Martingale System

Introduction to the Martingale Betting System

Let's start with the “what is the Martingale system” question. This is a strategy that actually emerged in the 18th century, shortly after roulette was invented, and no, it was not created by a person named “Martin Gale”. If you are to believe the urban legends, it was invented by a casino manager, and when he saw how effective the strategy was, he put it to work and became a millionaire… Fairy tales aside, all we know about this system is that it has been in use since the late 1700s, and it was Inspired by the St. Petersburg lottery paradox, which was quite famous during the same period.

This is a paradox invented by the Swedish mathematician Nicolas Bernoulli, and it simply asks the following question: Imagine playing a coin toss game. You start with 2 units and double the bet each time the outcome is “tails”. If the result is “heads”, the game will end. How advantageous is such a game for the player?

Bernoulli developed a rather lengthy mathematical formula to answer this question and theoretically proved that the player has an edge over the casino. However, here we need to put the emphasis on the “theoretical” part: Bernoulli used a scenario that would not be possible in the real world – we will explain what this means below.

Martingale works in much the same way as this paradox, and it's really simple: all the player has to do is double the bet when he loses - that's it. Set the initial wager amount and double it if you lose (until you win). Its simplicity is among the top reasons why this strategy is popular.

How the Martingale Strategy Works

We answered the question of what is Martingale strategy, but if we give a practical example, you can better understand how it works.

Start by determining the initial wager amount. This is the first bet amount will place when you join the game. In this regard, the strategy does not have any rules, but in general it is recommended to use 10% of your bankroll. In this example, we will assume that you have a bankroll of 100 CAD and set the initial wager to 10 CAD.

1. So, place a 10 CAD bet, start playing, and wait for the round result.
2. If you win, continue playing without changing the bet amount (until you lose).
3. If you lose, double the bet amount in the next round (20 CAD).
4. Remember that you will need to keep doing this as long as you lose. So, for example, if you lose twice in a row, the bet amounts should be 40 CAD and 80 CAD, respectively.
5. If you win at any point in the cycle, go back to the initial bet amount and repeat these steps.

Careful readers have already noticed the problem here: we assumed we had a bankroll of 100 CAD, but the increases in bet amount actually depleted our budget on the third loss. So, when we lost three times in a row, we went bankrupt. This is one of the main problems with this strategy, as we will explain in detail below: if you lose multiple times in a row, you can run out of money, which will make this strategy useless.

However, perhaps you think that we kept the budget too low in the example above, and that the results would be different if we used a larger budget and kept the initial wager lower. Let's imagine that this time we have a bankroll of 500 CAD, and we start playing with 1 CAD.

So, by the ninth round, we will exhaust our entire budget again. But we hear what you say: the odds of losing nine times in a row are very slim, right? So, if we think we'll win "occasionally", our budget won't run out – right? To answer these questions, let's take a closer look at the mathematics behind this strategy.

Mathematics Behind the Martingale Strategy

Without using complex mathematical formulas, we can say that this strategy is based on two simple principles. Martingale claims the following:

• The player will eventually win.
• When he wins, the payout will be large enough to cover all losses and leave some profit.

The interesting thing is that both propositions are true. Just like the St. Petersburg paradox, it is possible to create a formula that will mathematically prove that these propositions are valid. The player will indeed win at a certain point. And when this happens, the payout will be so large that he can recover the money he has invested so far and also make some profit. Because the bet amount will also grow: if you play with big bets, the payouts will also be big.

So, roulette strategy Martingale must work, right? Once again, theoretically the answer is yes. However, in the real world, the results will be much different.

To explain this, let's go back to the St. Petersburg paradox. In the formula where Bernoulli proved that the system worked, he assumed that the player had an infinitely large bankroll. Even though he specifically stated this, players focused only on the “evidence” and chose to believe that the system worked, ignoring the infinite bankroll requirement. However, in the real world, no one has an infinitely large budget. For the same reason, both the St. Petersburg paradox and the Martingale are propositions that are only theoretically true.

The main problem here is that it is not clear when the player will win. Yes, you will win eventually, but are you sure you can win before you use up your entire budget? As you can see in the example above, losing 9 times in a row will completely deplete a $500 CAD bankroll and cause you to go bankrupt. And if you think that the probability of losing 9 times in a row is very low, you are wrong: the probability of losing 6 times in a row in 200 spins is about 84%. The probability of losing 9 times is over 50%. And if you lose 10 times in a row, you lose 1,023 times the initial bet.

Of course, from time to time, you will be able to win every 2-3 spins. This can lead to a false belief that the strategy is working. All that happens is that you get lucky: it has nothing to do with the Martingale.

Advantages of the Martingale Method

Despite this limitation, we can say that Martingale system roulette has two advantages:

• It is good if you want to regain your losses in the short term. This system allows you to cover all your losses as soon as the win occurs. It is unique in this respect – no other strategy can do this (with a single win). However, let us remind you once again that it is not clear when the win will happen. All we can say is that if you win before you go bankrupt, you can cover all your losses.
• It is good for short-term gameplay. It can be a good option for a 15-20 round gaming session. We mentioned above that if you make 200 spins, your probability of losing 6 times in a row is 84%. However, if you only make 6 spins, the probability will be 1.8%. The longer you play, the more likely you are to lose repeatedly. In short-term games, the opposite will happen. Although there is no guarantee that you will win, Martingale can be a good option if you are not going to do more than 20 spins.

Limitations and Risks of the Martingale Betting Method

Let’s get to the point: does the martingale system work? The short answer is yes – as we explained above, it works on a theoretical level. But due to the “infinite bankroll” requirement, it rarely works in the real world. But this is not the only problem of this strategy:

The “table limit” problem

In the real world, every roulette table has a maximum bet limit. This is expressed as “1 CAD – 500 CAD”, for example. This means two things:

• To play at this table, you must bet at least 1 CAD (bets lower than that are not accepted)
• You can bet a maximum of 500 CAD on this table (bets higher than this are not accepted)

Do you see the problem? Let's go back to the example above once again: if you lose 9 times in a row, you need to bet 512 CAD on the tenth spin – only this way you can ensure that the payout is large enough to cover all your losses. However, this table does not accept bets larger than 500 CAD – the whole system becomes useless at this point. That is, for Martingale to work, the table limit must also be infinite, although such a thing is not possible in the real world.

The risk of significant financial loss

Losing ten times in a row causes your total loss to be 1.023 times the initial wager amount. Martingale can be an extremely risky strategy in this regard, especially for those on a limited budget. Let's say you have a bankroll of 1,000 CAD: this is larger than most Canadian players allocate to play roulette. But in this case, and even if you start playing with 1 CAD, you will lose all your money after just 10 unlucky spins. And rest assured, losing 10 times in a row happens more often than you think.

The gambler’s fallacy problem

Even experienced gamblers believe that having a particular outcome happen multiple times in a row will increase the chances of other outcomes. For example, if the result was “red” 10 times in a row, you would think that the odds of “black” on the eleventh spin would increase, right? Most people, except mathematicians, would answer yes to this question, but it is essentially the gambler's fallacy. All possibilities are reset with each spin. The fact that an outcome has occurred 20 times does not reduce or increase the probability of it occurring the 21st time. In August 1913, the result was “black” for 26 spins in a row at the Monte Carlo Casino, and this game caused dozens of players to go bankrupt. So, for example, don't think that your chances of losing or winning 10 times in a row are very low: just because you lost nine times does not mean that your chances will increase the tenth time.

Variations of the Martingale Algorithm

Roulette Martingale is one of the most popular strategies and has many variants for the same reason. The most well-known among these are:

The Reverse Martingale (Anti-Martingale) Strategy

This strategy asks you to double the bet amount after every win, rather than after every loss. Since you only increase when you win, it makes you less affected when you lose repeatedly. Indeed, consecutive losses will not cause you to go bankrupt, but a single loss will cause you to lose all the profit you have made so far. In the long run, it could be just as devastating as the original Martingale.

The Grand Martingale: Increasing the Stakes Further

This is a variant that boosts both the positives and negatives of the original strategy. You basically keep increasing the bet amount by twice after each loss but also add +1. So, for example, let's say you bet 20 CAD and lose: in the next round, you need to place a bet of 40 CAD + 10 CAD (50 CAD). It is better at covering your losses and leaving a profit in short-term sessions, but the risk of bankruptcy is much higher.

The Mini Martingale: Introducing Loss Limits

In this variant, an upper limit is set for the bet amount to be increased after a loss. For example, if you set 100 CAD as the limit, you will no longer increase the bet when you reach this until you win but continue playing with the same amount. It is a variant with a lower risk of bankruptcy, but if you do not win until the limit you set, it becomes completely useless.

Practical Tips for Using the Martingale

We can share some tips for you to use the Martingale roulette technique more efficiently:

• Choose games with high table limits. It's easy to see why: the higher the table limit, the longer it will take to reach it. In other words, you will have more opportunities for the system to deliver results.
• Keep the initial wager as low as possible. The amount you start playing with should be as low as possible. This way, you can reduce the chances of it growing uncontrollably.
• Choose the right bets. Use even money bets (red/black, odd/even, low/high) to increase your chances of winning. In the European variant, your odds of winning these are over 48%.
• Choose the right variant. Single-zero roulette variants (European/French) offer higher RTP – lower house edge. This causes them to offer a higher chance of winning with every bet. Use this strategy on single-zero roulette, not double-zero (American) roulette games.

Alternatives to the Martingale Roulette Strategy

Roulette Martingale falls into the “betting strategies” category and it is even the most well-known technique of this category. Betting strategies are based on increasing or decreasing the bet amount according to a certain order. But there are also strategies that focus on your chances of winning: these can be a good alternative to Martingale and all similar systems. For example, the James Bond strategy is based on placing a straight bet + a line bet + a high bet at the same time. This way, you can cover 25 of 37 possible outcomes.

The good thing is that you don't have to make a choice. You can use strategies based on different principles with Martingale. For example, James Bond and Martingale can be used simultaneously: this way, you can also increase your chances of winning. But keep in mind that in such a scenario, the bet amount may grow even faster (that is, you will take more risks).

Evaluating the Roulette Martingale System

Martingale roulette does not guarantee winning, and, like any other strategy, it has some problems. However, it can still be useful in certain scenarios and is especially good at covering your losses. The important thing here is not to see Martingale (or any other strategy) as a “miracle solution”. It's still imperative that you focus on playing responsibly, making informed decisions, and not risking more than you can afford to lose. Martingale can give you a more fun and productive experience, but only if used the right way – by knowing its strengths and weaknesses.