the D'Alembert System

The D'Alembert System | The Contra D'Alembert System | The Reduced D'Alembert System | Hands On the table

The D'Alembert System
     The D'Alembert System is the most famous progression born around the middle of 1700 and invented by one of the major mathematician and philosopher of the French Enlightenment.
The D'Alembert is also known as "The Pyramid", because of the shape of its fluctuating wagering structure.

General Concept
     It was designed for use on simple chances bets (Red/Black, Impair/Pair, Manque/Passe), where you alternate with two events but can be used on any even chance bet.
The scope for this progression is to reach a balance between two chances.
In other words, D'Alembert works under the assumption that over a period of time there will be an equal number of "Reds" and "Blacks".
Once you've reached the balance, you will register half unit winning for every bet (or one unit for every 2 bets).

Rule
     Its pretty easy: increase your bet one unit after every loss, and decrease one unit after every win.

Follow these simple points:
1) fix the unit value (chip = $1, $5 or any other value)
2) start the session by placing one unit on one of the even chance bets (e.g. "Black")
3) after a losing bet you increase the next bet by one unit.
4) after a winning bet you decrease the next bet by one unit.
5) when you win by placing one unit, on the next spin you have to bet one unit again.
6) stop bets when a balance between two chances is reached (equal number of "reds" and "blacks").
7) start a new betting session from point 1).

Pratical examples
     Let's follow this first example:

- Spin #1
place 1 unit on Black,
Red outcomes, you lose
the result of this spin is -1 unit
bankroll after the spin is -1 unit

- Spin #2
increase your bet one unit: place 2 units on Black
Red outcomes again, you lose
the result of this spin is -2 units
bankroll after this spin is -3 units

- Spin #3
increase your bet one unit: place 3 units on Black
Black outcomes, you win
result of this spin is +3 units
bankroll after this spin is 0

- Spin #4
decrease your bet one unit: place 2 units on Black
Red outcomes, you lose
result of this spin is -2 units
bankroll after this spin is -2 units

- Spin #5
increase your bet one unit: place 3 units on Black
Red outcomes, you lose
result of this spin is -3 units
bankroll after this spin is -5 units

- Spin #6
increase your bet one unit: place 4 units on Black
Black outcomes, you win
result of this spin is +4 units
bankroll after this spin is -1 unit

- Spin #7
decrease your bet one unit: place 3 units on Black
Black outcomes, you win
result of this spin is +3 units
bankroll after this spin is +2

- Spin #8
decrease your bet one unit: place 2 units on Black
Black outcomes, you win
result of this spin is +2 units
bankroll after this spin is +4 units

The two chances after 8 bets have reached the balance (4 "Reds" - 4 "Blacks"), the game on the Black has produced 4 winning pieces/units (8 spins divided by 2)

If we analyze three more hypothetical cases based on 12 bets, where the balance is reached, you can notice that the results are different.
You can see the examples referred to combination RED/BLACK supposed betting always on RED.

In all three examples presented there is a perfect balance as for the 12 spins taken into consideration you win 6 times.
However while in the first two examples Red and Black are distributed mainly in a normal way and the final result is positive, in the third case we register a lost of nine units.
In order to close the game with a positive result you must search for the balance not when the game starts but when the negative series of Black begins.
So in this case you would need extra spins to win the gaming session.
In these examples the figure 0 will not be taken into consideration.
Normally, during low bet series, it will not affect the gaming session.
But, if the zero outcomes during high bets, it will cause disastrous effects.

Conclusions
     D'Alembert gives you two bonuses, as first you do not increase your bets as rapidly which gives you the chance to stop a session and accept a small to medium lost.
Secondly, you can find that your bankroll is positive before a session is complete, this gives you the option to cut short a session with a small win.
The downside is that a session can last for many spins, so you should always give yourself time to run through a full session.
The main problem is the same as the other progressive systems: you will win little and often but when you lose it will probably wipe out all previous winnings and eat into your main bankroll.

As with all progressive systems you must be very careful when you use them, the D'Alembert is not as dangerous as the Martingale but it can still be the cause of very large losses.
The major negative aspect for the D'Alembert system is that you will win only if the balance is been achieved starting from a series of negative spins.
The D'Alembert system works correctly only when a balance has been reached between winning and losing bets.

The classic D'Alembert progression is been played with double chance (dozens and columns).
As the winning is for 2 pieces plus the bet, the game mechanism is the following: augment the bet with one unit after two bets lost and decrease by one unit after one winning bet.
There are numerous variations and many combinations but this one is for sure the most famous.

The Contra D'Alembert system
     This system presents a variant in comparison with the classic D'Alembert system and therefore all previous considerations made are just the same.
The Contra D'Alembert system has been projected when it was clear that the classic D'Alembert system required a great amount of money and the balance return would be delayed later with hundreds of spins.

General Concept
     As the word says the Contra D'Alembert system is exactly the opposite of the classic D'Alembert system and it has been conceived to gain as much as possible during the positive series (where as it doesn't occur in the classic D'Alembert).
In this case, the main purpose is to obtain profit on reaching the balance between two chances.

Rule
     Its pretty easy again: Increase your bet by one unit after every win and decrease your bet by one unit after every loss.

1) fix the unit value (chip = $1, $5 or any other value)
2) start the session by placing one unit on one of the even chance bets (e.g. "Black")
3) after a losing bet you decrease the next bet by one unit
4) after a winning bet you increase the next bet by one unit
5) when you lose by placing one unit, on the next spin you have to bet one unit again
6) stop bets when a balance between two chances is reached (equal number of "reds" and "blacks")
7) start a new betting session from point 1)

Pratical examples

- Spin #1
place 1 unit on Black
Red outcomes, you lose
the result of this spin is -1 unit
bankroll after the spin is -1 unit

- Spin #2
place 1 unit on Black again
Red outcomes again, you lose
the result of this spin is -1 unit
bankroll after this spin is -2 units

- Spin #3
place 1 unit on Black again
Black outcomes, you win
result of this spin is +1 unit
bankroll after this spin is -1

- Spin #4
increase your bet one unit: place 2 units on Black
Red outcomes, you lose
result of this spin is -2 units
bankroll after this spin is -3 units

- Spin #5
decrease your bet one unit: place 1 unit on Black
Red outcomes, you lose
result of this spin is -1 unit
bankroll after this spin is -4 units

- Spin #6
place 1 unit on Black again
Black outcomes, you win
result of this spin is +1 unit
bankroll after this spin is -3 unit

- Spin #7
increase your bet one unit: place 2 units on Black
Black outcomes, you win
result of this spin is +2 units
bankroll after this spin is -1

- Spin #8
increase your bet one unit: place 3 units on Black
Black outcomes, you win
result of this spin is +3 units
bankroll after this spin is 2 units

The two chances after 8 bets have reached the balance (4 "Reds" - 4 "Blacks"), the game on the Black has produced 2 winning units.

Once again in this case, when reaching the balance (not considering the zero) it can produce a negative result, see the following example:

Conclusions
     As this system offers reasonable protection of the downside, it's one of the best to try (if you're determined to play systems), because when losses come, your bets regress to the base level, where they will stay until the winnings return.
This means there are few large winnings and more smaller losses but also the winnings are likely to get fairly well wiped out with one loss after a group of winnings.
It's not bad to exploit a winning run, if it is used as a sporadic technique.
In fact, it has been known to employ betting schemes that are based around this concept!

Reduced D'Alembert
     A variation that permits to optimize the progressions.
We remind you the two principal faults present in the d'Alembert progression:

1) In certain balance stages, when the first bets are winning, on reaching the balance final result could be lost.
2) The balance could be reached after a certain time prior considering it useful.

General Concept
     This version has been projected to reduce the huge amount of wagered money you normally risk in the classic D'Alembert system and permits to extend your gaming sessions in a more confortable way.
This progression doesn't aim to reach the balance but mainly to win a few units.

Rule
     Increase your bet by one unit for every five units loss and decrease by one unit for every five units recovered.
Restart a new gaming session every time that session is a positive bankroll even with only one unit.

Follow these simple points:
1) fix the unit value (chip = $1, $5 or any other value)
2) start the session by placing one unit on one of the even chance bets (e.g. "Red")
3) Increase the bet by one unit every time the bankroll is negative for 5 units
4) Decrease the bet by 1 unit every time 5 units are recovered
5) Every time the temporary bankroll is positive (accumulated result) even with only one unit, start a new betting session from point 1)

Pratical examples
     See this example:

In the first two spins there are two gaming sessions both with one winning unit and therefore after two spins the bankroll is +2.
The third gaming session is longer, exactly 14 spins, before it can produce a positive accumulated result.
At the end of 16 spins the bankroll is +3 units.

Conclusions
     As already stated, this system permits to drastically reduce the risks but rely on a minor profit and therefore you can play this system in a relaxed manner with a small amount of money.

Hands on the table
     Now, you can test this progression on Prestige's French Roulette for practice or for real money.
At the beginning and until you will not feel acquainted with the system, we strongly advise you to try it during "For Practice" session.
You could also download this pdf file.
It contains a table suited to take notes of the spins result (coups), bets and bankroll.
We suggest to print and use it for your gaming sessions.
In order to save it on your computer right click on the link and select "Save Target as..."

Good luck and have fun

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