The “Martingale” and “Grand Martingale” Roulette Systems

The “D’Alembert” Roulette System

“Wells” System – the System of “The Man Who Broke the Bank at Monte Carlo”

The “Paroli” (Parlay) Roulette System

The "Philiberte" Roulette System

The “Jaggers” Roulette System

The "Labouchere" Roulette System ("Labby")

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Since Roulette established itself as a popular game at the end of the 18^th century in France, the players tried to beat the House with all kinds of systems. Literally hundreds of roulette systems have been created. Most of them are the variations of the few basic classic systems that players played in Monte Carlo and other European gambling resorts in the 18^th, 19^th and the beginning of the 20^th century.  Below are some of those systems.
It is impossible to beat roulette using a betting system, because any roulette bet has a built-in percentage for the House. A Roulette system is just a combination of the negative expectation (producing a guaranteed loss over a period of time) bets. It can’t produce a long-term positive outcome in principle. Nevertheless, the players can get lucky during a short period of time and come out a winner. Few players got lucky with the following systems and won considerable amounts of money. Some of them were able to break the Bank and not once but few times.  It is important to know the basics of playing roulette. When you don't, you can check a site like the onlinecasino-australia.com roulette guide to learn it.

The “Martingale” and “Grand Martingale” Roulette Systems

Martingale is one of the oldest betting roulette systems devised by Henry Martingale in the 18^th century. He was a gambling house operator. Casanova played that system in the gambling houses of Venice.
Martingale is a simple “doubling-up” progression, which wants a player to double up his bet after a loss. The bets made are even money bets – Red or Black, Odd or Even and 1-18 or 19-36. Thus the sequence of bets will look like 1, 2, 4, 8, 16, 32, 64,128, 256, 512, 1024 etc. If for ex, after first 4 losses a player wins a 5^th bet, his total profit will be one unit: 16-8-4-2-1=1. The purpose of the Martingale sequence is to get back all previous losses in one win plus a profit of one unit at the end of the progression. The weakness of this system is obvious. A player may be able to go on for a long period of time winning one unit at a time, but sooner or later he’ll hit a bad run, which will result in him reaching the maximum bet allowed by a casino. In result he won’t be able to double up further to win his money back. The progression will result in a tremendous loss probably wiping out player’s whole bankroll. If a player has an unlimited bankroll, can play for a very long period of time and there are no house limits, then simple Martingale will beat Roulette and any other game of chance. Since Martingale progression doubles-up a bet after a loss, it is called a “negative progression”.

The Grand Martingale Roulette System

The Grand Martingale is one of the most aggressive betting roulette systems. It aims at getting all the previous losses plus winning 1 unit per every previous bet played. The sequence of bets is: 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc. For ex, after 5^th winning bet which followed first 4 losses the end result will be 31-15-7-3-1= +5 units or one unit profit per every bet made. In Grand Martingale the increase of the bets happens a lot faster and the total bankroll wipeout will happen sooner.
Some players don’t run progression through the same type of bets. Instead, every time they choose an arbitrary sequence of bet types – for ex, Red, Red, Black, Odd, Red, Odd, Even…etc. That, of course, does not make Martingale any worse or better and the problems of the system remain the same.

The “D’Alembert” (or Montant D’Alembert) Roulette System

Jean de Rond D’Alembert was the 18^th century mathematician who believed in the “Law of Equilibrium”. He applied that law to the outcomes of the random events, which have equal probabilities of happening – for ex, “Odd” and “Even” in Roulette game. According to this law, D’Alembert insisted that if “Odd” showed up few times, then it’s only the question of time before “Even” will occur the same number of times. That line of thinking represents the belief in the “maturity of chances”, which is the “Gamblers Fallacy”. It’s a fallacy because roulette outcomes are independent from each other events. The previous results have no effects on the current or any future spin. On every particular spin the “Odd” and “Even” have the same chances to appear even if a 1000 of previous spins were all “Odd”. The Theory of Probability only states that over a very long period of time the numbers of “Odd” and “Even” results will be, in percentage terms, very close to each other. However, how long this period might be is impossible to predict. It can take as long as 100 spins or 100000 spins or even longer.
That’s how D’Alembert system is supposed to work. After every loss a player has to add one unit to his stake. After every win he has to deduct one unit from his bet. When the “equilibrium” occurs, he is sure to be a winner. For ex, suppose a player loses five times in a row. The total loss will be 1 + 2 + 3 + 4 + 5 = 15 units. Then he wins five times with the total win of 6 + 5 + 4 + 3 + 2 = 20 units. The net result is the win of 5 units or a half a unit win per every bet played.
On the other hand, if a player first wins 5 times for a win of 1 + 1 + 1 + 1 + 1 = 5 units and then loses 5 times for a loss of 1 + 2 + 3 + 4 + 5 = 15 units, the net result will be the loss of 10 units.
The main problem of the system, of course, comes with the uncertainty about the time necessary for D’Alembert equilibrium to materialize. If a player will be losing more often than winning for an extended period of time, he’ll be forced by the system to make huge bets due to a mandatory bet increase after each loss. He’ll soon hit the house limits and exhaust his whole bankroll.

“Wells” System – the System of “The Man Who Broke the Bank at Monte Carlo”

In 1892 Fred Gilbert wrote a popular vaudeville song “The Man Who Broke the Bank at Monte Carlo”. The song was inspired by the English gambler Charles Wells who managed to break the bank at Monte Carlo not once but at least three times.
He first came to Monte Carlo in the summer of 1891. During three days at the end of July he won close to 1,000,000 francs. Every day he played continuously for 11 hours without even taking a break to eat. On the way out with his win he stopped for a while at trente-et-quarante table and broke the Bank at that game also winning $160,000 francs.
He came back to Monte Carlo in November and broke the bank again taking from the casino $250,000 francs.
He returned for the third time in January 1892. This time Luck left him and he lost heavily. That was the last time he player roulette.
There are different reports on the system used by Wells. According to one source his method of betting was based on Martingale. When he was running lucky Wells doubled up his bet after every win all the way to the maximum bet allowed. If he won three times in a row with a maximum bet, he decreased the bet and tried to repeat the whole process again. When he was going through a rough stretch in his play, he always kept his bets low.

Another source contemporary to Wells claimed that Wells used a modified D’Alembert system. Supposedly, Wells stated that if you play even money bets – for ex, Red or Black – the results on those bets rarely exceed each other, let’s say, by 10 points. Wells modified D’Alembert on the basis of that belief.
Instead of starting his progressions with 1 unit required by D’Alembert, Wells preferred 10 units. If his bet during the game increased to 20 units or decreased to 0, he would finish his playing session. He was increasing his bet according to D'Alembert by 1 unit after a loss, and decreasing it by 1 after a win. If he won 10 times in a row, his progression would produce a win of 10+9+8+7+6+5+4+3+2+1= +55 units. On the other hand, the succession of 10 losses would result in a loss of -10-11-12-13-14-15-16-17-18-19-20= -165 units. That, of course, is an obvious weakness of his approach and Wells understood it perfectly. However, he insisted that these two results are extremes, which happen rarely. More often a regular session may look like a next sequence producing a profit of +59 units: +10+9-8+9+8+7-6+7+6+5-4+5+4+3-2+3+2+1= +59. Another similar but negative sequence would produce a loss. If a player wins and then his wins and losses alternate, then such choppy sequence will produce a positive result because every loss followed by a win on a bet increased by one unit produces a net profit of one unit.
Whatever roulette system Wells played it was eventually defeated (like all other roulette systems would be) by the House percentage guaranteed by a “0” in European roulette (More correct is to say that it is guaranteed by the discrepancy between payoff ratios and the true odds of the game).  American roulette, which has “0” and “00”, would defeat Wells system even faster and he would probably never break the Bank.

The “Paroli” (Parlay) Roulette System

This roulette system has been known since 18^th century, when the players tried to use it (among other roulette systems) against the game of faro (pharaoh). Like Martingale the Paroli betting progression is also a negative one asking a player to raise the bet size after a loss. The progression, however, develops a lot slower in comparison with Martingale.
The system can be used with any type of bet. The best chances for success are with the even money bets. The basic idea of the Paroli is to play until you have two wins in a row. After a first win a player parlays his winnings. His second bet will be two times (two units) of the original bet (one unit). If a player succeeds and wins both bets, his net profit is 4 – 1 = 3 units. The table below shows basic progression of the Paroli system for the even money bets.
The progression helps a player to recover the losses for all previous bets and show the profit at the end of the sequence. For ex, if you lost 5 bets in a row, the bet #6 must be 3 units in order to produce a profit. Two successive wins with the initial bet of 3 units produce a net profit of 6x2 -3(initial bet) -7(bets lost in the previous 5 attempts) = +2 units.

The table shows that the bet size can grow dangerously fast but not as fast as with Martingale system. Some players in order to keep the bet size under control don’t go through the whole progression. If for ex, they lose a bet #8, they might take a loss and stop the session. Later, they’ll start a new session with bet #1. Many big players prefer the Paroli system over other roulette systems. They modify it to make it fit better their bankroll and suit better their psychology.

The “Philiberte” Roulette System

A player using this roulette system hopes that the Bank will not be able to win 3 bets in a row. He plays progressions consisting of 3 increasing bets. If 3 losses happen, a player starts a new progression, which uses bigger bets.

Suppose that the bets are even money bets. The first progression employed is 1, 2, and 4. If the first one unit bet is lost and a second bet of 2 units wins, the net profit is one unit. If 2 bets are lost and the 3^rd one of 4 units won, the outcome is a positive return of 4-2-1= +1 unit. If all 3 bets for the amount of 7 units are lost in succession, a player starts a new 3 bets progression: 1, 3 and 7. He plays that progression until he gets back first 7 lost units. After that he goes back to his first progression of 1, 2. and 4 units. It the second progression goes bad and 1+3+7 = 11 units are lost, a player starts a third progression with increased bets: 2, 4 and 8. He tries to recover all the previous losses of 7 + 11 = 18 units. If he is successful, he goes back to the first progression.  If not, the 3^rd progression is replaced by the 4^th one, which is:  2, 6, and 14 and if still unsuccessful the 5^th progression starts – 3, 6, 12 to be followed by 3, 9, and 21 etc….
If you have a lot of patience and enough capital, that roulette system can keep you in the game for a considerable amount of time - a lot longer than Martingale and other roulette systems..

The “Garcia” Roulette System or “Tiers Et Tout A La Boule De Neige”

This roulette system was devised by the legendary Spanish gambler Thomas Garcia who used it in the Homburg Casino. Garcia tried many roulette systems but finally made that one his system of choice. It was also occasionally played by Charles Wells in Monte Carlo.
Garcia was a traveling salesman for the French company. In his spare time he gambled to increase his income. He was a cardsharper and used marked cards and loaded dice to get consistent wins. By August 1860 he accumulated a sizable gambling bankroll and went to Homburg for the first time to try himself against casino.
He liked to bet on Red and he was betting big. Sometimes he lost heavily, but at the end of his first visit he won 240,000 francs. He had enough common sense to take his win and leave.
Two weeks later he returned and had even more success. He managed to break the Bank 5 times and at one point in time he was ahead by 1,750,000 francs. He left with the profit of more than 500,000 francs of casino money. After his first two visits he was ahead by 800,000 francs.
He came back for the third time one year later in the autumn of 1861. This time he lost all the money he brought with himself plus the money he could borrow from others during his stay. Garcia left Homburg and never returned.

When a player plays the “Garcia” system, he hopes that the Bank will not win 2 times in a row. Beginning play with a capital of 9 units, Garcia would place one third of it (3 units) on the table as his first bet. In case of a loss, the remaining two thirds (6 units) would be the second bet.  That’s why the initial bankroll of 9 units is needed. If a player wins his first bet of 3 units, his capital grows to 9 + 3 = 12 units if he bets on even money bets. The next bet is one third of the new capital of 12 units or 4 units. If this bet is lost, the two thirds from 12 or 8 units become the next bet. In case of a win, the new capital is 8 + 8 = 16 units. After that the bet is one third of 16 or 5 units. If won, the new bankroll is 16 + 5 = 21 units. The next bet, obviously, is 7 units and the progression continues in the same fashion. If a player makes a dozen of wins with this system without encountering the two consecutive losses, he can run up his initial capital of 9 units to 200 units or so. If 2 losses happen in a row, the most he can lose is his initial bankroll of 9 units only – no more, no less. If that happens, a player stops his session.
As you see, this roulette system consists in always dividing your capital by three, and staking first a third, and in the event of a loss, the remaining two thirds. Many players like to make bets on a color opposite to the previous winning color. If a player comes to a table and sees that Black appears, he puts 3 units on Red. His session could look like the sequence shown in the table below. The session will result in increasing his initial 9 unit stake to 202 units.

The strength and attractiveness of that roulette system in comparison with other roulette systems is that a player won’t lose more than 9 units, but if lucky, can win a significant amount of money.

The “Jaggers” Roulette System

In the History of Monte Carlo, Joseph Jaggers became a legend. He was an intelligent mechanic or engineer from the north of England. He was not a gambler, but he had heard of Monte Carlo, and of the wonderful roulette-wheels so ingeniously made that no one could beat them. Mechanic by trade he knew how impossible it is to maintain a delicate machine in an absolutely perfect condition for a length of time. He consequently realized that at least some Roulette Wheels in the rooms of Monte Carlo were sure to be untrue, in a greater or less degree, and he did not see why he should not use his knowledge to try to gain an advantage in casino. Thus, the Jaggers' system exploited faulty equipment instead of relying like other roulette systems on any betting progression or a particular combination of bets.
When he arrived in Monte Carlo he did not intend to play. It was the wheels themselves that he wished to see. He found out that he was not supposed to keep a seat at the table and watch the game for a long time without playing.  In order to study it in peace he began playing with minimum bets. He had a favorite table where he happened to feel more at home than at any other; and, while laboriously taking down numbers in order to make a record, he hit upon an astonishing discovery. Some of the numbers appeared more often in a day’s play of about five hundred bets than they had a right to do mathematically, according to the Theory of Probability. Jaggers continued his tests for several days, until he was satisfied that the particular roulette wheel under observation had some mechanical defect – that it was not truly balanced, but had a bias in one direction which caused the ball to fall more often in one quarter of the cylinder than in the others.
On that fault, not of roulette in general as a game, but of this roulette wheel in particular, did Jaggers then and there found his amazingly successful “system”. He decided to risk in his roulette venture all the money he had, knowing that, though he must fail occasionally, he ought to win far more often than lose. At first he played quietly, with small stakes. Then he increased them until soon he was playing with maximum on the wheel’s favorite numbers, and winning immense sums of money. Feeling sure of his ground, Jaggers now engaged a staff of men to play for him, taking turns at the table as the croupiers do, and his wins continued till the Casino authorities became seriously alarmed. Never had the Casino, in the whole history of gambling at Monte Carlo, suffered so severely. Seeing that Jaggers always played at the same table, the management removed the cylinder from that table at night and transferred it to another table.
Jaggers, however, had expected the possible change in luck because his wheel of fortune was lost among other wheels useless for his “system”. To avoid that, he had observed on his cylinder a tiny white speck by which he could identify it among many others apparently alike. Each morning, on arriving at the table, he glanced at the wheel and made sure of the white speck before starting to “work”. As soon as he saw the white speck, he and his staff of clerks began to kill the table again.
In four days Jaggers had taken from the Casino the unprecedented sum of 1,500,000 francs. The authorities began to suspect that all the cylinders were imperfect. The maker was sent for, and each wheel was subjected to a rigid scrutiny. The faulty one was discovered and taken away, and next morning Jaggers' tide of fortune turned. For a few days he went on playing, and lost back to the Casino some 500,000 francs of his enormous winnings. Then he was wise enough to see that he was finally beaten. He discharged his staff, ceased play, and retired with the comfortable sum of 1,000,000 francs. Never did he appear again at Monte Carlo; but his memory lived there since as a classic one.