The Labouchere System

french_rouletteThe third betting system, which enjoys wide popularity worldwide, is the Labouchere system, also known as a cancellation system. Similar to the Martingale approach, it focuses on progressive betting, but unlike the latter, it has a lesser chance to encounter the table limit.

The name appears to be French in origin, but history has shown a link to a minister of finance, who was in the service of Alexandrina Victoria, Queen of Great Britain and Ireland from 1837 until her death in 1901. The name of this finance minister was Labouchere, a man famous for his passion for gambling. However, there has been no evidence that he actually devised the betting system.

System Specifics

What a player is faced with in this case, is a more elaborate system, which can be applied only to even-money outside bets. The whole betting process begins with an arbitrary line of numbers, for example, as the following: 1-1-2-3. The original bet usually represents the sum of the first and the last numbers in the sequence, or in our case it is 4 (1 + 3). We place the initial bet of 4 and, if it turns out to be a winner, we need to cancel the first and the last numbers in the sequence above. This way we will come to the following: 1-2, the sum of which will give us our second bet (1 + 2 = 3). In case it wins as well, we need to remove the first line of numbers and begin a new one, which is precisely the same. An important moment to note is that whenever a line is removed, the net result will equal the sum of the numbers featured in the original line. In our case it will be 7 (1 + 1 + 2 +3).

What should we do, if the opposite scenario unfolds – our initial bet loses? Taking into account the sequence above, our first bet equals 4 units. If it indeed loses, its amount needs to be added to the end of the sequence. This way we come to a new number sequence: 1-1-2-3-4. From this point on, our second bet will equal the sum of the first and the last numbers in the new sequence, or 5 (1 + 4). In case the second bet loses as well, its amount will be added to the end of the sequence, or the latter will be extended to: 1-1-2-3-4-5. Let us take a look at the following example:

Bet Number Bet Amount Outcome Net Result
1-1-2-3 4 loss -4
1-1-2-3-4 5 loss -9
1-1-2-3-4-5 6 loss -15
1-1-2-3-4-5-6 7 win -8
1-2-3-4-5 6 win -2
2-3-4 6 loss -8
2-3-4-6 8 loss -16
2-3-4-6-8 10 win -6
3-4-6 9 win 3
4 4 loss -1
4-4 8 win 7

As can be seen from the table, the last win enabled us to clear the sequence with a net result of 7 units, which equals the sum of the numbers in the original sequence. In addition, note that we achieved a net result (gain) of 7 units by placing 6 losing bets and only 5 winners, which simply confirms how advantageous the Labouchere system is when compared to the D’Alembert approach, for instance.

The table also shows that when the sequence was reduced to as short as a single 4, the bet that followed was also equal to 4. It is not a coincidence! As a rule, in case the sequence is reduced to a single digit, the latter is considered as the sum of the first and the last numbers.

Players are free to determine the length of their original sequences as well as the numbers they will feature. The larger the numbers and the longer the sequence is, the more ”aggressive” the play itself becomes. If one chooses a longer sequence, he/she will not obtain any other advantage than a higher net result (gain). And let us not forget, that longer sequences will require a longer period of time to be played out.

By choosing a short starting sequence with large numbers, a player will likely achieve a higher net result (gain), but this will also raise the betting levels and, respectively the amount of money required. A betting sequence can be abandoned whenever one wishes to, but a player can secure a potential net gain for himself/herself, only if he/she plays out the entire sequence. Because a loss adds one number and a win cancels two numbers, any sequence will eventually be played out. A long series of losses can lead to higher betting levels, but the chance of the table limit being hit is relatively low. However, that is not the case with more aggressive original sequences.

The initial number sequences may range from very mild to very aggressive, as shown in the table below.

Mild vs Aggressive
Mild

1-1
1-2
1-1-1
1-2-2
Aggressive 1-2-3-4

Reverse Labouchere system

Similar to the regular system, a sequence of numbers is chosen, while the first bet represents the sum of the first and the last numbers in that sequence. From this point on, the rules of play are reversed. In case a win occurs, a player needs to add the amount of the bet to the end of the sequence. In case a loss occurs, the player needs to cancel the first and the last numbers in the sequence. When the line of numbers is cleared, the result achieved by the player will be a net loss instead of a net gain.

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