Martingale is probably the best-known casino and gambling betting system, often presented as a way to “make money from roulette.” The principle of this system is quite simple – a starting bet size is chosen, which is doubled in case of a loss to recover the lost money and make a small profit.
The history of Martingale's origin is unclear and shrouded in rumors, but it most likely emerged in the 18th century when gambling was done simply by flipping a coin. The idea originated when gamblers devised a system to double the amounts since the chances of winning are 50%. By doubling the amount from the chosen bet, players would recover all losses, return the initial amount, and earn the amount of the last bet:
| Bets | Win | Profit |
| €1 | X | -€1 |
| €2 | X | -€3 |
| €4 | V | €5 |
The Martingale system became the most popular betting system in the world due to its simplicity and intuitive effectiveness. Now it is most commonly used when playing in casinos to 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 ineffective. Its problems can be divided into several categories – practical, psychological, and theoretical.
Here is a short video in English discussing these issues:
Practical Problems of Martingale
The Martingale system relies on increasing the bet amount after each loss. This means that the increase in the bet amount is exponential or, simply put, grows very quickly. Even starting with a very small amount (for example, 1 euro), a player can quickly reach an amount that is too large (or exceeds the casino's maximum bet). Starting with a 2-euro initial bet and losing 8 times in a row, the next bet would be 512 euros.
It may seem almost impossible to lose that many times in a row in roulette, but mathematically it is different, as past wins or losses have no impact on future results.
Psychological and Mathematical Problems of Martingale
Many gamblers believe that if red has come up several times in a row in roulette, the probability that black will come up next is higher. This kind of thinking is called the gambler's fallacy, which arises from a misunderstanding of the law of large numbers.
One of the main principles of probability theory is the definition of independent events. Two events are independent if the outcome of one does not affect the probabilities of the other. The most common example is flipping the same coin twice. If heads came up the first time, the probability that heads will come up the next time remains the same – ½. No matter how many independent events there are and what the results are, the probabilities never change. The belief that the probability changes after N specific results is the gambler's fallacy.
The gambler's fallacy arises from the law of large numbers. When flipping a coin, we expect that over a long enough period, the occurrences of heads and tails will distribute close to 50 percent. This distribution theoretically occurs only as the number of flips approaches infinity. Over 10,000 or 100,000 flips, the coin can land in any way, in any distribution. It is possible that there will be moments when heads will come up 10, 15, or 30 times in a row, but after these occurrences, the probability of heads or tails does not change.
We can apply the same to roulette. Even if red has come up 10 times in a row, the probability of red remains the same as always. Simply put, this means that the player cannot influence or outplay the probabilities of roulette. No matter what betting system is chosen, the gambler always loses because the probabilities, which are skewed in favor of the casino, 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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