From the name of a 14th century English politician, Henry Labouchère, the Labouchère betting system is very popular and has always fascinated for its mathematical subtlety and apparent complexity.
Although it remains difficult to apply in real conditions because it requires a rigor in its progression, the Labouchère method is very simple to understand. Like the other systems with negative progression (Classic Martingale, Fibonacci or d’Alembert), the Labouchère system allows to erase the losses by increasing the bets, but its peculiarity is that it does not erase all the losses with a single win but a package of several small winnings.
Rules of the Labouchère method
Although it can be applied to any type of betting; sports, horse racing or even in trading, the Labouchère bet system works better with double odds, the same chances of loss or gain as with roulette.
Before starting, the first thing to do is to divide the unit of betting into a sequence of numbers. Theoretically, the gambler is free to choose the division he wants. We will see later the importance of the distribution of this sequence.
For example, for a bet unit of $10, a possible division is 1-2-3-4. The sum of these four numbers equals 10. Note this sequence before you start.
Four rules :
- For each bet, the amount to bet is the sum of the first and last digit of the sequence, in this example the starting bet is 5 (1 + 4)
- Following a winning bet, we bar the first and the last digits of the sequence and we continue, in this example we bar 1 and 4 if we win. The sequence becomes 2-3 and we replay 5 (2 + 3)
- Following a losing bet, we add the last bet played at the end of the sequence, in this example we would have added 5 at the end of the sequence 1-2-3-4-5
- The goal is to bar all the numbers in the sequence (finish the cycle). Then start a new cycle with the same starting sequence
A clear example is the best way to understand this system :
In this example simulated on GSimulator, played Odds are 2 (US +100), probability 50% and the bet sequence is 1-2-3-4 :
|#||Sequence||Cost ($)||Result||Win ($)||Bankroll ($)|
|1||1-2-3-4||– 5||0||– 5|
|2||1-2-3-4-5||– 6||+ 6||1|
|3||2-3-4||– 6||0||– 5|
|4||2-3-4-6||– 8||0||– 13|
|5||2-3-4-6-8||– 10||0||– 23|
|6||2-3-4-6-8-10||– 12||+ 12||– 11|
|7||3-4-6-8||– 11||+ 11||0|
|8||4-6||– 10||+ 10||10|
- In this example, we start by betting the sum of the first and last digits of the Labouchère sequence, 1 + 4 = $5.
- Following the loss of the first bet, we add the played bet to the sequence, it becomes 1-2-3-4-5, and we bet 1 + 5 = $6.
- Following the win of the second bet, we delete the first and last digits of the sequence, it becomes 2-3-4, we play 2 + 4 = $6.
- After the eighth winning bet, the sequence is over, because there are two digits left, we reset the list and start again.
Benefits and risks
The concept of cycle is the principle of the Labouchère strategy, regardless of the length of the cycle, at the end of it, the gambler would have won the amount of his starting bet.
The biggest advantage of the Labouchère method is its flexibility. By adjusting the starting sequence, the gambler can control the level of risk or increase his potential profit by using large numbers in the sequence. The risk of the bet amout going up after a series of losses can be reduced by inserting zeros into the chain.
In theory, the Labouchère betting system makes it possible to make a profit even if it achieves fewer winning bets than losing bets. But it has a disadvantage, it is slow! It is often necessary to chain a long cycle before generating profit.
Another disadvantage common to all the negative progression methods such as the Classic Martingale, or d’Alembert system, is the uncertainty of the game. A series of successive losses can very quickly increase the amount of stakes in a Labouchère sequence. Certainly less than in the Classic Martingale, but enough to explode the gambler’s bankroll.
The flexibility of the Labouchère betting system lies in the possibilities of infinite combinations by changing the starting sequence and the odds used (in sports betting for example, football, basketball, baseball, hockey, tennis …).
GSimulator makes it possible to launch a simulation of the Labouchère strategy under real conditions with the possibility of changing in real time several parameters such as starting bet, odds other than 2, number of repetitions or even the limit of the bankroll. The simulator also provides the tools needed to analyze results and compare cost differences with other strategies.
Other betting systems
Other strategies and betting systems exist and try to limit the losses, or to increase the profit, by making changes to the rules of stakes following the losses (negative progression) or following the wins (positive progression) :
- Classic Martingale
Increase stake after every loss
- Great Martingale
Increase stake + unit bet, after every loss
- Fibonacci (Whittacker)
Increase and decrease stake based on the Fibonacci sequence
- Reverse Martingale (Paroli)
Increase stake after winning until stop limit
Increase stakes after a loss, descrease after a win
- Contra d’Alembert
Increase stakes after a win, descrease after a loss
- Reverse Labouchère
Remove first and last number in the Labouchere sequence after a loss, add the last bet to the sequence after a win