This is the famous Roulette system that originated with play on the French Rivera. In it you start with a series of about 2-5 numbers totaling the amount you will win after you have cancelled out all of your losses. You always bet the total of the two outside numbers in your bet series. Every lost bet just adds one number to your series and every win cancels 2 numbers.
Therefore, you must come out ahead if you win a little more than 1/3 of your bets, even if you don't manage to run into the house limit.
Like I just said, this system will produce a lot of small profits, but it's actually pretty dangerous. When you have a run of losses, the amount you're betting with accelerate with alarming speed, when you compare it to the amount of money you're trying to win. To cut a long story short, it's a pretty bad system unless you are very careful and keep your mind on the game.
I recommend that you should stop whenever your net loss in a single series approaches around 10X the profit you're aiming for. Think of the loss as a single game in tennis, basically as a small part of a bigger game.
I'll give you an example:
Suppose you want a unit profit of say, $6, a conservative series then may be 1-1-2-2 or 1-2-1-2. With such a series, you should have a fairly good chance of winning 10 times or more for each time you reach the $60 (see before) pre-set loss limit, especially if you limit yourself to even-chance sleepers, limiting yourself to one win and a maximum of 3 bets per sleeper. Any even chance that has not shown in 3, or even 2 spins would be eligible for this system.
If you wish to try this system without recording all spins, then it will be worth your while to learn a bet-selection procedure as a good alternative to betting on sleepers.
As a parting word on Labououchere, find somewhere where you can lay small bets, with say 10c or 25c chips and play there.
Once you get a feel for the system you may want to get more confident, but remember you're playing to win money with the best odds in tour favor, not lose money to the Roulette casino.