Simple Martingale Betting versus Labouchere Betting at Roulette: Simulations and Statistical Evaluations

Abstract

This paper investigates Labouchere betting systems through extensive simulations and a comprehensive comparison with martingale betting strategies. The analysis focuses on the statistical profit distribution of a Labouchere round, revealing it as a mixed random variable where the continuous part is approximated by the Gumbel-Gompertz distribution. The intricate nature of Labouchere's profit distribution is examined through simulations and statistical modeling, providing insights into its characteristics and significance. The study extends to practical considerations, presenting simulated outcomes under unlimited stakes, further enriching the understanding of Labouchere betting dynamics. The paper contributes to both theoretical and applied aspects of Labouchere betting, shedding light on its complexities and implications for players and researchers alike.