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

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.