The Labouchere Strategy: the number-crossing-out method

The Labouchere strategy is a bet-management system in roulette on even-money chances, based on a chain of numbers and their successive crossing out. The Labouchere system in roulette relies not on blind doubling after a loss, like the Martingale, but on a more flexible principle: you set in advance how much you want to win, write this amount out as a line of numbers and close it bet by bet. Players like the crossing-out method because it lets you plan the goal of the run and see the progress, but it does not remove the house edge and requires discipline with the bankroll.

How the Labouchere system works

The principle is built around a line of numbers. Before the run the player writes down a short chain, for example 1-2-3-4. The sum of all the numbers in the line is the target profit of the run in conventional units: here 1+2+3+4=10 units.

The bet size is determined simply: take the first and last numbers of the line and add them. For the line 1-2-3-4 the bet equals 1+4=5 units. Then the crossing-out rule applies:

• on a win you cross out the end numbers - the first and the last;
• on a loss you append the size of the lost bet to the end of the line.

The goal is to cross out all the numbers. When the line is empty, the run is closed and the planned profit is collected. The logic is in the asymmetry: one win removes two numbers at once, while one loss adds only one. That is why closing the line does not require a string of wins in a row - it is enough for the wins to add up over time to roughly a third of the rounds played.

Step-by-step example by rounds

Let's take the line 1-2-3-4 with a target of 10 units and bet on even-money chances, for example on red. Let's follow a run of five rounds. The balance in the table is the running total of the run in units.

The line is closed, the run brought the target 10 units. Note: the outcomes were equal by the sign of the money result, three wins and two losses, and it is exactly the asymmetry of the rule (two numbers gone per win, one added per loss) that brought the run to the target result. Had more losses come in a row, the line and the bets would have kept growing.

Flexibility: the profit profile is set by the line

The main difference from rigid progressions is that the line can be composed to suit you. The sum of the numbers sets the target profit, while their count and size set the step of the bets and the overall character of the run.

• A long line of small numbers, for example 1-1-1-1-1-1, gives a slow and gentle course with a large number of small bets.
• A short line of large numbers, for example 5-5, is more aggressive: the target is reached faster, but the bets also grow more sharply.
• The same target of 10 units can be assembled both with the line 1-2-3-4 and with the line 2-2-2-2-2, but they behave differently.

This is convenient for bankroll planning: you see the target of the run and the approximate range of bets in advance, which means you can estimate how large a reserve of funds you need for a bad stretch.

Risks and limitations

The main danger is a string of losses. Each loss lengthens the line, and the bet grows with it, since it equals the sum of the end numbers. Several failures in a row quickly inflate both the line and the bet size, running into the player's bankroll or the table's maximum limit.

It is important to understand the maths. The European wheel is 37 pockets (0-36), and the zero belongs neither to red nor black, nor to odd and even. Because of the zero the house edge on even-money chances is 2.7%, and the theoretical return (RTP) is about 97.3%. No order of bets changes this: every spin is independent, the wheel does not remember past results, and the probability of red on the next spin is the same, however many blacks came up before it.

The Labouchere does not raise the chance of an individual bet and does not remove the house edge. It merely structures how you distribute your bets within a run and how you keep track of the goal. A breakdown of other systems and their weak points is in the review of roulette strategies, and a selection of ready-made schemes - in the piece on schemes for playing roulette.

The reverse Labouchere

The reverse Labouchere flips the crossing-out rule. Now on a win a number is appended to the end of the line, and on a loss the end numbers are crossed out. The meaning turns into its opposite: the player tries to spin up a winning streak, risking small amounts on losses, and to lock in the result on a lucky stretch.

In the direct Labouchere wins extinguish the line while losses build it up; in the reverse everything is the other way round. The reverse version is usually limited by a preset ceiling on the line or on the profit amount, otherwise one long lucky streak will sooner or later give way to a pullback and return what was accumulated. The house edge stays the same - the reverse scheme merely redistributes the bets over time differently.

Which bets to use it on

The Labouchere is designed for bets that pay 1:1, the so-called even-money chances:

• red or black;
• even or odd;
• low numbers (1-18) or high (19-36).

On these bets the win roughly equals the amount staked, so the arithmetic of crossing out works cleanly. On bets with a different payout - dozens and columns pay 2:1, a straight bet 35:1 - the classic scheme loses its sense, because the ratio of bet to win stops matching the logic of the line. For live tables it is useful to track the distribution of red and black, odd and even over the spin history: this helps you look at streaks soberly rather than imagining patterns where there are none.

A reasonable approach is to practise the system on small units, to set a limit on the length of the line and on the loss in advance, and to remember that it is a tool for keeping track of bets, not a way to beat roulette. You can follow the real statistics of live tables, how much red and black have come up and what the streaks actually were, in our free roulette statistics tracker.