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 . 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.
- Gambling theory
- Labouchere system
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty