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Reverse Labouchere

The Labouchere system can also be played as a positive progression betting system, this is known as playing the reverse Labouchere. In this version after a win, instead of deleting numbers from the line the player adds the previous bet amount to the end of the line. You continue building up your Labouchere line until you hit the table maximum. After a loss, the player deletes the outside numbers and continues working on the shorter line. The player starts their line again if they run out numbers to bet.^[1]

The Reverse Labouchere system is often used because where the Labouchere list represents how much the player wants to win, a reverse Labouchere line represents the most that the player will lose during the betting cycle. It is with this that a player with a bankroll of x can create their own line, or lines, representative of the maximum amount that they can sustain in losses.

Additionally, a player does not necessarily have to continue the system until the table limit is met or exceeded, but could instead pick a single bet that the player does not wish to exceed and make that bet their own personal limit.

Unlike the Labouchere system which (when adhered to strictly) requires a winning percentage of at least 33.34% to complete, the winning percentage needed to complete a Reverse Labouchere line is going to be dependent on both the table limit (or the maximum single bet a player is willing to make) as well as the numbers on the initial line in relation to the table limit.

For instance, if a table had a limit of $500 and a player composed a Labouchere line as follows:

50, 50, 50, 50, 50

Nine consecutive wins (100, 150, 200, 250, 300, 350, 400, 450, 500) would cause the next bet in the system to exceed the table limit, and thus the line would be completed with a player profit of $2700.

In contrast, if a player composed a Labouchere line such as:

25, 25, 25, 25, 25

Nineteen consecutive wins (50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500) would cause the next bet in the system to exceed the table limit, thus the line would be completed with a player profit of $5,225.

The length of the line in the Reverse Labouchere system is also important as it relates to the percentage of wins necessary to complete the system. For instance, if a line of:

50, 50, 50, 50, 50

Suffers three consecutive losses as soon as the system begins, then the line is completed and a new line must be started, or the player may choose to quit.

In contrast, if a line of:

50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50

Suffers three consecutive losses, then there are still six numbers remaining on the list. In the line immediately above, it would take an opening streak of six consecutive losses for the line to be completed.

All other things remaining the same, the longer a player’s line, the more the player is risking losing, however, the longer the player’s line, the better winning percentage the casino need have in order to break the player’s line.

Advocates of this system point out that when a player uses the Labouchere System, where a streak in the casino’s favor, or many mini-streaks in the casino’s favor, will cause the player to sustain a huge loss, a single streak, or a few streaks in the player’s favor using the Reverse Labouchere system will cause the player to have a huge gain.

A formula that can be used to determine how this system could fail is as follows:

Where:

    x = Number of Wins
    y = Number of Losses
    Z = Numbers on original List

When:

    x + z ≤ y * 2

The system has failed, and all numbers on the line are crossed completely out.

Given an infinite line, the Labouchere System when played by the player requires a winning percentage of at least 33.34% to complete. In contrast, for the Reverse Labouchere to fail requires only that the player lose 33.34% of the time.

Once again, the winning percentage necessary for the system completing to success depends upon a number of variables.

References

1. ^ Ontario Problem Gambling Research Center

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.