<![CDATA[Gambler's Ruin Problem (GRP) is a basic stochastic model used to analyze the probability of a player reaching a target wealth versus losing all capital through sequential random games. This study has two main objectives: to validate the Monte Carlo simulation model against established theoretical results and to conduct a comprehensive sensitivity analysis of the probability of bankruptcy and game duration relative to the probability of winning , initial capital , and target capital . The simulation model was developed in Python as a one-dimensional random walk model, using replications for initial validation. The results show a high degree of conformity, with an empirical simulation probability of 0.5004 compared to a theoretical value of 0.5000, in accordance with the Law of Large Numbers. Sensitivity analysis shows that a small deviation in (e.g., drastically increases the probability of bankruptcy to over 88%. Furthermore, the average game duration peaks in the fair scenario at 2,502 steps and decreases significantly under biased conditions. This study confirms the effectiveness of the Monte Carlo method in measuring the impact of the “house advantage” and provides counterintuitive insights into the dynamics of stochastic games.]]>
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