Of all the different roulette betting systems, Labouchère system is one of the favourite, as it doesn't require a bankroll as high as the one needed using the Martignale betting system, and it has a sound mathematical theory as its basis.
To use the Labouchère roulette system, you first have to determine how much you intend to win; then, you split the chosen amount in a series of numbers in a line (at least 2, and no more than 5-7 – it's not advisable to have a long starting line of numbers).
As other roulette betting systems, Labouchère betting pattern is applied to even money bets only, such as red/black, odd/even or low (roulette numbers 1-18)/high (roulette numbers 19-36).
First of all, choose an amount of units you want to win (let's say, 10 units); than split this number in a series of number (you could choose to split it like this: 1-2-3-4; or a more conservative 1-2-1-3-1-2; or finally an all out offensive 3-4-3). Remember to stick with what you've chosen, as this will determine how much you'll bet on each roulette spin.
Let's assume our starting line of numbers is 1-2-3-4.
To know the size of your roulette bet, just add the the numbers at the front and end of the line: in our examples, our first bet should be 1+4 = 5.
If the bet wins, delete both the numbers (1 and 4), and add up again the numbers at the front and at the end of the betting line to determine the amount of the next roulette bet (in our example, having deleted 1 and 4, our next bet should be 3+2 = 5).
If you lose, add the number of your previous bet on the right end of your series of numbers, and don't delete any number. In the above example, bet 5 (3+2); if you lose, add a 5 at the right end of the betting line of number (which would now be 3-2-5). In this case, your next roulette bet should be 5+3 = 8.
Repeat this process until you win (then you can delete the numbers onf the left and right end of the sequence).
When you delete all the numbers in your original betting line, you will win the total of all those numbers added together (i.e. the amount you decided before starting to play).
It goes without saying that – as for all the even money bets – you should always bet on red (or black), high (or low), odd (or even), and never change your roulette bet (only its amount).
Pay close attention to your starting numbers: they mustn't be too high (as you will obviously need a higher bankroll), and the starting series of numbers must not be too long, otherwise it'll take you time to complete it, and your bets bay get out of control if you get a series of loss (even if your bets doesn't goes high as fast as with the Martingale roulette system).