An analysis of the classical gambler's ruin problem through multiple devices variation

Abstract

In this study, we propose a variant of classic 2-player ruin's problem. We advocate the use of simultaneous operation of multiple devices to conclude upon the game. The suggested scheme is rigorously analysed and shown to be balancing the game duration to a notable extend in order to achieve desirable features of giving both players opportunity to comeback as well as avoiding the stalemates. The proposed scheme, at first, mathematically elaborated by providing general expressions of the ruin probability, the ruin time, the conditional ruin time and the variance of the game. The foundational blocks of the devised game are tested and validated in-concordance with the various pre-fixation adapted by Stern (1975) and Samuels (1975). In pursuit of the objectives, the mathematical outcomes are rigorously verified by simulating various adaptations under diverse parametric settings.

Keywords

• classical gambler's ruin problem
• ruin probability
• ruin time
• conditional ruin time
• simultaneous operation