Martingale Strategy Simulation

An overview and simulation of the Martingale betting system.

The Martingale Strategy is a popular betting system most commonly used in games like roulette and blackjack. It is based on the principle of doubling your bet after each loss, with the idea that a win will eventually occur, offsetting all previous losses and providing a profit equal to the original stake.
The strategy is typically applied to bets that have close to a 50% chance of winning, such as betting on red or black, odd or even, or high or low in roulette.

To illustrate, consider a player using the Martingale Strategy in a game of roulette by placing an initial bet of $1 on black. If the bet loses, the strategy dictates that the next bet should be doubled to $2. If this second bet loses as well, the next bet should be doubled again to $4. This process is repeated until a winning bet occurs. When the player eventually wins, the payout will cover all previous losses and provide a profit equal to the initial $1 bet. The player then restarts the process with another $1 bet.

However, the Martingale Strategy is not without its pitfalls. The most significant risk is that a prolonged losing streak can lead to extremely large bets, which may either exceed the player's budget or hit the table's betting limit. This situation renders the strategy ineffective and can lead to substantial financial losses. Additionally, the strategy doesn’t change the house edge in games like roulette, meaning that the odds remain in favor of the casino in the long term. Therefore, while the Martingale Strategy can provide short-term wins, it is not a foolproof or risk-free system and should be used with caution and awareness of its limitations.

Key Point: The Martingale Strategy involves doubling your bet after every loss.

Simulating the Martingale Strategy

Starting Wallet Amount $

Minimum Bet Amount $

Number of Greens

Simulating Multiple Games

We can run the simulation above many times (using the same parameters selected) to understand the maximum value range that can be achieved using this method. Once the simulations are run, the boxplot below will show the range of the maximum wallet value achieved for each game.

Number of Games

That concludes the Martingale Stratergy!

Key Point: You will lose eventually. Sometimes a lot soon than you want. However - some of the high values achieved are very impressive and will occur at a better rate compared to some other gambling choices i.e Lotteries.