, 409-419. crossref(new window)

15.
Ross, S. (1997). A First Course in Probability, 5th Ed. Prentice-Hall.

16.
Struyck, N. (1716). Calcul des Rentes viageres, Reprinted in Oeuvres (1912), 194-210.

17.
Thatcher, A. R. (1957). A note on early solutions of the problem of the duration of play, Biometrika, 44, 515-518.