# What is the martingle problem

## Martingale systems

### Martingale strategy at a glance

Conceptually, Martingale systems are derived from the Provencal city of Martigues (Carmargue). The residents were considered daring, which is why the winged expression "jouga a la martegalo" stands for a high-risk way of playing. Thanks to its widespread use in games like Pharo and Roulette, Martingale theories were derived from game strategy. These represent an independent sub-area of Probability theory The mathematician Paul Lévy introduced the term to stochastics.

### Martingale systems: principle and functionality

The The best known and most widespread form of the Martingale systems is doubling or doubling. A common name for the Martingale is therefore the doubling strategy. The principle is to double the stake in the next game in each case of loss until a win is achieved. In the event of a win, the player sets the stake back to the original level. If there is a profit, on the one hand the losses incurred so far are compensated and on the other hand there is a profit in the amount of the original stake.

Due to the original field of application of the Martingale in roulette, this game of chance is suitable for illustrating how it works. For example, a player bets a piece on red. The ball remains on black. The player loses his stake accordingly. Now he makes his first Martingale progression and places two pieces on red. So he doubles his bet. If the ball lands on red, he wins the two pieces.

In this way he compensates for the loss from the first round and makes a bit of profit. If, on the other hand, a loss occurs again in the second round, the Martingale player would place four pieces on red in the third round, i.e. double the stake again.

Theoretically, this game strategy can be continued indefinitely. The player doubles the stake after each loss and, in the event of a win, will always make up for everything lost and receive a piece of profit in addition. If you play several games in a row, the probability of winning one of the games increases. This means that the likelihood of losing all games in a row gets smaller and smaller as the number of games increases. In this example, the possible profit is always the same (one piece), while the possible loss increases due to the increasing stakes.

In practice, the Martingale reaches its limits due to several factors. The most important are the available capital and the maximum stake (determined by the casino).

Martingale strategies are versatile. In trading, the Martingale is especially used on foreign exchange markets (Forex). Trading in stocks or leverage products is also possible using a Martingale. In the Forex example, the trader trades with currency pairs, so he is betting on the price gain of one currency against another.

The Martingale can be used regardless of the type of currency pair and the time windows.

When trading financial products, the trader selects a certain position and places an order using Stop Loss and Take Profit at the same distance. If there is a loss (Stop Loss is triggered), he doubles his stake, so he chooses a double position size. If there is a profit (Take Profit is triggered), the trader places a new order with the original stake. Here, too, the increasing probability of winning is countered by an ever greater possible loss with every order.

### Martingale systems - opportunities and risks

In the theory of probability, the Martingale is a safe system, since the probability of winning is very high even with a few repetitions. A single win is enough to offset all previous losses and make a small profit. After just a few repetitions, there is an attractive probability of the desired event occurring.

However, it must be taken into account that the constant doubling of the stake allows the possible loss to grow just as quickly (exponentially). The possible profit amount also remains the same, while the possible loss increases disproportionately.

The ratio of the possible winnings and the possible losses therefore becomes less attractive with each repetition

If the loss is repeated several times, the start-up capital is quickly used up, so there is a risk of total loss. Furthermore, betting limits are a problem. The Martingale cannot be used any longer if the bet is no longer allowed to be doubled from a certain point. Compensation for previously incurred losses is then no longer possible. Provided that a player or investor has infinite capital and there is no limit to the maximum bet, the Martingale leads to a safe way to win. However, these prerequisites are not met in practice, which is why the strategy is considered problematic.

### Martingale systems summary

• simple game strategy with increased stakes in the event of a loss
• fast growing probability of winning with multiple repetitions
• rapidly increasing potential loss with multiple reps
• Martingale systems can only be used to a limited extent in practice
• requires high start-up capital