Martingale is perhaps the best known casino and gaming betting system, and is often presented as a way to "make money from roulette". The principle of this system is quite simple - you choose an initial bet amount, which is doubled in the event of a loss, in order to make up for lost money and earn a little profit.
The origins of Martingale are unclear and surrounded by rumours, but most likely date back to the 18th century, when it was played simply by tossing a coin. The origins lie in gamblers devising a system of doubling the amounts, since the odds of winning are 50%. Doubling the amount of the chosen bet would allow players to undo any losses, return the original bet and earn the amount of the last bet:
| Bets | Winning | Earnings |
| €1 | X | -€1 |
| €2 | X | -€3 |
| €4 | V | €5 |
The Martingale system has become the most popular betting system in the world thanks to its simplicity and intuitive efficiency. It is now the most commonly used playing in casinosto profit from roulette. In roulette, bets are usually placed on red or black using the same system, although the probability of winning is lower - 48.6% or 47.4% (in European and American roulette). Unfortunately, Martingale, like all roulette betting systems, is mathematically unsound and broken. Its problems can be divided into several types - practical, psychological and theoretical.
Here's a short video in English discussing these issues:
Practical problems in Martingale
The Martingale system is based on increasing the amount of bets after each loss. This means that the increase in the bet amount is exponential or, in simple terms, increases very quickly. Even starting from a very small amount (e.g. €1), it can quickly become too large for the player (or exceed the maximum bet of the casino house). Starting with an initial bet of €2 and losing 8 times in a row, the next bet would reach €512.
It may seem almost impossible to lose so many times in a row on roulette, but mathematically it's not, as past wins and losses have no effect on future results.
Psychological and mathematical problems in Martingale
Many gamblers feel that if the roulette wheel has red on it several times in a row, then the chances of getting black next time are higher. This thinking is called gambler's error. gambler's fallacy), which arises from a misunderstanding of the law of large numbers. law of large numbers).
One of the key statements of probability theory is the definition of independent events. Two independent events are independent if the outcome of one of them does not affect the probability of the other in any way. The most common example is the tossing of the same coin twice. If a number comes up the first time, the probability of getting a number the next time remains the same - ½. No matter how many independent events there are and no matter what the outcome, the probabilities never change. Thinking that the probability changes after N number of specific outcomes is a gambler's fallacy.
The gambler's error comes from the law of large numbers. By flipping a coin, we expect the drops in the coat of arms and the number to be distributed close to 50% over a sufficiently long period of time. This distribution theoretically occurs only as the number of tosses approaches infinity. In 10 000 or 100 000 tosses, the coin can fall any way, with any distribution. It is possible that there will be times when the coat of arms will fall 10, 15 or 30 times in a row, but after these times neither the coat of arms nor the number of times the probability of the coin falling changes.
The same can be applied to roulette. Even if red comes up 10 times in a row, the probability of red remains the same as always. In simple terms, this means that the player cannot make any difference and cannot play the roulette probabilities in any way. No matter which betting system is chosen, the gambler always loses because the probabilities, which are tilted in favour of the casino house, do not change. This means that by increasing the bet amounts we should only expect to lose more in the long run.
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