**Martingale is a betting strategy that originated in 18th century France**. The main idea of this strategy is that the player doubles the stake after each loss , so that the first win recovers all previous losses and wins a profit equal to the original stake. Thus, this strategy is closely related to the **St. Petersburg paradox**. The Martingale system is similar to the Labouchère system, Due Column betting and Oscar’s Grind. The similarity stems from the fact that all four of these systems rely on the fact that if one has time and an infinite amount of money to bet, each session will yield a profit. When these conditions are not met, it results in losing the entire stake over a longer period of time.

The aforementioned systems follow the pattern of human behavior. The gambler willingly takes more and more risks because he aims to make up for any losses. The gambler maintains behavior that is irrational, but consistent with previous decisions and actions. This phenomenon is known as Escalation of commitment.

The fundamental reason why all martingale-type betting systems fail is that no amount of information about the results of past bets can be used to predict the results of a future bet with accuracy better than chance. Alright, so let’s check out how the Martingale system works.

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## How does the Martingale system work?

**The way the Martingale system works is that it uses the uncomplicated principle of intensified rematches when a player makes a wrong bet.** As a result of losing $10, the player places another bet for $20 to make up for the loss and have a profit. The main idea is that if you double your bet, the odds must be at least 2.0 ( in decimal format). So it is important to search for sports bets with such odds. **This system is very often used in roulette**, where you bet on even/odd or black/red. The probability there is close to 50%.

Let’s go back to explain the system.

To explain in depth how the system works, an earlier example can be used. In a situation where the second bet turns out to be a loser, the player should place another bet, also doubling the stake. In this case, the stake will be $40. This action should continue until the bet is won. Applying the principle of doubling the stake, for each loss, and the correct odds are key. Consistency will ensure that 1 winning bet will cancel out all previous losses. What about when you finally manage to place a correct bet? To what point should you double your stakes? The **classic Martingale system** clearly states that it’s a descending progression, so stakes are increased only after losing bets. In the situation when the bet is hit, you should return to the initial stake.

Let me now present an example.

## Martingale system – an example

The game according to the Martingale system involves a sharp increase in the stakes of successive bets when you lose. Therefore, at the very beginning **the player should decide how many stages of the game he would like to play**. It is also necessary for him to determine what budget he is able to allocate for the game and what the starting stake will be. Below I will present a simple example of using the Martingale system.

We assume that the starting stake is $2, the player wants to place at least 10 bets. This means that each hit bet will bring $2 profit. Looks okay? Now let’s see what kind of budget we need to make at least 10 bets.

The necessary budget to achieve this goal is as much as $2046. This seems to be quite a large amount. However, looking more closely at how quickly the stakes increase after each loss, everything becomes understandable. In the example mentioned, it looks as follows : 2, 4, 8, 16, 32, 64, 128, 256, 512 i 1024$. Why do we need as much as $2046? It’s simple. We need to add up all the previous losses. So in the first example we lost $2, then $4, $8 and so on. The sum of losses in the first 9 bets is $1022. To place the tenth bet we need $1024, and to this we have to add what we lost before so $1022. The total is $2046.

Here you have to remember that even if the tenth bet is won, your profit will be only $2. Pretty absurd, right? And what does it look like if our starting stake is $10? 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120. So you need $10230 to place at least 10 bets and to earn $10 from each winning bet.

Let’s go back to our example with a $2 stake. With the assumptions made and betting at 2.0 odds each time, the game could look like this:

**The first stage of the game – a stake of $2**

- winning bet: win $4, profit from the game $2, return to the initial stake ($2),
- losing bet: loss of $2, moving to the 2nd stage (another bet for a stake of $4)

**Second stage of the game – stake of $4**

- winning bet: win $8, profit from the game $2, return to the starting stake ($2),
- losing bet: total loss of $6, moving to the 3rd stage (another bet for a stake of $8)

**Third stage of the game – stake of $8**

- winning bet: win $16, profit from the game $2, return to the starting stake ($2),
- losing bet: total loss of $14, moving to the 4th stage (another bet for a stake of $16), etc.

Let’s now analyze whether the Martignale system is worth using.

## Martingale system – is it worth using?

Based on the above example, it is possible to draw concrete conclusions as to whether this system is at all worthy of attention. In my opinion, it is not, which I will try to prove below. There is no denying that the amount of stakes grows rapidly. Betting at random is key here. Likewise in roulette, potentially even the longest string of failures will eventually be broken and one will be able to make up all losses. However, one has to assume that our budget will turn out to be sufficient, which will not necessarily be the case. In our example, in order to pass 10 stages we needed $2046, which is undoubtedly a considerable sum.

We also need to take into account the fact that we may simply fail to make a hit bet even in 10 or more stages. The second important fact is the bookmaker’s limits. A bookmaker can prevent a player from playing for a sufficiently high stake, for example, through a top-down stake limit for a given match. Even if the player has the necessary funds to continue playing.

When we look closely at our example we notice another important point. No matter at what stage of the game we manage to place a winning bet, the profit from the game is the same every time. It doesn’t matter if it’s at the first or tenth stage of the game. Starting with a stake of $2, placing bets with odds of 2.0, our final profit is only $2. We are risking a lot, only to make a not-so-great profit in the end. The only reasonable justification for using this system is the guarantee of making up for losses with 1 winning bet. We can lose a lot and gain very little. Let’s see how it looks from a mathematical point of view.

## Mathematical analysis

According to mathematical analysis, **the use of this system is not effective in the long run**. The main reason why Martingale-type betting systems fail is that completely no knowledge of past betting results can be used to predict future results. It is simply random. In mathematical nomenclature, this corresponds to the thesis that the results of both winners and losers of each bet are independent and identically distributed random variables.

The **Kelly criterion is another important concept in the mathematical analysis of betting systems**. This criterion defines the optimal bet size as a fraction of one’s capital, while keeping in mind the proposed odds and probability of winning. Kelly’s criterion is not quite compatible with the Martingale system for one main reason. The Martingale system does not take into account the probability of winning.

The use of the Martingale system is quite popular in spread betting and fixed-odds betting. This system, unfortunately, is exposed to the risk of the **gambler’s ruin**. We are talking about a situation where the player, due to a series of failures, loses all his capital.

Let me introduce some formulas below.

Let q be the probability of losing (e.g. for American double-zero roulette, it is 20/38 for a bet on black or red). “b” is the amount of the initial bet, and “n” is the finite number of bets a player can lose. The probability that the gambler will lose all *n* bets is *q ^{n}*. When all bets lose, the total loss is

The probability that the player does not lose all n bets is 1 − *q*^{n}. In all other cases, the player wins the initial bet (B.) Thus, the expected profit per round is as in the following formula:

Whenever q > 1/2, the expression 1 − (2*q*)^{n} < 0 < 0 for all n > 0. Thus, for all games in which a gambler is more likely to lose than win on a given bet, he is expected to lose money on average in each round. Increasing the bet size for each round according to the martingale system only serves to increase the average loss. [1]

## What is Anti-martingale?

**The Anti-martingale system is the opposite of the Martingale system**. Bets are increased as a result of winning, while they are decreased as a result of losing. The concept of a winning streak is purely an example of a **Gambler’s fallacy**, since individual bets are independent of each other, so the anti-martingale strategy does not yield any profit.

If we are talking about the Gambler’s fallacy, it is worth mentioning the psychological aspects at this point.

## The Gambler’s Mind: Psychological Aspects of the Martingale System

The popularity of the Martingale system is mainly based on the gambler’s illusion. The gambler is convinced that several losses will eventually be followed by a win. This leads to the wrongful belief that the casino can be outsmarted.

The gambler’s brain’s production of dopamine is also an important issue. As a result of winning, due to the euphoria, the player has the urge to continue playing and win again.

The use of the Martingale system can lead to a deepening gambling addiction. The gambler falls into the trap of “chasing losses” naively believing that another doubling of the stakes will eventually bring the desired win, which in turn leads to a loss of control over spending and huge financial problems.

Using the Martingale system leads to a misleading sense of self-confidence and overestimation of one’s skills. The player takes more and more risks, which leads to skyrocketing losses.

The most important thing is to know about the above-mentioned psychological pitfalls of using the Martingale system. Education on the Gambling mathematics can help players make rational decisions.

## Alternatives to the Martingale system

There are many other options for placing bets. **One alternative is the Kelly criterion**, which determines the size of the bet, taking into account the probability of winning and the offered odds. The main advantage of this strategy is that it maximizes the expected logarithmic capital growth and minimizes the risk of Gambler’s ruin.

Other **alternatives to the Martingale system are Due Column betting and the Labouchère system** I mentioned at the beginning of my article.

**D’Alembert’s strategy is that a series of losses should be followed by a win.** The player is supposed to increase the stake by one unit after each loss, and decrease it by one unit in case of a win. Admittedly, this strategy does not guarantee profits in the long run, but it is to some extent less risky than the Martingale system.

Gambling always involves risk. It does not matter what strategy a player chooses. None of the previously mentioned strategies can overcome the casino’s advantage of probability in the long run.