The Labouchere system:
This system is also called the 'Cancellation' system. There are many variations. In its simplest form, you write down a series or a set of numbers; say, 1 2 3 4 5 6. The series can be short or long and not necessarily sequential such as 1 1 1 3 3 5 7. The choice of a particular series depends on the type of game you want to apply it to and the odds of the bet.
Each number represents the amount in units or chips to bet. You bet the first and last of these numbers. In this example 1 and 6, which totals 7 units.
If you win, you cross out the two numbers and bet the next two 'ends' (the outside numbers). In this instance 2 and 5. If you win again you bet on the next two remaining numbers 3 and 4, and if you win that too, you would have made a 'coup' or completed one game. Then you start all over again.
If you lose, then you add that one number to the end of the series. Say you lost your first bet of 7 units (1+ 6). Then you add number 7 to the end of the series to look like this: 1 2 3 4 5 6 7 and your next bet would be 8 units (1+ 7). If you won the first bet but lost the second 2 and 5, then the series of numbers would look like this: 2 3 4 5 7.
If you work it out, you will see that when the series is completed or when you make a 'coup', there is always a profit. The negative side of this system is that you could end up betting large sums of money even if your initial bet is small.
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Gambling Betting Systems Index