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**.

- The Gambler's Fallacy
- Key Principles
- The Most Popular Roulette Systems
- Where Progressive Roulette Systems Fall Flat

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.

### 2Streaks

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.

### 3Patterns

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.

- American and European Wheel Sequences
- European Roulette
- French Roulette
- American Roulette
- Roulette Strategies
- Roulette Rules
- Outside Bets
- Inside Bets
- Roulette – From a Perpetual Motion Machine to a Casino Landmark
- Roulette Basics and Rules of Table Conduct
- Roulette's Bet Types
- The French Roulette Layout
- Independent Trials, Odds, and Casino Edge in Roulette
- En Prison and La Partage
- Taking Your Roulette Game to the Next Level with Call Bets
- The Many Faces of Roulette – Interesting Variations to Try
- Reading Biased Wheels and Other Predictive Methods
- The Master of the Wheel Gonzalo Garcia Pelayo
- Improving Your Roulette Game
- Dispelling Roulette Myths
- How to Protect a Roulette Bankroll
- Software Providers of Online Roulette
- Roulette Games with Progressive Jackpots
- Live Dealer Roulette
- Roulette Goes Mobile
- Roulette in Literature, Film, and Television

## 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 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.

## The Most Popular Roulette Systems

### Martingale - The King of Betting Progressions

The Martingale is easily **the most popular strategy among gamblers** and is used in games like roulette, blackjack, craps, and baccarat. It is not clear who exactly devised this strategy although some sources suggest it was named after 17th-century casino owner Henry Martindale. The pronunciation eventually changed over time.

This is a **negative progressive system** where you double your stake each time you lose and reduce it to your base unit after you score a win. It can be applied to all types of roulette bets but is mostly used for even-money propositions like red/black, even/odd, and high/low. The player can use any size of base unit they prefer although smaller units are recommendable.

Let’s see **how the Martingale works** with an example from roulette. Suppose you decide to use $10 as your base unit and bet on black. If black hits, you continue betting $10 until a loss occurs. Red shows, you lose your $10 and double up to $20 on the next spin. If red comes again, you increase your next wager to $40. Should another loss occur, your next bet should be to the amount of $80 and so on.

Stake | Outcome | Profit |
---|---|---|

$10 on black | Black/Win | $10 |

$10 on red | Black/Loss | -$10 |

$20 on red | Black/Loss | -$30 |

$40 on black | Red/Loss | -$70 |

$80 on red | Red/Win | $10 |

The idea here is that you will eventually register a win which will offset your previous losses, leaving you with a profit equal to your base bet unit, $10 in this instance. Regardless of how many losses you have incurred in a row and what size of base unit you use, **you will win exactly the amount you have staked on the first spin**.

The Martingale can yield positive results in the short term but the trouble is there is no way for the player to know with certainty when the losing streak will break. Six or seven consecutive losing spins are not all that improbable in roulette.

The bet increase is rapid with the Martingale and a longer losing streak may either wipe out your entire bankroll or **cause you to reach the table limits** so that you are unable to continue with the progression. You ultimately risk large amounts just to offset your losses and end up with one base unit in profits.

### The Fibonacci – How Nature's Code is Used at the Roulette Table

The Fibonacci sequence was first put down on paper by Italian mathematician Leonardo **Pisano Bigollo** (also known as Leonardo of Pisa or Fibonacci). In his 1202 book Liber Abaci, he wrote about a sequence of numbers that goes way beyond the scope of mathematics. Often called “Nature’s Code”, this sequence can be found everywhere in nature and even in arts.

It runs in the following way – 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 510 etcetera. **Each number to follow is equal to the sum of the two numbers that precede it**, a process which can continue indefinitely. So how is this used in roulette and to what purpose?

In the context of gambling, the Fibonacci is a **negative progressive system** where the player increases their stake after each loss according to the famed sequence. When they register a win, they go two numbers back in the sequence. If the very first wager wins, you continue flat betting your base unit until a loss eventually occurs, calling for a bet increase.

**The zero is ignored here** so that the sequence runs 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The system is mainly used on outside propositions in roulette and pass line wagers in the dice game of craps. Here is how the Fibonacci is applied in practice if you start with a base unit of $10:

Stake | Outcome | Profit |
---|---|---|

$10 on odd | 32 red hits/Loss | -$10 |

$10 on odd | 10 black hits/Loss | -$20 |

$20 on odd | 12 red hits/Loss | -$40 |

$30 on even | 33 black hits/Loss | -$70 |

$50 on red | 24 black hits/Loss | -$120 |

$80 on black | 9 red hits/Loss | -$200 |

$130 on black | 22 black hits/Win | -$70 |

$50 on red | 9 red hits/Win | -$20 |

It is obvious this system has a much steeper betting progression than the Martingale so that the player would inevitably expose huge amounts at risk should a long losing streak occur. This system is **suitable for players who have large bankrolls to play with** and are comfortable with the high level of risk involved.

### Henry Labouchere's Contribution to Progressive Systems

The Labouchere system was discovered by keen gambler Henry Labouchere who applied it specifically to the game of roulette. It is also known as **the Cancellation Method and Split Martingale**. However, the original inventor of this system is said to be the French mathematician and philosopher Marquis de Condorcet.

This is a negative progressive system that stands out with a **higher level of complexity** so be sure to have a pen and a notepad nearby if you decide to use it. Like other strategies, this one is also used predominantly for even-money propositions in roulette. You start by writing down a sequence of positive numbers. Choose your sequence carefully since your potential profit is equal to the total of the numbers you pick.

Let’s use an example with the sequence 1, 2, 3, 4, 5, with each of these numbers corresponding to the number of units you need to stake. Your potential winnings should amount to 15 units in this case. We shall use $1 for our base unit but you can choose any amount you are comfortable with.

Your first wager should be equal to the total of the first (1) and the last (5) number in the sequence, in this case, $6. **Each time you suffer a loss, you add the total of the losing wager at the end of the sequence**.

Thus, if you lose on the very first round of play, your sequence would look like this: 1, 2, 3, 4, 5, 6 and your next bet would be $7. Provided that you win this time, you end up with a net profit of 1 base unit, or $1.

Every time your wager wins, you cross out the first and the last number in the sequence like so 1, 2, 3, 4, 5, 6 and bet the total of the first and last uncrossed numbers, or $7 (2+5). You win again and your sequence becomes 1, 2, 3, 4, 5, 6. Therefore, you bet 7 units (3+4) or another $7. **A betting cycle ends successfully when you cross out all numbers in your sequence**.

Sequence | Stake with Base Unit of $1 | Outcome | Profits |
---|---|---|---|

1, 2, 3, 4, 5 | $6 (1+5) | Loss | -$6 |

1, 2, 3, 4, 5, 6 | $7 (1+6) | Win | $1 |

2, 3, 4, 5 | $7 (2+5) | Win | $8 |

3, 4 | $7 (3+4) | Loss | $1 |

3, 4, 7 | $10 (3+7) | Loss | -$9 |

3, 4, 7, 10 | $13 (3+10) | Win | $4 |

4, 7 | $11 (4+7) | Win | $15 in profit for this cycle |

Keep in mind that the longer your sequence is, the more money you need to bring with you to the roulette table. If you hit a longer losing streak, you will **keep adding numbers to the sequence** until you either lose your entire session bankroll or reach the table maximum.

Many roulette players who resort to the Labouchere determine how much they want to win (in units) beforehand and pick a sequence of numbers whose total adds up to that amount. For example, if your win goal is 20 units, you use a sequence like 1, 2, 3, 4, 5, 5.

### On the Positive Side of Things – The Paroli

So far we have discussed only roulette systems that rely on negative betting progressions. The Paroli is different because **it is based on a positive progression** where you increase the stakes when you win and reduce them after you lose. Respectively, this system aims at profit maximization instead of loss control and reduction.

The root of the word “paroli” comes from the Latin “par”, which means “match”. This system is practically the opposite of the infamous Martingale but **it sets limits on the player’s maximum bet**. It is intended for even-money bets in games like roulette, baccarat, craps, and blackjack.

You again start by deciding on a fixed base bet unit, which should be proportionate to your session’s bankroll. For example, if you allocate $400 or $500 per session, **your fixed unit should be no more than $10**. Each time you win, you double your bet for the next round. So if your first bet is to the amount of $10 and you win, you stake $20 on the next spin. Win again and your next bet is $40.

The difference here is that this doubling does not go on indefinitely. It stops as soon as you score three wins in a row, after which you reduce your next wager to your chosen base unit. Should a loss occur, you drop down to the base bet unit and continue to flat bet this amount until you win.

Stake with Base Unit of $10 | Outcome | Net Profit |
---|---|---|

$10 on red | 26 black/Loss | -$10 |

$10 on red | 9 red/Win | $0 (break even) |

$20 on black | 15 black/Win | $20 |

$40 on even | 12 red/Win | $60 |

$10 on black | 23 red/Loss | $50 |

$10 on a high number (19-36) | 3 red, low/Loss | $40 |

The Paroli has several advantages in the short term. First, **it prevents you from chasing your losses** by dramatically increasing your wagers during a bad run. Second, it helps you generate small but consistent short-term profits. And third, it sets a limit on your maximum stake which prevents you from exposing too much money to risk.

### D'Alembert and the Theory of Equilibrium

The D’Alembert system is named after the French mathematician, music theorist, and physicist **Jean le Rond D’Alembert**, who introduced a concept known as the Theory of Equilibrium. In his 1754 article Croix eu Pile, D’Alembert claimed that the probability of a coin toss producing heads increases with each consecutive outcome of tails that occurs.

Sounds familiar, right? As brilliant as this French mathematician was, he, too, succumbed to the **Gambler’s Fallacy**. The probabilities of a fair coin are not affected by previous results, which did not prevent gamblers from devising an entire betting system based on D’Alembert’s false notion.

The D’Alembert is a **negative progressive system** that relies on the notion of equilibrium, i.e. the player would lose approximately the same number of even-money propositions as they would win. In other words, the idea here is that red, odd, and low outcomes will occur roughly the same number of times as black, even, and high outcomes during a betting session.

The system is quite straightforward and easy to use in roulette. You start the session with a stake equal to one base unit and increase your bet with one unit after each consecutive loss. Thus, if you start the session with a base unit of $10 and lose, your next stake would be $20. If another loss occurs on the next round, your next bet should be equal to $30 and so on.

This continues until a win occurs, in which case **the next wager is reduced by one base unit**. If you win with your very first wager at the start of the session, you continue flat betting the base unit until you lose and increase the next wager.

Stake with a Base Unit of $10 | Outcome | Profits |
---|---|---|

$10 on red | 17 black/Loss | -$10 |

$20 on black | 18 red/Loss | -$30 |

$30 on black | 21 red/Loss | -$60 |

$40 on red | 34 red/Win | -$20 |

$30 on even | 28 even/Win | $10 |

$20 on red | 12 red/Win | $30 |

$10 on high | 5 red, low/Loss | $20 |

You can register some profits with **the D’Alembert** provided that you win approximately the same number of bets as those you lose. The winning bets are made at higher stakes than the losing ones, which potentially enables you to end the session on profit.

However, there is no guarantee this equilibrium between winning and losing wagers will occur during any given session in the short-term. **A longer losing streak can eat up your bankroll** with the D’Alembert despite its less steep negative progression.

### Oscar's Grind – A Simple System

The Oscar’s Grind system first gained prominence after the publication of **The Casino Gambler’s Guide book by Allan Wilson**. It is based on a positive betting progression where you increase your stakes by one base unit after each win but stake the same amount when you lose. This should result in a win of one base unit at the end of each betting cycle. The idea here is that the player never exposes more money to risk than the amount they need to recover their previous losses and turn up a profit of one base unit. Here is how the Oscar’s Grind applies in practice:

Stake with Base Unit of $10 | Outcome | Net Profits |
---|---|---|

$10 on even | 35 black/Loss | -$10 |

$10 on black | 14 red/Loss | -$20 |

$10 on red | 6 black/Loss | -$30 |

$10 on red | 9 red/Win | -$20 |

$20 on black | 10 black/Win | $0 (you break even) |

$10 on red | 20 black/Loss | -$10 |

$10 on red | 30 red/Win | $0 |

$10 on black | 11 black/Win | $10 |

Here the player has succeeded in recouping their prior losses and has ended up with profits of exactly one unit. If they decide to continue playing, they need to start another cycle at the first level with one base unit.

## 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.