# The Labouchere System

This popular system has existed for nearly a century and relies on even-money bets to turn a profit. It requires you to first select a profit goal, divide it into a sequence of numbers and play until the profit goal is reached. Keep reading to find out how to use this system at the roulette table.

## The Mathematical Theory of Labouchere

The Labouchere gets its name from an 18th century British politician. He based it on a system invented by 17th century mathematician Condorcet, a student of d'Alembert's work. d'Alembert believed that a win was very likely to follow soon after a loss making even-chance bets the basis for his own roulette system. Today, this is known as 'the gamblers fallacy.' Labouchere followed form choosing even-chance bets as the basis for his new system.

## How Does the Labouchere Work?

This system follows a negative bet progression pattern. Follow these steps to apply the Labouchere to your gameplay.

To apply this system to roulette, follow these basic steps:

- Select a profit goal. For example, $15.
- Divide that number into a series of units that, when added together, equals your profit goal. For the sake of simplicity, we will use $1 units. The order and number are entirely at your discretion.
- Add the first number to the last number and place units in that amount on an even-money bet.
- On a win, cross out the first and last numbers of the series. Then, use the first and last numbers of the new series to determine the number of units to bet.
- On a win, cross out the first and last numbers of the series. Then, use the first and last numbers of the new series to determine the number of units to bet.
- Repeat steps 4 and 5 until there are no numbers left in the series, and you have reached your profit goal.

3 + 2 = 5 units

2, 3, 4, 3, 2, 1, 3

2 + 3 = 5 units

Keep in mind that, the longer the series, the more difficult it can be to keep track. Many people find it useful to jot the numbers down and cross them off as they play.

Lower profit goals and shorter number series are ideal for optimum success. The higher each is, the longer it will take to gain a profit or finish a session. Time is the enemy of most roulette systems."

## Which Kind of Bets Work Best?

This particular system relies on even-money bets. These offer a 47% chance to win each spin and a low payout of 1/1. In roulette, even-chance bets include high18/low 18, black/red and even/odd. They are considered to be the lowest risk bets available in this game of chance.

## Applying the Labouchere to the Table

You decide to give the system a whirl at your favorite casino, so you start a roulette session with a profit goal of C$30 in mind. Dividing that goal into 6 units of $5 apiece, you keep things simple by choosing the number series 1, 1, 1, 1, 1, 1. Adding the first and last number together, you place 2 units on odd.

- The ball lands on 12 red for a loss of 2 units. Your net cash loss at this point is C$10. So, you add 2 to your number series 1, 1, 1, 1, 1, 1, 2 and place a 3 unit bet on odd.
- This time, the ball lands on 17 black and pays out 3 units for a net profit of C$5. This time, you cross out the first and last numbers of the series 1,1, 1, 1, 1, 1,2 and place a 2 unit bet on odd.
- Another lucky spin pays out 2 units for a total net profit of C$15. At this point, you are halfway to your goal. You cross out the leftmost and rightmost numbers again 1,1,1,1,1 and place another 2 unit bet on odd.
- You win again leaving you with only 1 number left in the series and C$5 short of your goal, so you place a 1 unit bet on odd.
- Only, the ball lands on 4 black for a loss. Undeterred, you add 1 to your series 1,1 and place a 2 unit bet on odd.
- At last, success with 3 red for a payout of C$10 which puts you at your net profit goal of C$30.

Notice how adding your losing bet amount to the series allows you to recoup your loss plus gain a small profit if the next spin is a win. This session could also have been shortened or lengthened depending on your luck. Obviously, a losing streak would result in a much longer number series stretching your budget and time limit.

## The Labouchere's Logic

Essentially, the system is designed to reach a target profit by using even-chance bets. What Labouchere failed to account for is the house edge and short-term variance in number selection. The house edge reduces the probability of achieving a win with an even-chance bet from 50% to around 47%. And, even that probability only holds true after thousands of spins.

Short-term sessions tend to play out with variances we recognize as winning or losing streaks. Some numbers turn up several times in the same hour while others don't turn up at all.

Taking all of this into consideration, it is best to make your profit goals low and number series brief. This is so that your sessions can remain as short as possible for maximum success.

## Advantages of this System

This roulette system takes advantage of high, even-chance odds. When used correctly, it can be a useful tool to keep track of losses and profit goals.

## Some Disadvantages to Consider

If you use too long a number series, you run the risk of getting stuck playing much longer than is healthy for your bankroll. This system struggles to recover from losing streaks. Each loss adds a more expensive bet to the line. Experienced players end their session before getting in too deep.

## Variations of the Labouchere

- The Johnson Progression
- Split Loss Sequencing

## The Johnson Progression Variation

Some players try to avoid rapid bet progression by using this variation. It uses a bet series that consists mostly of zeros and ends with a 1: 0,0,0,0,0,0,0,0,0,0,1. The initial bet is 0 + 1 unit. If it loses, then the 0 to the left of the 1 in the series must be replaced by a 1. The next bet is 1 unit again. It is considered a safer version, but the profit potential is lower too.

## Split Loss Sequencing

This variation was developed in an attempt to lower the cost of the bet after a lengthy losing streak. For example, the series 14, 18, 24, 34, 50, could be divided into 2 or more separate series.

14, 18, 24, 34, 50 | |
---|---|

7,9,12,17,25 | 7,9,12,17,25 |

Now, the player can add 7 + 25 for a new bet of 32 instead of 64 going into the next spin. It gives the chance to slow spending while trying to recoup some loss.

## Does This System Really Work?

When tested with a computer simulation, the Labouchere system won 95% of the time due to even-chance bets with 5% consistently going to the house. Keep in mind, this was a simulation of an unrealistic session extending thousands of spins.

As mentioned earlier, variance comes into play in real life scenarios. That is where this, or any other system, has the chance to profit or fail.

With a bit of luck and proper application, you can make it work to your advantage. Let's have a look at how this plays out when you hit a losing streak of 4 at the start of a session. The series is only 4 numbers long.

Round | Series | Unit Bet | Win/ Lose | Net Units |
---|---|---|---|---|

1 | 2,2,2,2 | 4 | Lose | -4 |

2 | 2,2,2,2,4 | 6 | Lose | -10 |

3 | 2,2,2,2,4,6 | 8 | Lose | -18 |

4 | 2,2,2,2,4,6,8 | 10 | Lose | -28 |

5 | 2,2,2,2,4,6,8,10 | 12 | Win | -16 |

6 | 2,2,2,2,4,6,8 | 10 | Win | -6 |

7 | 2,2,4,6 | 8 | Win | 2 |

Notice how the system recovers with 3 wins after 4 losses. With a bit of good fortune, you can achieve a profit even if you lose more than you win.

Of course, computer simulations don't take into account table limits and budgeting. The Labouchere can really push both when it hits a losing streak. Have a look at the bet progression for a 7 spin losing streak. This example uses a profit goal of $40 and number series of 2,2,2,2:

Unit Bet | Net Unit Loss ($5/ea) | Net Cash Loss |
---|---|---|

4 | -4 | C$20 |

6 | -10 | C$50 |

8 | -18 | C$90 |

10 | -28 | C$140 |

12 | -40 | C$200 |

14 | -54 | C$270 |

16 | -70 | C$350 |

Of course, this is a worst case scenario, but these longer losing streaks occur commonly enough to be worth planning for. Trying to come back from a losing streak this lengthy, could take a really, really long time. Unless, you happen to be lucky enough to get 5 wins right after.

## Always Gamble Responsibly

- The Labouchere instructs you to continue playing until you reach your profit goal. Put your loss limits first.
- Count the cost before beginning each session and select a bet worth of 1%-4% of your spending limit.
- Depending on the amount of your profit goal and luck, the bet progression can get costly fast. Know the table limit at the start to avoid losses.
- No roulette system is guaranteed to work! At the end of the day, it all comes down to luck.

## Is This the Method for You?

This strategy is best for players that like to have a tool to track profit goals. That said, many seasoned gamblers modify the rules to walk away after achieving a profit. The longer the session, the more likely it is that the house will win.

## The Reverse Labouchere

If you like this system but want to make the most of your winning streaks, have a look at how things play out with a positive bet progression pattern. The Reverse Labouchere uses similar rules. Only, you add your bet to the end of the series on a win and cross out the first/last numbers on a loss.