# Labouchere Betting System

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The Labouchere Roulette Betting System is elegantly simple and easy to learn. It is sometimes referred to as the “cancellation system.” It involves betting in a progressive manner that begins as a predetermined series of numbers. Whenever the player wins, two numbers are crossed off from the series. Whenever the player loses, a number corresponding to the amount lost is added at the end of the series.

Because numbers are crossed off twice as frequently as they are added to the series, the Labouchere Betting System is particularly well suited to “even money” wagers like Black or Red bets at the Roulette table, Pass or Don’t Pass bets at the Craps table and Banker or Player bets at the Baccarat table.

Judging from the name of this system, one might imagine it was developed in France. However, all the credit goes to a very accomplished Roulette player from Britain named Henry Du Pré Labouchere (1831-1912). He was a writer, publisher and Victorian theater-owner, who served twice in Parliament (1865~67, 1880~1906). One of Labouchere’s favourite hobbies was gambling, which led him to believe he could beat the Roulette wheel with the right betting strategy.

Among the many betting systems Labouchere studied was a betting progression proposed by the 18th-century French mathematician Jean Le Rond d’Alembert. Based upon the “principles of equilibrium,” d’Alembert called for increasing a wager by one unit after a loss and decreasing it by one unit after a win. His premise was based on the belief that for any even-money game the number of wins and losses would gradually become equal over time. The d’Alembert progression would conclude with a profit whenever the required next bet became zero.

Although Labouchere readily embraced the idea of equilibrium for Roulette, he believed it would often take too many spins to achieve the necessary balance of wins and losses. He therefore proposed a way to profit more quickly by requiring only one win out of every three wagers to succeed rather than one out of two.

Labouchere also devised a way for the player to sequence the initial bets for greater profitability. His new progression would deliver not just a single unit of profit; it would yield whatever amount of profit the player desired. Hence, the first step in the Labouchere Betting System is to set a profit objective.

Take, for example, the player who has a goal of winning five units. This objective is expressed as the sum of two or more smaller bets, such as (a) 2+3 or (b) 1+2+2 or (c) 1+2+1+1. The order of the numbers makes no difference, nor does it matter how many numbers appear in the series. All that’s important is that the total is equal to the profit desired.

The initial wager in the Labouchere Betting System is equal to the sum of the first and last numbers in the series. For series (a), this would be 2+3 or three units; for series (b), it would be 1+2 or three units; and for series (c), it would be 1+1 or two units.

Upon winning, the player crosses off both of the numbers that were combined to determine the amount to wager. For series (a), all numbers would be crossed off; for series (b), only the middle 2 would remain; and for series (c), the central 1+2 would be left.

For the next bet, the amount wagered would again be the sum of the first and last numbers. If no numbers remain, as in series (a), the progression ends and a new one can begin. If just one number remains, as in example (b), that becomes the amount of the bet—two units. Otherwise, as in series (c), the wager would be 1+2 or three units.

Upon winning again, the remaining units would be crossed off in all three series. The progression would end, the player would claim five units in profit and a new progression could begin. However, upon losing, the player would add the amount lost at the end of the series. For series (b), this would result in 2+2. For series (c), it would be 1+2+3. The next bet must be the sum of the first and last numbers: four units for either series (b) or (c).

Playing and betting continues in this fashion, two numbers crossed off each time a win occurs or one number added to the end of the series for each loss. Gradually, all of the numbers will be crossed off, yielding a profit of five units. All that’s required is for the player to win about one spin out of every three.

If the Labouchere Betting System has a drawback, it is that as the original small numbers are crossed off with wins, any losses add bigger numbers to the series. These numbers can become large rather quickly should a losing streak occur. A series starting out as 1+2+2 can soon end up looking like 12+18+24, requiring a wager of 36 units as the next bet.

Should this occur, a solution is to break the large numbers up into smaller series, such as (2+3+3+4)+(4+4+5+5)+(6+6+6+6). Then wager only eight units (2+6) as the next bet, rather like beginning anew with a longer series that includes all losses to this point.

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