The elegantly simple Labouchere Roulette Betting System is sometimes called the “cancellation system.” It consists of a progression of bets that start off as a series of predetermined numbers. Every time the player wins, two of the numbers are crossed off. Every time the player loses, a number representing whatever amount was lost is added to the end of the series. By crossing off numbers twice as frequently as they are added, the Labouchere system is especially well suited to even money wagering such as the outside betting areas of Roulette.

Born in Britain

In spite of his French-sounding name, Henry Du Pré Labouchere (1831-1912) was British. He worked as a writer, publisher, and Victorian theater-owner, and he served twice in Parliament, from 1865 to 1867 and again in 1880~1906. Among avocations, Labouchere loved to gamble, spending much of his time playing Roulette, a game he believed could be beat with the right betting strategy.

Upon reading the works of 18^th-century French mathematician Jean Le Rond d’Alembert, Labouchere came across the d’Alembert betting progression. It was based upon the “principles of equilibrium” and had attracted a popular following. Briefly, d’Alembert had recommended increasing a wager by one unit following a loss and decreasing it by one unit following a win. He reasoned that for any even-money game the wins and losses would become equal over time. The progression would end whenever the required next bet was zero.

Labouchere appreciated the concept of equilibrium, but he thought it often took too many spins to achieve the required balance of wins and losses. The politician therefore set about devising a way to profit that would require just one win out of every three wagers instead of one out of two. He also came up with a way for the player to set up the initial bets, so that completion of the progression would yield not just a single unit of profit but whatever profit objective was desired.

Playing the Progression

The Labouchere Roulette Betting System begins by setting a profit goal, such as five units. The player writes down the desired amount a sum of smaller bet, such as (a) 1+2+2 or (b) 1+1+2+1 or (c) 2+3. The order of the numbers is not important, and neither is how many numbers appear in the series. All that matters is that the total is identical to the profit goal.

The amount that is wagered initially is the sum of the first and last numbers in the series. For series (a), this would be 1+2 or three units, while for series (b) it would be 1+1 or two units and for series (c) it would be 2+3 or five units.

Upon winning, the player crosses off the two numbers just wagered. For series (a), only the middle 2 would remain. For series (b), what remains would be 1+2. For series (c), all numbers would be crossed off. Again, the next bet would be the sum of the first and last numbers. If only one number remains, as in example (a), that is the bet—two units. If no numbers remain, as in the case of (c), the progression ends and a new one can begin.

Upon winning again, the remaining units would be crossed off in all examples, the progression ends, and the player would claim a profit of five units. Upon a loss, however, the player would add the amount of the loss at the end of the series. For series (a), this would result in 2+2. For series (b), it would be 1+2+3. The next bet must be the sum of the first and last numbers, i.e. four units for either series (a) or (b).

Playing and betting goes on in this way, crossing off two numbers each time a win is recorded or adding one to the end of the series for each amount lost. Over time, all of the numbers are crossed off, resulting in five units of profit, as long as the player can win about one spin out of ever three.