Your bets seesaw up and down quite a bit, but eventually you will find yourself back at the basic bet of one unit. Your losses have been balances off by an equal numbers of wins (see example above). Therefore, your one-unit increases have been balanced off by your one-unit decreases, bringing you back to your starting point. The amazing thing that, when this happens, you will find you have won a net profit of one unit for every win in the sequence. Although you lost as many times as you won, instead of breaking even, you have made a profit.

This system is based on a theory (see origins below) that doesn't work. It requires the wheel to come up with the same amount of wins as losses. There is no law of nature to make this happen. The wheel or dice don't have a memory, so the previous spins / rolls won't affect the subsequent ones. It is only the ratio of the difference between the number of red spins and the number of black spins that becomes smaller as the number of trials increases, just as the "Law of Large Numbers" dictates. The absolute difference between red trials and black trials will actually keep getting larger as the number of trial increases. Nature is actually moving away from equilibrium (same amount of red and black)., in the sense in which d'Alembert used the term.

The d'Alembert system is not as dangerous as the Martingale, because it does not involve such a steep progression. However, it still forces you to increase your wagers when you are losing. So you will get stuck when your bankroll runs out.

Named after Jean Le Rond d'Alembert, an eighteenth-century French mathematician best known for formulation the law of equilibrium. This system holds that when two events have an equal chance of occurring, if one begins to happen more frequently than the other, the alternative event must eventually begin to occur more often in order to achieve equilibrium. 

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Your bets seesaw up and down quite a bit, but eventually you will find yourself back at the basic bet of one unit. Your losses have been balances off by an equal numbers of wins (see example above). The amazing thing that, when this happens, you will find you have won a net profit in the sequence. Although you lost as many times as you won, instead of breaking even, you have made a profit. 

1) This system is based on a theory that doesn't work: It requires the wheel, dice or whatever to come up with the same amount of wins as losses. There is no law of nature to make this happen. The wheel or dice don't have a memory, so the previous spins / rolls won't affect the subsequent ones.

2) When you have a bad session and keep hitting more losers than winners, your bets steadily escalate until the required bet exceeds the table limit, or your bankroll runs out, which is more likely to happen.

3) You are constantly in the risk of losing a lot of money against winning a small amount of $.

4) Statistically a Labouchere / Cancellation System with a 30-unit target (e.g. $30) wins 20 out of 21 times. The hitch: The 20 winning sequences produce a gross profit of 600 units, while the 1 losing sequence produces an average loss of 1,024 units, giving the player a net loss of 412 units.

The Labouchere / Cancellation System was invented by a French mathematician, the Marquis de Cordorcet, who died in 1794. It was first popularized by Henry Labouchere, an English world traveler, member of Parliament, and gambler, who died in 1912.

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Players figure, doubling up after every loss, they eventually win one bet, and when that wager is won, they'll come out ahead. 

This system doesn't work and never has.

1) Betting this way, the numbers soon become large, and after nine losses in a row, the tenth bet has to be $512. At this point the player is  exceeding the usual house limit of $500. Should he lose this wager too, he would now be behind $1011, with no way to break even using this system. Even if he won the tenth bet at $500, he'd still be down $11. And even if there was no table maximum or an very high one, you have to consider points 2) through 4).

2) To lose ten times in a row is mathematically more likely to happen than to win 1000 of those bets, especially at American Roulette with a house edge of 5.26%.

3) All those wagers, all that aggravation, all that heart-stopping anxiety to win the initial bet of $1 makes this system look foolish. When you lose, you lose big. And when you win, you win small.

4) When playing with real money, a player already down to $255 may lose heart and either lower the next bet or skip it altogether.

Variation I
The Grand Martingale System

This is similar to the simple Martingale System, but you add one extra unit to each double up. This method escalates the bets even more wildly and makes you lose your money more fast.

Example with $500 maximum bet table

The Martingale System is probably the oldest, easily the most popular, and definitely the most dangerous of all betting systems.
The source of the name is uncertain. The most plausible theory is that it was named after Henry Martindale, a West End London gambling house operator during the late 1700s.
With time, the word became altered to Martingale. 
The system is known to every casino employee in the world, all of whom consider playing it a sign of a true amateur. It is also known as the double-up system.
The Martingale System first became famous when Charles Wells used it in 1891 to win forty thousand pounds in three days of play in Monte Carlo, starting with a stake of only four hundred pounds. Well's fame spread when his achievement was immortalized in "The Man Who Broke the Bank at Monte Carlo", a popular song at the turn of the century. 

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