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The Splendors and Miseries of MartingalesÉmile Borel’s Denumerable Martingales, 1909–1949

The Splendors and Miseries of Martingales: Émile Borel’s Denumerable Martingales, 1909–1949 [At infinity, a fair game can become unfair. This paradox was first fully understood and mastered in the 1940s by Émile Borel, who resolved it using the theory of denumerable probability he had introduced in 1909 and the theory of martingales developed by his student Jean VilleVille, Jean in the 1930s. Borel’s reflections on the paradoxes of infinite play were stimulated by a debate beginning around 1910 with Félix Le DantecLe Dantec, Félix, who questioned the practical value of probability theory. Borel learned from Le Dantec that probability’s applications generally depend on equating a small or zero probability with impossibility, and he struggled to reconcile this insight with his denumerable probabilities. By 1949, the struggle had led him to the optional stopping theorem for heads and tails.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesÉmile Borel’s Denumerable Martingales, 1909–1949

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn
Bru, Marie-France; Bru, Bernard
The Splendors and Miseries of Martingales — Oct 18, 2022
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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05987-2
Pages
51 –65
DOI
10.1007/978-3-031-05988-9_3
Publisher site
See Chapter on Publisher Site

Abstract

[At infinity, a fair game can become unfair. This paradox was first fully understood and mastered in the 1940s by Émile Borel, who resolved it using the theory of denumerable probability he had introduced in 1909 and the theory of martingales developed by his student Jean VilleVille, Jean in the 1930s. Borel’s reflections on the paradoxes of infinite play were stimulated by a debate beginning around 1910 with Félix Le DantecLe Dantec, Félix, who questioned the practical value of probability theory. Borel learned from Le Dantec that probability’s applications generally depend on equating a small or zero probability with impossibility, and he struggled to reconcile this insight with his denumerable probabilities. By 1949, the struggle had led him to the optional stopping theorem for heads and tails.]

Published: Oct 18, 2022

Keywords: History of probability theory; Émile Borel; Laplace; Martingales; Optional stopping; St. Petersburg paradox

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