The Labouchere Staking Plan is a bet that is laid in a series of steps within a specially devised betting cycle. It has been devised specifically to ensure that out all the losses you incur along the way in the betting cycle will be cancelled out, so that, once the betting cycle has been completed, you can be sure that you will have won overall.
The Labouchere is a method of stake calculation, used principally for roulette, which operates by you selecting a series of numbers, where the first and last numbers are added together to determine the value of your stake for each successive bet. However, it can also be applied to Asian Handicap soccer betting and even to soccer "Under/Over" betting (but where, in both cases, the matches need to be carefully selected to ensure that the offered Odds return at least, and preferably more than, 1 additional Unit for each Unit placed).
The series of number selected can be as long as you wish but should not be less than four number, and so could be as simple as 1, 2, 3, 4 (but which is not recommended, because at "5" the very first bet is quite high).
The numbers need not be sequential and can even be duplicated, so a series could be, for example, 1, 1, 1, 3, 2, 2. The choice of both the particular series and the actual length of the set to be employed depends on the type of betting you want to apply it to and the Odds attaching to the bet (but never lose sight of the fact that it was designed to work for 50/50 ("evens") betting scenarios).
Your first bet would be the total of the first and last numbers in the series. If you win, you then strike those two numbers off the list, and your next stake will be the sum of the next two end numbers (the "new" first and last numbers). Should you lose, however, you add the combined value of those two numbers to the right-hand end of the list, and the next stake is that number plus the remaining first number. For this reason, it is always best to write the original series down, remembering to add to the end of the list after every loss and to strike out the two end numbers each time you have won on a bet.
You continue in this manner until you have struck out all the numbers in the list, at which point you will be considered to have achieved a coup. Then you start all over again.
Your gross winnings from each coup will be the sum of the numbers in the original list plus the value of all the numbers you had to add to the end of the list because of losses. However, your NET winnings will only ever be the sum of the numbers in your original list, no matter how many you have had to add to the end because of losses along the way.
The above explains why this system is also called the "Cancellation" system (it cancels all your losses - provided you don't hit the "house ceiling" (the maximum stake allowed by the casino) - so that you will, in theory, always make a net return equal to the total base stake amount).
There are many variations, and the Labouchere has many advocates. Whatever else we may have to say about it, at least it is far preferable to the Martingale (which, you may have noticed, we don't particularly like!).
Now, let us look at how the Labouchere works in practice when applied to roulette betting on "reds" or "blacks" (where 1 Unit stake returns 1 Unit extra on a win).
Taking the example of where your set of numbers is 1, 1, 1, 3, 2, 2, suppose you lose your first bet of 3 units (1+ 2). What you then do is add the number 3 to the end of the series so that it now looks like this: 1, 1, 1, 3, 2, 2, 3, and your next bet would be 4 units (1+ 3). If you go on to win the second and third bets, the series of numbers would then look like this: 1, 3, 2. The following table may help you to see what happens more clearly (where "Stake", "Losses" and "Winnings" all refer to "Units"):
The drawback to the Labouchere Staking Plan is that, if you lose many more times than you win within a given cycle, then the list of numbers could end up very long and require you to lay out large sums of money. This can occur even though your initial numbers (and therefore the early bets) are small. What this means is that it is possible for you to hit the "house ceiling" more often than you probably would expect, and therefore you have to spend all night playing catch-up as a result (and even then still going home with your bank severely in the red). But on a good night, when Lady Luck is smiling on you...... who knows?