Finiteness in the Beggar-My-Neighbor card game

Finiteness in the Beggar-My-Neighbor card game 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Finiteness in the Beggar-My-Neighbor card game

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Publisher
Springer US
Copyright
Copyright © 2013 by Pleiades Publishing, Ltd.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946013020051
Publisher site
See Article on Publisher Site

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.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 13, 2013

References

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