Progressive Roulette Systems

Ever since roulette first made it to the floors of gambling houses, players have been trying to come up with methods that would allow them to beat the Devil’s Wheel. This never-ending strive to prevail over the house has led to the emergence of numerous roulette systems, most of which are based either on negative or on positive betting progressions.

Progressive systems have proved to be extremely popular among roulette players, a fact which can be attributed to two main reasons. Firstly, most of them rely on a relatively simple set of rules enabling players to incorporate them without much difficulty in their gaming sessions.

And secondly, progressive systems leave gamblers with the deceptive impression they work when they don’t, or at least not over the long term. You may generate some profits occasionally but the fact of the matter is such systems have zero influence on your odds of winning in the long run.

With this in view, we shall delve deeper into the most popular progressive roulette systems, explaining how they work and why they inevitably prove ineffective. By the time you finish reading, you will have a better understanding of progressive betting so that you can decide on your own whether you should use this method or not.

A Few Words on the Concept of the Gambler's Fallacy

1The Concept

Before we proceed with any further explanations on progressive systems, we would like to say a few words about a concept, known as the Gambler’s Fallacy. Also called the Fallacy of the Maturity of Chances, it results from a cognitive bias where a person mistakenly infers that if a random event occurs more frequently during a specific short period, it will occur less frequently in the future.

In the context of roulette (which is a random game, based on independent events), this means a player may feel that the ball is due to land on black because red has hit multiple times in a row. The most notorious instance where this inference proved wrong occurred in August 1913 at the Monte Carlo Casino, which is why this cognitive bias is sometimes referred to as the Monte Carlo Fallacy.

Millions were lost that night when the ball produced 26 outcomes of black in a row, an extremely rare occurrence (1 in 66.6 million). Gamblers continued to stubbornly bet on red when they noticed the streak, assuming it was due to hit because the long sequence of black outcomes had caused an imbalance in the wheel.


Interestingly enough, the Gambler’s Fallacy also manifests itself in reverse. It happens when a player assumes that black is more likely on the next spin after seeing the ball landing in black pockets several times in a row. This reasoning results from the gamblers’ belief in streaks.

However, this line of thinking is also faulty, even more so when one is playing against a balanced wheel that yields completely random results and shows no bias towards specific numbers or sections. One such “fair” game of roulette lacks predictability and each outcome is completely independent from the previous ones.


Moreover, streaks have no impact on the results of future spins. Roulette is based on independent trials and therefore, red and black are always equally probable (the odds of each outcome are 18 to 19 on a wheel with one zero). Humans are prone to look for short-term patterns but these cannot be trusted although our brains would go to extreme lengths to convince us otherwise.

Many roulette players fall prey to the Gambler’s Fallacy because they believe they have noticed a short-term pattern that will enable them to beat the game. They resort to betting progressions because they do not think it is possible for a long enough streak to occur and negatively impact their chances of winning. Sadly, this belief often leads to disastrous results from a financial perspective.

Key Principles of Positive and Negative Roulette Progressions

The two most common types of roulette systems are based either on positive or on negative betting progressions. Both types of systems rely on previous outcomes to determine the amount the player bets on subsequent spins. The exact bet sizing depends on the type of system one uses and whether it is based on a positive or a negative progression.

Positive progression systems
Negative progression systems

Positive progression systems like the Paroli require the player to increase their stake after a winning round and reduce it after a loss occurs. These are less damaging than negative progression systems.

Negative progression systems work in the opposite manner as they require you to increase your wager after a losing spin and decrease it after you register a win. Exactly how you adjust the wagers after losing depends on the particular progression you use.

Their primary purpose is to help gamblers win more and capitalize on winning streaks. A positive progressive system can earn you decent profits during a long favorable streak and is less likely to destroy your bankroll during a losing one. Despite this, it has no impact on your overall odds of winning or losing a bet.

Some negative systems like the Fibonacci rely on extremely steep progressions. If you are playing on a shoestring budget, they can wipe out your session bankroll in several consecutive losses only.

The main premise behind negative progressions is they help the player recover their losses during a long bad streak. Here you are not trying to boost your profits but are aiming at diminishing your losses instead. Let's now delve into some of the most popular negative progression systems for roulette, starting with the infamous Martingale.

Martingale - The King of Betting Progressions
The Fibonacci – How Nature's Code is Used at the Roulette Table
Henry Labouchere's Contribution to Progressive Systems
On the Positive Side of Things – The Paroli
D'Alembert and the Theory of Equilibrium
Oscar's Grind – A Simple System

Where Progressive Roulette Systems Fall Flat

1No impact on the odds

Progressive roulette systems fall flat in several aspects, starting with the fact the adjustments in the bet size are based on previous results. These systems have no impact on one’s odds of winning which remain the same for each spin of the wheel. Each number has the same odds of winning during any given round as all other numbers. The number of times you have won or lost on previous rounds is irrelevant to the wheel.

2The House Edge

Furthermore, progressive-system play does nothing to reduce the house edge. Each bet you place, no matter how big or small, is exposed to the same casino advantage (2.70% in European and 5.26% in American roulette). No matter how smartly you size your wagers, your profits will never suffice for you to overcome the house edge.

3Computer Simulations

Most systems based on this principle may perform well in the short term but prove useless in the long run. Experts have tested popular betting progressions like the ones described above with the help of computer simulations. The result was always the same over the course of millions of trials. The ratio of money lost to money wagered is equal to that of flat betting because of the house edge.

Some proponents of betting progressions would argue no one can play millions of rounds in an actual casino. Such people swear by the systems they are using, claiming they fail to produce good results in computer simulations but would work without a hitch in “real life”.

Unfortunately, one such excuse holds no weight where mathematics is concerned. A simulation involves millions of rounds simply to prove a given system is flawed. If the system performed poorly on a computer, there is no reason for it to produce positive results in the “real” casino environment.

4Bad run

There are two other problems associated with system play, particularly if you are using a negative progression to size your bets. What happens if you are underbankrolled or are playing at a table with a low maximum limit?

In the first case, a devastating losing streak (not that uncommon in roulette) will completely wipe out your bankroll. You will be unable to continue with the progression and will fail to recoup your huge losses. The same goes for the table maximum. When you hit it during a bad run, you cannot offset your previously incurred losses, even if you have more money to go on increasing your bets according to the negative system.

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