Finiteness in the Beggar-My-Neighbor card game
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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.
KeywordsInformation Transmission Mathematical Expectation Rule Function Card Game Bernoulli Trial
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- 4.Dickens, C., Great Expectations, London: Chapman & Hall, 1861.Google Scholar