The conditional gambler's ruin problem with ties allowed

DOI10.1016/j.aml.2008.04.007zbMath1156.91327OpenAlexW2077750721MaRDI QIDQ1003871

Tamás Lengyel

Publication date: 4 March 2009

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2008.04.007

zbMATH Keywords

generating functionChebyshev polynomials of the second kindgambler's ruinlattice path combinatoricscontinued fraction representation by polynomials

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Stopping times; optimal stopping problems; gambling theory (60G40) Probabilistic games; gambling (91A60)

Related Items (12)

A novel version for three-player gambler's ruin problem ⋮ Localization of Defects Via Residence Time Measures ⋮ Generalized gambler's ruin problem: explicit formulas via Siegmund duality ⋮ Variance of the asymmetric n-player gambler’s ruin problem with ties allowed ⋮ The ruin time for 3-player gambler’s problem: an approximate formula ⋮ Gambler's ruin and winning a series by \(m\) games ⋮ The asymmetric \(n\)-player gambler's ruin problem with ties allowed and simulation ⋮ Variance of the game duration in the gambler's ruin problem ⋮ On the gambler's ruin problem for a finite Markov chain ⋮ Unnamed Item ⋮ Deciding when to quit the gambler's ruin game with unknown probabilities ⋮ Reaching consensus on a connected graph

Cites Work

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• The asymmetric \(n\)-player gambler's ruin problem with equal initial fortunes
• The gambler's ruin problem with \(n\) players and asymmetric play
• n-point, win-by-k games
• Conditional Expectation of the Duration in the Classical Ruin Problem
• The Classical Ruin Problem with Equal Initial Fortunes
• Symmetries for Conditioned Ruin Problems
• The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions

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