The Equity-Based Modeling for Two-Player Gambler's Ruin Problem
Muhammad Asim Masood, Abid Hussain, Ehtasham ul Haq, Ishfaq Ahmad
Asian Journal of Probability and Statistics · pp. 57–71 · Published 19 Aug 2022
10.9734/ajpas/2022/v19i230467Abstract
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.
References (11)
- 1 Prediction of company failure: Past, present and promising directions for the future [DOI]
- 2 The conditional gambler’s ruin problem with ties allowed [DOI]
- 3 Gambler's Ruin Problem in Several Dimensions [DOI]
- 4 On the gambler’s ruin problem for a finite Markov chain [DOI]
- 5 A game based on successive events [DOI]
- 6 Analytical Solution to Transport in Brownian Ratchets via the Gambler’s Ruin Model [DOI]
- 7 The gambler’s ruin problem for a Markov chain related to the Bessel process [DOI]
- 8 Statistical Testing of PRNG: Generalized Gambler’s Ruin Problem [DOI]
- 9 The classic two‐player gambler's ruin problem with successive events: A generalized variance [DOI]
- 10 An analysis of the classical gambler's ruin problem through multiple devices variation [DOI]
- 11 Fast Simulation of Random Walks on the Endoplasmic Reticulum by Reduction to the Gambler's Ruin Problem
Cited by 0
No indexed citations yet.
Related research
- Comparison of Automated System Vitek-2 with Conventional Methods, for Identification and Antibiotic Sensitivity in Gram Negative Organisms — shares topic coverage
- Comparison between Indirect ELISA and TBIA for Detection of Some Viruses in Naturally Infected Faba Bean Plants — shares topic coverage
- Comparison for the Effectiveness of Column Purified Fractions of Allium cepa Bulbs and Allium sativum Cloves against Bulinus globosus (Intermediate Host of Urinary Schistosomiasis) in Sokoto, Nigeria — shares topic coverage
- Anthropometric Comparison of Nasal Indices between Hausa and Yoruba Ethnic Groups in Nigeria — shares topic coverage
- Comparison of Differences in TOEFL and TEM and Its Implications for Chinese Higher Education — shares topic coverage
Article metrics
Real usage data collected on this platform.
25
Page views
0
PDF downloads
1
Outbound clicks
0
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.