Betting systems based on doubling stakes, such as the Martingale system, are fundamentally flawed in the long term despite their superficial appeal. These strategies, which involve doubling bets after losses to recover previous losses and secure a small profit, may appear to work over short betting sequences but are ultimately unsustainable due to the inevitability of encountering a long losing streak (Zarattini & Aziz, 2024). The Martingale system, which traces its origins to 18th-century France, is a well-documented example of such approaches, with historical analyses highlighting the dangers of exponential bet increases (Kucharski, 2012). The primary weakness of the system lies in its assumption of unlimited capital and absence of betting limits, neither of which hold true in real-world gambling scenarios (Babbage, n.d.).
The financial risks associated with the Martingale system are particularly evident in its impact on variance and bankroll depletion. By continually doubling the stake, bettors face exponentially growing wagers that can rapidly exceed their available funds or the bookmaker’s maximum bet limits, leading to inevitable failure (Turner & Horbay, 2003). Research has shown that similar progressive betting systems, such as the Labouchere system, suffer from the same fundamental issue—an expected largest bet size that approaches infinity when the probability of winning is 50% or less (Han & Wang, 2018). This reinforces the mathematical reality that such systems cannot alter the house edge, no matter how they are structured.
Additionally, the psychological impact of progressive betting strategies can contribute to problem gambling, as they create the illusion of control and a false expectation of eventual profit (Turner & Horbay, 2003). The “martingale index” has been proposed as a measure of how much perceived expected returns are artificially inflated by risky betting strategies, further illustrating how these approaches mislead bettors into believing they can overcome inherent probabilities (Dimitrov & Shafer, 2023). Ultimately, while systems like Martingale may appear profitable in controlled conditions or limited trials, they are mathematically unsound and pose significant financial and psychological risks to bettors.
By continually doubling the stake, bettors face exponentially growing wagers that can rapidly exceed their available funds or the bookmaker’s maximum bet limits, leading to inevitable failure
Summary of: Turney & Horbay 2003
Anecdote
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The story of doubling rice is a classic illustration of exponential growth. It originates from an ancient Indian legend about a wise man who challenged a king’s understanding of numbers. The wise man asked for what seemed like a modest reward—just one grain of rice on the first square of a chessboard, with the amount doubling on each subsequent square. The king, believing this to be a trivial request, agreed without hesitation. However, as the doubling continued, the numbers quickly spiraled out of control. By the 20th square, the total had surpassed one million grains, and by the 40th square, the amount was in the trillions. By the final, 64th square, the total number of grains required was over 18 quintillion, far more rice than had ever been harvested in the kingdom. This parable illustrates the power of exponential progression and how quickly doubling can lead to an unsustainable outcome.
This concept directly relates to the Martingale betting system, which relies on doubling bets after each loss to recover previous losses and secure a small profit. In theory, if a bettor has infinite funds, they will eventually win a round, reclaiming all prior losses plus the original stake. However, just like the king who underestimated the exponential nature of the rice doubling, many gamblers fail to appreciate how quickly bet sizes escalate. A losing streak of just ten rounds requires a bet that is over a thousand times the original stake, and a streak of twenty losses demands more than a million times the initial bet. In reality, bankroll limitations and table limits prevent bettors from continuing indefinitely, ensuring that a sufficiently long losing streak will eventually result in financial ruin. The story of the rice grains serves as a cautionary tale, demonstrating that while the doubling strategy may appear logical in the short term, its exponential nature makes it fundamentally flawed as a long-term betting approach.
Articles Cited
- “- (-): Martingale and Anti‐Martingale, https://doi.org/10.1002/9781119798835.ch1
- The abstract summarizes the key differences between Martingale and anti-Martingale money management systems in trading, and suggests that most people tend to prefer the Martingale approach.”
- “Carlo Zarattini, Andrew Aziz (2024): The Art of Financial Illusion: How to Use Martingale Betting Systems to Fool People, https://doi.org/10.2139/ssrn.4678427
- This paper provides a comprehensive exploration of financial scams, with a focus on how Martingale betting systems can create an illusion of short-term profitability to mislead investors.”
- “C. Babbage (-): X. An Examination of some Questions connected with Games of Chance, https://doi.org/10.1017/S0263593300037548
- The paper examines methods of betting on a series of events with a probability of success less than or equal to 1/2 in order to realize a profit.”
- “A. Kucharski (2012): How to be wrong but useful, https://doi.org/10.1186/gb-2012-13-12-180
- The paper discusses two flawed betting/investment strategies, the martingale system and collateralized debt obligations, which were popular but ultimately failed due to their reliance on mathematical models that did not account for rare events.”
- “N. Turner, Roger Horbay (2003): Doubling Revisited: The Mathematical and Psychological Effect of Betting Strategy, –
- The paper examines the effects of different incremental betting strategies on the gambling experience, finding that these strategies can create an illusion of success and amplify the variance of betting outcomes, which may be an important factor in the development and continuation of problem gambling.”
- “T. Ferguson (1965): Betting Systems Which Minimize the Probability of Ruin, https://doi.org/10.1137/0113051
- The paper discusses the development of betting systems that minimize the probability of ruin when gambling.”
- “V. Dimitrov, G. Shafer (2023): The Martingale Index, https://doi.org/10.2139/ssrn.4488359
- The paper introduces and defines a new metric called the “”martingale index”” which measures the portion of the apparent expected return of a gambling, trading, or investment strategy that can be attributed to the use of a martingale betting strategy.”
- “Yanjun Han, Guanyang Wang (2018): Expectation of the largest bet size in the Labouchere system, https://doi.org/10.1214/19-ECP220
- The expectation of the largest bet size in the Labouchere betting system is finite if the winning probability is greater than 1/2, and infinite if the winning probability is less than or equal to 1/2.”
Insufficient Detail?
At times it is difficult to answer the question as there are not enough relevant published journal articles to relate. It could be that the topic is niche, there’s a significant edge (and researchers prefer not to publish), there is no edge or simply no one has thought to investigate.
