The Labouchere, or cancellation system, uses a list of numbers to set even-money stakes. A completed sequence reaches a chosen target, but there is no guarantee of completion before the bankroll or table limit is reached.
The practical issue is the staking rule and its risks. The name or history of a system is not evidence that it produces reliable profits.
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, like 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:
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| 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 |
The selected example ends seven units ahead after six losses and five winners. This shows that stake sizes matter as well as win counts; it does not prove an advantage over another system or over the casino.
When only one number remains, stake it once: a remaining 4 calls for four units, not eight. A win clears it; a loss appends another 4.
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The sum of the starting list is the target profit if the sequence is completed. Longer lists or larger numbers can increase stakes, exposure and time needed. A larger target is not a mathematical advantage.
A short list with large numbers still creates large cash risks. Players can stop at any time. Do not continue solely to clear a list after reaching an affordable loss limit.
A loss normally adds one entry and a win removes two, or one if only one remains. This does not guarantee completion with finite funds. An unfavourable sequence can require bets beyond the budget or table maximum.
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.
Further reading: Gambling Commission explanation of house edge.
