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Variance of the game duration in the gambler’s ruin problem


  • Anděl, Jiří
  • Hudecová, Šárka


We derive the variance of the duration of play in the classical gambler’s ruin problem of two players with ties allowed. The variance of the game duration for the three-tower problem, one of the possible extensions of the game for the case of three players, is presented as well.

Suggested Citation

  • Anděl, Jiří & Hudecová, Šárka, 2012. "Variance of the game duration in the gambler’s ruin problem," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1750-1754.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1750-1754
    DOI: 10.1016/j.spl.2012.05.023

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    References listed on IDEAS

    1. Chang, Derek K., 1995. "A game with four players," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 111-115, May.
    2. Bach, Eric, 1997. "Moments in the duration of play," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 1-7, November.
    3. Rocha, Amy L. & Stern, Frederick, 1999. "The gambler's ruin problem with n players and asymmetric play," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 87-95, August.
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