# What is the martingale system?

The Martingale strategy is one of the most popular methods in sports betting. Its pitfalls are known to many experienced bettors. But if you understand the mathematical principles of the strategy well, then you can easily find quite profitable options for its application. In this article, we will consider what benefits the Martingale method can bring to sports betting and gambling entertainment.

## What is the Martingale strategy?

This is a popular progressive betting system aimed at actively increasing the bet amount after each loss. Increasing the amount of the next bet allows you to compensate for previous expenses. But experts do not recommend seriously considering this technique to restore financial losses. There are a lot of materials on the Internet, where mathematically proven facts are clearly shown, why this cannot be done.

With respect to various bank management plans where the player’s perceived advantage over positive and negative odds is constant for all sports betting, changing the bet amount does not change that advantage. All that is in the power of the bettor is to change the distribution of risks and rewards. The Martingale strategy implies the purchase of a large reward, but with a high risk of draining the entire budget.

Given these features, we decided to consider the Martingale in more detail and show you how to use it with better management. This article is to show in detail how sports betting has a delicate balance between risk and reward. Remember one simple but important thing – the larger you want to get a reward, the more risk you need to take.

## How to win at the casino?

In gambling establishments, there are mainly games with negative expectations. But the ability to count cards in blackjack will increase your chances of winning. But if the dealer notices that you are counting cards, you will be kicked out of the room, as this is against the rules of the new UK casino.

If we talk about betting on roulette, then all of them are inherently losing. This game is calculated mathematically and the house gets an advantage thanks to the “zero”. Even if the dishonest roulettes are discarded, the player will still not be able to maintain a profitable advantage.

Based on the features of playing in a real money casino listed above, we will try to consider how to enjoy playing in a gambling establishment and make your stay in it longer. Let’s evaluate this question only from the side of one-to-one bets in roulette. We will take into account even and odd results, black and red sectors.

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## How effective is a fixed rate?

Flat stake is the simplest betting format, where any bet is accompanied by the same amount. For example, let’s take a situation in which we bet 1 dollar for each spin of the wheel. What income to expect when betting on 1000 games? The expected profit will depend on the binomial distribution. You can see the chart below:

The blue curve represents the range of expected outcomes with fair odds. And the red curve takes into account shows the results if the player plays roulette with “zero”. At this table, the house edge is 2.7 percent.

Even if you play roulette without a “zero”, you still cannot count on an increase in your bank. The chance of winning \$50 is only 5.7 percent. And if we take into account the advantage of the gambling club, then the prospects are even less bright – a meager 0.74 percent. This indicator is offset by a small risk of losing \$50. Even if the casino has an advantage, the probability of losing this amount is only 23 percent. And the risk of losing \$100 is only 1 percent.

Fixed bets are safer, but they are not able to bring big winnings and significantly increase the bankroll. Therefore, it is worth considering more interesting and profitable options for playing in a casino.

## Martingale with guaranteed financial losses

The most primitive method of applying Martingale is doubling the size of the next bet after the lost current bet. The bet sizes are doubled until the player wins. After that, the bet amount is reduced to the original, and the progression starts again.

Even a person far from gambling and betting understands that the Martingale strategy is quite dangerous. Using it, the player risks losing all the money. Only overly self-confident players consider it seriously. Prolonged aggressive play very often leads to a series of defeats. The longer a player plays this strategy, the more he risks getting stuck in a losing streak.

The longest losing streak that you are likely to see over the Nth number of bets is set to the logarithm of N to the base of the quotes divided by the odds minus one. For one-to-one bets, the losing streak can be:

• 3 out of 8 bets;
• 4 out of 16 bets;
• 5 out of 32 bets;
• 9-10 out of 1000 bets.

## Modeling the Results of the Martingale Strategy

Suppose you have an inexhaustible supply of funds and at the same time play in a very generous gambling club with no limits on the maximum bet sizes. The expected profit after 1000 spins will be \$500. But this is only when playing roulette without zero. And in roulette with “zero”, which gives an advantage to the gambling establishment, the player can win a maximum of 486 dollars.

Neither one nor the second condition is feasible in real life. There will definitely be a losing streak that will bankrupt you or take a lot of money, after which you are unlikely to want to continue playing.

What is the reasonable approach in this situation? It is necessary to decide on the goals that you want to achieve during the game. Also set clear rules and limits for yourself. It is important to model the probabilities of different outcomes in the same way as in the case of flat stakes.

For example, consider the following development of events:

1. With an initial bet of \$1, let’s set ourselves the goal of winning \$500 for 1,000 roulette spins.
2. Let’s reduce the probability of draining the budget at any time during 1000 spins to 50 percent.
3. Let’s determine the maximum allowable budget spending before deciding to stop, taking into account the first two points.

To determine the amount of bankroll loss, you need to use Monte Carlo simulation. Below you will see the results of a series of 10,000 Monte Carlo launches:

For each series, which includes 1,000 spins, there is a maximum bankroll size. If the threshold is exceeded, the player stops playing, and the strategy is considered ineffective. If the amount of lost funds has not reached the threshold, the game continues for 1000 spins, and the strategy is considered winning. In this example, zero was not taken into account in the roulette wheel. That is, the casino had no advantage.

## Changed wording

The larger the amount a player is willing to lose, regardless of the moment of the series, the higher his chances of winning using the Martingale method. The minus \$300 threshold gives the gamer a 50 percent chance of winning \$500 by spinning the roulette wheel 1,000 times. But if you look at this bet in the context of risk, then the player will most likely lose the same \$500.

If the betting offer is shown in a different wording, it will look like this: Risk \$500 to win \$500. In this case, the offer ratio varies within 2.00, or one to one.

Bet offer odds are exactly the ratio of average win to average loss. This ratio is an indicator of the player’s real chances. For fair roulette, where there is no “zero”, the ratio must be equal.

If you’re ready for the \$1,000 threshold, you can survive longer losing streaks. Lesions occur much less frequently and their coefficient is also less – only 1.29. In order not to risk losing \$1,725, it is recommended to reduce the starting bet amount. This will reduce both the risks and the progression provided by the Martingale strategy. A starting bet of \$0.29 would win approximately \$145 for a \$500 risk.

Unlike the more primitive fixed-stakes method, here the player faces high risks of losing larger sums. But the chances of winning also increase. A player can never lose \$500 in roulette for 1000 spins of the wheel if he bets \$1 per spin. But under such conditions, it is impossible to replenish your bankroll with \$500. The chances of winning and losing this amount are very small.

## What is the essence of the advantage of the casino?

Thanks to the “zero”, the gambling club has a guaranteed advantage of 2.7 percent. And this fundamentally changes the situation. The chart you will see below compares the losses of players when playing roulette with and without zero. By running roulette with a house edge and a threshold of -\$300, losses will occur on 58 percent of spins.

To take advantage of the 50 percent guaranteed offer, the maximum financial loss threshold must be increased to -440 dollars. In this case, there is a risk of losing about \$670 with a profit of \$486. Due to the fact that the expectation of winning the bet is 48.6 percent, the expected profit in the case of a winning streak is \$486 instead of \$500.

This ratio implies a probability of winning of 1.73. This is slightly lower than the odds of a 2.00 offer that was calculated at risk of failure. You see a loss of value, which is significantly higher than the guaranteed profit of the establishment.

## Distribution of risks and rewards

The use of the guided Martingale technique allows you to see firsthand the change in the offer of bets on the distribution of outcomes chart:

10,000 Monte Carlo simulations are displayed here. This uses a bankroll loss limit of -300 dollars in fair roulette. The graph shows the division of win and loss zones. They can be compared with the original distribution from fixed amounts, displayed by the dotted orange line.

## What are the changes in coefficients?

We consider the Martingale technique using primitive 1:1 sentences as an example. But it can be used for any quotes and any betting markets. The player only needs to change the scale of the progression. To set the required size of the value, the coefficient must be divided by the same coefficient, but less by one unit. That is, if the odds of 2.60 are set on the outcome, then the amount of the bet after the defeat increases by 1.25 times.

The higher the odds you wish to bet on, the higher the effective risk rate. But keep in mind that betting on higher priced selections is fraught with longer losing streaks.

For example, betting on honest quotes of 5.00, you will have to risk approximately \$800 to count on the same amount of winnings. And if you bet on small odds, for example, 1.50, then the amount that the player risks is no longer so large – only \$ 333 with a similar potential win. Moreover, it is always possible to change the starting amount of the bet to increase or decrease the progression.

## Don’t use progressive betting systems

We want to dissuade you from using the Martingale strategy and any other methods that involve progression. But you need to understand that any gambling and sports bets are associated with risk and reward. And you need to manage your capital in order to change the bankroll and correctly distribute your risks and rewards.

Regarding the exciting game in the casino, you can deposit \$500 one-time and complete the game after one spin, regardless of the result – victory or defeat. But after such a quick game, you need to find other entertainment.

Unlike gambling establishments, there is a positive expectation in bookmakers. If you are among those players who really get that kind of expectation, then there is no need to think about the Martingale technique and other progressive systems. Let the law of large numbers work in your favor.

Eric Schfter (UK)
Casino Games Expert
The Martingale strategy is also known as catch-up. This betting system is used to offset previous losses. For the technique to work effectively, you need to look for events with coefficients of at least 2.00. Only in this way, by increasing the size of the next bet, you will cover the costs of the previous ones.

Most often, Martingale is used in casinos. But it should only be used if you have a large bankroll. The player just needs to double the size of the next bet if the current one has not entered. This is a very risky technique, as the player risks losing his entire bank and going into big losses.

FAQ
Why is Martingale often confused with Dogon banking?
These are almost the same strategies in principle, which have few differences.
Can the Martingale strategy be combined with other strategies?
Yes. It is often used in conjunction with a financial model called flat. But in this case it is important to analyze each game. This will increase the patency of bets and make profit more often.
For which sporting events is the Martingale system effective?
It is the same for betting on any sports and eSports.
Does this strategy have risks?
Yes. This is a progressive system that doubles the stakes after each loss. And this implies the likelihood of an early drain of the entire budget with a prolonged losing streak.

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