Expectation of the largest bet size in the labouchere system

Yanjun Han, Guanyang Wang

Research output: Contribution to journalArticlepeer-review


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 >1 2, and is infinite if p ≤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.

Original languageEnglish (US)
Article number11
JournalElectronic Communications in Probability
StatePublished - 2019


  • Combinatorics
  • Gambling theory
  • Labouchere system
  • Martingale

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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