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Finiteness in the Beggar-My-Neighbor card game

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Abstract

For card games of the Beggar-My-Neighbor type, we prove finiteness of the mathematical expectation of the game duration under the conditions that a player to play the first card is chosen randomly and that cards in a pile are shuffled before being placed to the deck. The result is also valid for general-type modifications of the game rules. In other words, we show that the graph of the Markov chain for the Beggar-My-Neighbor game is absorbing; i.e., from any vertex there is at least one path leading to the end of the game.

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References

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Authors and Affiliations

  1. Department of Mathematics, Aveiro University, Aveiro, Portugal

    E. L. Lakshtanov & A. I. Aleksenko

Authors
  1. E. L. Lakshtanov
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  2. A. I. Aleksenko
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Correspondence to E. L. Lakshtanov.

Additional information

Original Russian Text © E.L. Lakshtanov, A.I. Aleksenko, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 2, pp. 73–77.

Supported by the European Union Funds FEDER/COMPETE, project no. FCOMP-01-0124-FEDER-022690, cofinanced by the Portuguese Foundation for Science and Technology (FCT, Fundção para a Ciência e a Tecnologia), project no. PEst-C/MAT/UI4106/2011.

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Lakshtanov, E.L., Aleksenko, A.I. Finiteness in the Beggar-My-Neighbor card game. Probl Inf Transm 49, 163–166 (2013). https://doi.org/10.1134/S0032946013020051

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  • DOI: https://doi.org/10.1134/S0032946013020051

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