A novel version for three-player gambler’s ruin problem. (English) Zbl 07602421
Summary: In the classic three-player ruin problem, the play continues until at least one of the players is completely ruined. In this research, we present a novel version of the classic three-player game with interest lies in a specific player. We determine the ruin probabilities and expected durations of the game given that our player (i.e. the gambler or the casino’s player) wins or loses. The desired game plan is executed for both the cases, i.e. symmetric and asymmetric with all of the players having equal initial stakes. We also obtained the asymptotic results of the ruin probabilities and expected durations of the proposed game plan. Further, the validity of the desired game structure is also verified through a Monte Carlo simulation study.
MSC:
| 62-XX | Statistics |
Keywords:
classic three-player problem; novel version of three-player; equal initial stakes; symmetric and asymmetric play; ruin probability; expected duration of the gameSoftware:
BookIndRandSamplingMethodsReferences:
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