Lester Dubins (April 27, 1920 – February 11, 2010) was an American mathematician noted primarily for his research in

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

. He was a faculty member at the

University of California at Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant uni ...

from 1962 through 2004, and in retirement was Professor Emeritus of Mathematics and Statistics. It has been thought that, since classic red-and-black casino roulette is a game in which the house on average wins more than the gambler, that "bold play", i.e. betting one's whole purse on a single trial, is a uniquely optimal strategy. While a graduate student at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

, Dubins surprised his teacher

Leonard Jimmie Savage Leonard Jimmie Savage (born Leonard Ogashevitz; 20 November 1917 – 1 November 1971) was an American mathematician and statistician. Economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a ge ...

with a mathematical demonstration that this is not true. Dubins and Savage wrote a book that appeared in 1965 titled ''How to Gamble if You Must (Inequalities for Stochastic Processes)'' which presented a mathematical theory of

gambling Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three el ...

processes and optimal behavior in gambling situations, pointing out their relevance to traditional approaches to probability. Under the influence of the work of

Bruno de Finetti Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability. The classic exposition of his distinctive theory is the 1937 "La prévision: ...

, Dubins and Savage worked in the context of

finitely additive In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, \mu(A \cup B) = \mu(A) + \mu(B). If this additivit ...

rather than

countably additive In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, \mu(A \cup B) = \mu(A) + \mu(B). If this additivit ...

probability theory, thereby bypassing some technical difficulties. Dubins was the author of nearly a hundred scholarly publications. Besides probability, some of these were on curves of minimal length under constraints on curvature and initial and final tangents (see

Dubins path In geometry, the term Dubins path typically refers to the shortest curve that connects two points in the two-dimensional Euclidean plane (i.e. ''x-y'' plane) with a constraint on the curvature of the path and with prescribed initial and terminal tan ...

), Tarski's circle squaring problem,

convex analysis Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory. Convex sets A subset C \subseteq X of som ...

, and

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

. His doctoral students include Theodore Hill.

Publications

Dubins–Spanier theorems The Dubins–Spanier theorems are several theorems in the theory of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although the original motivation for these theorems is fair division, they are in fact general ...

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References

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* {{DEFAULTSORT:Dubins, Lester 20th-century American mathematicians 21st-century American mathematicians 1920 births 2010 deaths University of California, Berkeley College of Letters and Science faculty Scientists from New York City University of Chicago alumni Probability theorists Mathematicians from New York (state) Fair division researchers