Expectation of the largest bet size in the Labouchere system
| Autor: | Yanjun Han, Guanyang Wang |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Computer Science::Computer Science and Game Theory Conjecture martingale Representation (systemics) Martingale (betting system) General family Labouchere system Combinatorics combinatorics 60C05 Gambling and information theory Statistics Probability and Uncertainty gambling theory 60G40 Mathematics |
| Zdroj: | Electron. Commun. Probab. |
| ISSN: | 1083-589X |
| DOI: | 10.1214/19-ecp220 |
| Popis: | For the Labouchere system with winning probability $p$ at each coup, we prove that the expectation of the largest bet size under any initial list is finite if $p>\frac{1} {2}$, and is infinite if $p\le \frac{1} {2}$, solving the open conjecture in [6]. The same result holds for a general family of betting systems, and the proof builds upon a recursive representation of the optimal betting system in the larger family. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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