Abstract
The Labouchere gambling system is hypothesized to increase the probability of winning a predetermined arbitrary profit in a gambling system such as a coin flip or a roulette game in which both payouts and odds are 1:1. However, use of the system increases the downside monetary risk in the event of a streak of multiple losses. To begin, a player creates an arbitrary series of consecutive integers with a sum equal to the desired profit from multiple rounds of betting. Using the system, a player will either win an amount equal to the sum of the elements of the initial series or lose all of their available capital. This sequence was simulated multiple times to determine the statistical characteristics of both the return and of the loss in an average round of betting. By running the simulations of millions of rounds of Labouchere, it was possible to discern the probable outcomes of running the system using the Labouche gambling sequence and plotting the results on a graph to map the average return on the initial capital investment. The Labouchere system is very psychologically appealing to players because when applied over time it provides very consistent linear returns. However, there is eventually a critical moment at which the available capital for betting is exceeded and a player loses all of their available capital. It was found that as the number of bets increased, the outcome of applying the sequence approached zero.
Highlights
The Labouchère system is designed for zero sum betting systems in which the chance of winning is 50%
This was mapped with an exponential function y = 1026.3e-0.806x. This regression equation was found to account for 93.1% of the outcomes in this experiment which can be seen by the R-squared value of R2 = 0.93172
This was mapped with an exponential function y = 106e-0.131x. This regression equation was found to account for 86.9% of the outcomes in this experiment which can be seen by the R-squared value of R2 = 0
Summary
The Labouchère system is designed for zero sum betting systems in which the chance of winning is 50% This can be thought of as two players betting equal amounts of money on the outcome of a coin flip. The Labouchère betting sequence strategy attempts to increase the chances of a positive return over multiple rounds of betting This is applied to a wagering system, such as coin flip, sports outcome, or online casino. Using this strategy, the player decides the desired return ahead of time by writing a sequence of consecutive integers where the sum is the desired return from multiple rounds of betting. As determined by the parameters for termination of recursion, the only cases in which the algorithm will terminate are those in which the player has either won an amount equal to the summation of the original sequence or has lost all of their available capital
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