Martingale: A 200-year-old Roulette Strategy

The Martingale system is one of the oldest roulette strategies around. It originated in 18th Century France, and was designed for traditional gambling games based around a coin-flip. The Martingale strategy has since been applied to several games where the odds of winning a single round are close to 50%, making it perfect for modern game. Roulette has several 50/50 bets players can make, including red vs. black, odd vs. even and high vs. low. The odds of a win are not strictly 50% given the presence of the zero on roulette wheels, but it is close enough for the strategy to be effective, and is still considered the best strategy to this day.

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The Martingale System
Mathematical calculation for the martingale strategy formula
Year: 1934
Inventor: Paul Pierre Lévy
Application: 1:1 betting
Best for: short-term success

How does the Martingale System work?

The Martingale system, also known as ‘doubling strategy’ is relatively simple. It works on the principle that you can cover any loss by betting twice the amount of your stake during the next round of betting. This process of doubling your bet can be repeated an unlimited number of times to ensure that all losses are covered as soon as you win. Theoretically at least, a gambler with infinite wealth will eventually win a round, recouping all loses and making a profit equal to the original bet. Of course, no gambler actually possesses infinite wealth, so there is still a way for casinos to bankrupt players who go on a losing streak. Table limits are also used to prevent to the system being used in many land-based but casinos. These limits are much wider online, where Martingale is still used.

The strategy is also popular with Blackjack players. The chance of losing a single hand in Blackjack is 49%. The win is 43%, and a push is 8%. It’s not the magic 50/50 Martingale System enthusiasts seek, but it’s pretty close.

The Martingale System (Doubling Strategy)
Round: Bet amount: Total loss: Profitability: Expected Value: Expected Return:
1 1 1 0.49292929 0.49292929 0.49292929
2 2 3 0.24995001 0.74985002 0.24995001
3 4 7 0.12674233 0.88719628 0.12674233
4 8 15 0.06426732 0.96400981 0.06426732
5 16 31 0.03258808 1.01023035 0.03258808
6 32 63 0.01652446 1.04104089 0.01652446
7 64 127 0.00837907 1.06414175 0.00837907
8 128 255 0.00424878 1.08343900 0.00424878
9 256 511 0.00215443 1.10091479 0.00215443
10 512 1023 0.00109245 1.11757574 0.00109245

The betting strategy is reset once the player wins a round. Therefore, it is essential to keep doubling the bet until a win is registered. This method requires bravery, as it can be daunting to continue to bet larger and larger amounts in the middle of a losing streak.

Martingale Strategy in Practice

Let’s take a look an example to demonstrate this system in practice. Imagine we choose to bet ‘black’ on a roulette table. We are starting with a £2 bet, as this is small enough to allow us room for multiple double-ups.

So, we place £2 on black in the first round, and we lose. A loss means doubling, so we place £4 on black in the second round. We lose again. We’re now £6 down, but there’s no need to panic. In the third round we place £8 on black, and this time it comes in! Those odds for a bet on black or red are 1:1. In total we receive £16 back. Our total outlay was £14 (£2 + £4 + £8 = £14) meaning we have a profit of £2, the same as our original stake.

martingale strategy in practice with a £2 stake

In our example, we managed to win a round at the third time of asking but unlucky players may have to wait longer. The important thing to remember is that, providing you have the bankroll to keep doubling, your money is not really at risk. A win recoups all losses whether you played two rounds or 20.

Even the Best Roulette Strategy has Flaws

There are flaws in roulette strategy such a Martingale if used over a long period of time. For a start, the original theory was based on a coin-flip; i.e. a game with a perfect 50% chance of a win, and 50% chance of a loss. It doesn’t matter how many times you flip it, you can expect to win half of the time.

However, in roulette the chance of a win when betting on black or red is only 48.65%. This is due to the zero on a traditional French roulette wheel, which is neither red nor black. You can of course treat a zero as a loss, and simply double your next bet, and this can negate the effect of the zero over a short period. The zero effect over longer game sessions though is significant, as Martingale strategy relies on a 50% win ratio to succeed long-term.

From a mathematical perspective, the reason why all Martingale-type betting systems fail over an unlimited period is because future outcomes cannot be predicted based on the results of past events. This idea that an event which has not occurred for a long time becomes more likely to occur in the future is known as ‘gambler’s fallacy’. Whilst hugely unlikely, it is entirely possible – mathematically at least – that a coin will land on heads an infinite amount of times in a row. A winning round is never guaranteed. Therefore, it is only when the player has unlimited money and unlimited time that Martingale can be classed as a winning strategy.

A Brief History of Roulette Strategies

Despite its flaws from a mathematical and theoretical stance, Martingale has been used successfully for roulette throughout history.

Charles De Ville Wells, also known as ‘the man who broke the bank at Monte Carlo’, was a successful gambler who used the system. Wells visited the Monte Carlo Casino several times in the summer and autumn of 1891. Wells increased his initial stake of £4,000 to around £60,000, the equivalent of approximately £6 million in today’s money. If a gambler won an amount large enough that it could not be paid from the cash reserves at the roulette table, play would be suspended while extra funds were gathered from the casino vault. During the restock, a black cloth was laid over the table. This was an indication that someone had ‘broken the bank’, boosting the gambler’s fame.

In the world of online casino, roulette has been a source of some serious payouts. On 1st December 2015, a German player by the name of Henrik Z. landed roulette wins of €45,000 or more no fewer than 28 times whilst playing Premium European Roulette at EuroGrand Casino. It is unclear whether Henrik was using a Martingale-style betting system, but it’s highly likely. Other gamblers have used a variation known as Reverse Martingale. The idea is that instead of doubling the bet on a loss, you double it on a win. This removes the need for a large bankroll as players gamble with their winnings. After a pre-determined number of consecutive wins, the player simply takes the profit and starts again. Reverse Martingale strategy relies heavily on gambler’s fallacy and is not as mathematically sound other betting systems, but it can result in huge gains for lucky players.