A gambling system and a Markov chain (Q1354842)
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scientific article; zbMATH DE number 1008583
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A gambling system and a Markov chain |
scientific article; zbMATH DE number 1008583 |
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A gambling system and a Markov chain (English)
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29 October 1997
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The authors investigate a gambling system known as Oscar's system in which the aim is to win one betting unit, at least with high probability, and then start over again. The system is modeled by an irreducible Markov chain in a subset of the two-dimensional integer lattice. It is shown that the Markov chain, which depends on a parameter \(p\) representing the single-trial win probability, is transient if \(p<0.5\) and positive recurrent if \(p\geq 0.5\).
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gambling system
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Markov chain
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Oscar's system
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transient
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positive recurrent
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