Lester Dubins (April 27, 1920 – February 11, 2010) was an American mathematician noted primarily for his research in
probability theory. He was a faculty member at the
University of California at Berkeley 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, Dubins surprised his teacher
Leonard Jimmie Savage 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 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, Dubins and Savage worked in the context of
finitely additive rather than
countably additive probability theory, thereby bypassing some technical difficulties.[1]
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),
Tarski's circle squaring problem,
convex analysis, and
geometry.
Dubins, L. E. (1957). "On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents". American Journal of Mathematics. 79 (3): 497–516.
doi:
10.2307/2372560.
JSTOR2372560.
Dubins, Lester E. (1960). "Another Proof of the Four Vertex Theorem". The American Mathematical Monthly. 67 (6): 573–574.
doi:
10.2307/2309181.
JSTOR2309181.
Dubins, Lester E. (1960). "On Differentiation of Series Term-By-Term". The American Mathematical Monthly. 67 (8): 771–772.
doi:
10.2307/2308657.
JSTOR2308657.
Dubins, Lester E.; Morgenthaler, George W. (1961). "Inclusion of Detection in Probability of Survival Models". Operations Research. 9 (6): 782–801.
doi:
10.1287/opre.9.6.782.
JSTOR167046.
Dubins, Lester E.; Savage, Leonard J. (1965). How to gamble if you must: inequalities for stochastic processes. McGraw–Hill series in probability and statistics. McGraw–Hill.
References
^David Gilat; Ted Hill; Bill Sudderth (27 May 2010).
"Obituary for Lester Eli Dubins". The Bernoulli Society for Mathematical Statistics and Probability.
Lester Dubins (April 27, 1920 – February 11, 2010) was an American mathematician noted primarily for his research in
probability theory. He was a faculty member at the
University of California at Berkeley 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, Dubins surprised his teacher
Leonard Jimmie Savage 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 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, Dubins and Savage worked in the context of
finitely additive rather than
countably additive probability theory, thereby bypassing some technical difficulties.[1]
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),
Tarski's circle squaring problem,
convex analysis, and
geometry.
Dubins, L. E. (1957). "On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents". American Journal of Mathematics. 79 (3): 497–516.
doi:
10.2307/2372560.
JSTOR2372560.
Dubins, Lester E. (1960). "Another Proof of the Four Vertex Theorem". The American Mathematical Monthly. 67 (6): 573–574.
doi:
10.2307/2309181.
JSTOR2309181.
Dubins, Lester E. (1960). "On Differentiation of Series Term-By-Term". The American Mathematical Monthly. 67 (8): 771–772.
doi:
10.2307/2308657.
JSTOR2308657.
Dubins, Lester E.; Morgenthaler, George W. (1961). "Inclusion of Detection in Probability of Survival Models". Operations Research. 9 (6): 782–801.
doi:
10.1287/opre.9.6.782.
JSTOR167046.
Dubins, Lester E.; Savage, Leonard J. (1965). How to gamble if you must: inequalities for stochastic processes. McGraw–Hill series in probability and statistics. McGraw–Hill.
References
^David Gilat; Ted Hill; Bill Sudderth (27 May 2010).
"Obituary for Lester Eli Dubins". The Bernoulli Society for Mathematical Statistics and Probability.