The Labouchère system only works with a factor or odds of 2. Such odds are found in roulette when betting on black or red. In sports betting it is also easy to find such odds.
With the Labouchère system you must decide in advance how much you want to win. For example, say you want to win 10 dollars. You then distribute these 10 dollars over a series of numbers, e.g.:
1 1 1 1 1 1 1 1 1 1
2 2 2 2 2
1 2 4 2 1
Say you start with the series: 1 2 4 2 1
You must then make a stake equal to the sum of the two outermost numbers: 1+1=2
If you win, you drop these two outermost numbers and are left with the series 2 4 2. You then continue playing with the new outermost numbers combined as your stake. In this case: 2+2=4.
If you lose, you add the loss to the right side of the series and get the new series 1 2 4 2 1 2, then continue to play with the two outermost numbers as your stake. In this case: 1+2=3.
After winning multiple times you will have dropped all the numbers and earned your desired 10 dollars.
In the case of consecutive losses, the series will get longer and longer and the amounts at stake will escalate.
Pros and cons:
As with any progressive gambling system, the stake can quickly escalate. As such, there is no guarantee that you will win more than you lose in a series of bets. For this reason it should be noted that this method entails serious risks.
If the stake you have to put in starts escalating too quickly, you can divide the highest amount by two and then play on with two series.
With high stakes, you can also try to win back your high stake first using a separate Labouchère series. Once you've won this back, you can return to the actual series.
For a more cautious approach, read more about the reverse Labouchère system.