Electronic Communications in Probability

Expectation of the largest bet size in the Labouchere system

Yanjun Han and Guanyang Wang

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For the Labouchere system with winning probability $p$ at each coup, we prove that the expectation of the largest bet size under any initial list is finite if $p>\frac{1} {2}$, and is infinite if $p\le \frac{1} {2}$, solving the open conjecture in [6]. The same result holds for a general family of betting systems, and the proof builds upon a recursive representation of the optimal betting system in the larger family.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 11, 10 pp.

Received: 7 January 2019
Accepted: 18 February 2019
First available in Project Euclid: 22 February 2019

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Digital Object Identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60C05: Combinatorial probability

Labouchere system gambling theory martingale combinatorics

Creative Commons Attribution 4.0 International License.


Han, Yanjun; Wang, Guanyang. Expectation of the largest bet size in the Labouchere system. Electron. Commun. Probab. 24 (2019), paper no. 11, 10 pp. doi:10.1214/19-ECP220. https://projecteuclid.org/euclid.ecp/1550826036

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