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

Hussain, Abid; Cheema, Salman; Hanif, Muhammad

doi:10.1080/16583655.2022.2029326

Cited by 1 publication

(2 citation statements)

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“…The pioneering work related to gambler's problem is coined with a well-known mathematician Pascal; see for example [1]. For the significance about this problem with applications in various disciplines, someone can consult [2] for business, [3] for quantum mechanics, [4] for anomaly detection, [5] for material properties and [6] for biological phenomena, etc…”

Section: Introductionmentioning

confidence: 99%

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The Equity-Based Modeling for Two-Player Gambler's Ruin Problem

Masood

Hussain²,

Haq

et al. 2022

AJPAS

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In the context of the classical two-player gambler's ruin problem, the winning probabilities and initial stakes are pre-decided. If a player (who is in financial crisis) starts with less amount than his/her opponent in the symmetric game, has more chances to be ruined. Besides, a player (based on previous record data) with more winning probability than his/her competitor, has fewer chances to be ruined. We observe that most of the time, usually a weaker player is not fully willing to make a contest with a strong player. To give a fair chance to fight back for a weaker player and to develop the audience's interest, equity-based modeling is required. In this research, we propose some new equity-based models for the game of two players. In this way, we advocate the weaker player (with less winning probability or less amount to start the game) is motivated to participate in the contest because of a fair chance to make a comeback. The working methodology of newly proposed schemes is executed by deriving general expressions of the ruin probabilities for mathematical evaluation along with observing the ruin times, and then findings are compared with the results of a classic two-player game. Hence, the prime objectives related to the study are achieved by taking diverse parametric settings in the favor of equity-based modeling.

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Section: Introductionmentioning

confidence: 99%

“…Also, they claimed that their strategy is in favor of both competitors. The most recent advancement in the literature, [1] advocated the use of simultaneous operation of multiple devices to conclude this game.…”

Section: Introductionmentioning

confidence: 99%