MARKOV CHAINS APPLIED TO THE GAMBLER’S RUIN AS AN ARGUMENT AGAINST GAMBLING

Abstract

The present article aims to investigate, using Markov chains as an argumentative tool, the probability of player ruin in gambling, based on the game "Fortune Tiger." The analysis begins by questioning the viability of betting strategies and proposes a mathematical approach to show how the odds involved lead the player to ruin, regardless of the betting style. Our theoretical basis relies on the use of Markov chains, a probabilistic model that allows the analysis of stochastic processes in order to identify the transition between possible states, such as consecutive wins and losses in a game. In this case, we focus specifically on an application to the adapted problem of the gambler's ruin, which is frequently discussed in game theory and probability. The methodology consists of applying the ruin problem with probabilistic data extracted through measurements from the game in question and comparing the results with numerical simulations performed in Python, using as an analysis criterion the state transitions throughout the game in two different situations: first, when the house has more money than the player, and second, when the player and the house have equal amounts of money. The results confirm the hypothesis that, regardless of the betting style or strategy, the player faces a high probability of ruin as the number of plays increases. These findings strengthen the argument against the viability of gambling, highlighting the inevitability of loss, even in scenarios where the player adopts conservative strategies.