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Martingale is probably the best-known casino and gambling betting system, often presented as a way to “earn from roulette.” The principle of this system is quite simple โ a starting bet size is chosen, which is doubled in case of a loss to recover lost money and make a small profit.
The history of Martingale's origin is unclear and shrouded in rumors, but it most likely originated in the 18th century when gambling was simply done by flipping a coin. The idea emerged when gamblers devised a system to double 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 |
| โฌ1 | X | -โฌ1 |
| โฌ2 | X | -โฌ3 |
| โฌ4 | V | โฌ5 |
The Martingale system became the most popular betting system in the world due to its simplicity and intuitive effectiveness. It is now most commonly used when playing in casinos, aiming 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 unfounded and ineffective. Its problems can be divided into several categories โ practical, psychological, and theoretical.
Here's a short video in English discussing these issues:
Practical Martingale problems
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 from 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 so many times in a row on roulette, but mathematically it's different, as past wins or losses have no impact on future results.
Psychological and mathematical Martingale problems
Many gamblers think that if red has appeared several times in a row on roulette, then the probability of black appearing next is higher. This kind of thinking is called the gambler's fallacy (in English, gambler's fallacy), which arises from a misunderstanding of the law of large numbers (in English, law of large numbers).
One of the main principles of probability theory is the definition of independent events. Two independent events are such that the result of one does not affect the probabilities of the other event. The most common example is flipping the same coin twice. If heads came up the first time, the probability of heads coming up the next time remains the same – ยฝ. No matter how many independent events there are and what the results are, the probabilities never change. The thinking that after N specific results the probability changes 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 sufficiently long 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, with 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 times, 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 and cannot 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 term.
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