Labouchere Betting System

The Labouchere system is a common betting strategy that was primarily created for roulette. However, it is only useful for even-money bets – bets that pay 1:1 and have a roughly 50% chance to win. In standard roulette, this means wagers like Red, Black, Odd, Even, 1-18 and 19-36.

The system can also theoretically be used with other even-money bets, such as baccarat, sports betting, and even blackjack. However, the odds of those games are somewhat different from roulette, so we suggest sticking to the good old wheel at first.

Here’s how the strategy works:

• Step 1: Designate a win goal – how much money you want to win. For example, let’s say you wish to earn $30.
• Step 2: Split your win goal into a sequence of numbers that will be used as individual stakes. For example, our $30 goal can be split into 5-5-5-5-5-5.
  • Not all parts of the sequence have to be the same size. However, we recommend using equal units to make things easier.
  • We also recommend using multiples of 5 or 10 to make the maths easier.
• Step 3: Sum the first and last numbers in the sequence and make an even money bet. In our example, that would be 5+5=$10
  • If the bet wins, remove these two numbers from the sequence. In our example, the sequence would now be 5-5-5-5.
  • If the bet loses, add the lost stake to the end of the sequence. The sequence would now look like this: 5-5-5-5-5-5-10.
• Step 4: Repeat the process with the new adjusted stake.
  • If the previous bet won and the sequence is 5-5-5-5, the new bet would also be $10.
  • If the previous bet lost and the sequence is 5-5-5-5-5-5-10, the new bet would use a $15 stake.
• Step 5: Repeat until there are no more numbers in the sequence, or you can no longer afford to place the bets.
  • If there is only one number left in the sequence, simply use that number as your stake.

Step-by-step Examples

The Labouchere strategy is not complicated, but the number sequence changes can seem daunting to beginners.

With that in mind, we’ll go through a few examples of simulated sessions, highlighting how varied outcomes affect stakes.

Example A

Our first example will be an “average” streak of mixed results, highlighting how the Labouchere system works.

Let’s say our win goal is $25. We split the total into five units, making the following sequence:

5-5-5-5-5

The table below shows a string of 10 even money bets in roulette. Note how the number sequence is affected by bet results as well as the total bankroll change.

Example B

Example B highlights the main weakness of betting systems, which is losing streaks. Long strings of losses can skyrocket your stakes, potentially running through your bankroll or exceeding table limits.

We’ll start with the same goal and bet string – a $25 goal split into the following sequence:

5-5-5-5-5

While the escalation of stakes is not as sharp as in, say, Martingale, it’s noteworthy that lost bets continually extend the sequence. This moves the goalpost further back, which means you’ll need more bets to clear the sequence and expose yourself to more risk.

However, it’s important ot note that winning bets reduce the sequence by 2 numbers, while losing bets only add one number. Since even money bets have a roughly 50% chance to win, that means that you’re very likely to finish the sequence.

However, a single loss can sometimes wipe out the success of many smaller wins, which makes money management a priority.

Reverse Labouchere

The Reverse Labouchere is an alternate strategy that aims to capitalize on winning streaks.

As the name implies, it’s just a reversed version of the Labouchere. This means that you add the last stake to the sequence after a winning bet while crossing off numbers after a loss.

To clarify, here’s a short example of how the Reverse Labouchere system works.

• We have a win goal of $25 and split it into the following sequence: 5-5-5-5-5.
• Bet the first and last numbers in the sequence (5+5=$10)
• If the bet loses, cross off these two numbers, leaving you with the following sequence: 5-5-5.
• If the bet wins, add the stake as the last number in the sequence: 5-5-5-5-5-10
• Repeat until you reach the winning goal, or all numbers are removed.

This approach is meant to keep your losses in check while capitalizing on winning streaks.

However, we should still point out that the Reverse Labouchere does not decrease the house edge of casino games.

Where People Use It (and What Changes)

Labouchere is a fairly versatile strategy that can be applied to many games and situations. However, some stand out as the most common:

• Roulette: The Labouchere primarily works with even money bets in roulette: Red, Black, Odd, Even, 1-18 and 19-36. Note that these bets have a 48.60% chance to win in any round rather than 50%, which accounts for the game’s house edge. American roulette variants are even worse with 47.40%, while French Roulette is noticeably better with 49.32%. The higher the chance to win, the better the Labouchere will perform, which is why we recommend finding a French table with La Partage or En Prison
• Blackjack: Some players use the Labouchere as a money management system in blackjack. However, betting systems aren’t a great fit for blackjack. For starters, the main bet of blackjack has a roughly 42% chance to win, assuming basic blackjack strategy. Moreover, the player has a chance to win 3:2 instead of 1:1, which throws off the math even more. In short, using proper strategy charts is much more important in blackjack than betting systems, so using stake plans is low on the priority list.
• Baccarat: The Player and Banker bets in Baccarat are a good fit for betting systems, Labouchere included. However, the strategy still won’t help you overcome the inherent house edge. This house edge is also lower on Banker bets, which is why they’re the preferred wager. However, banker bets typically pay 0.95:1 instead of 1:1, which can complicate a lot of the maths used in Labouchere.

Risk Math You Must Understand

The best part about this strategy is that it will win a small profit most of the time.

The probability of reaching the winning goal by completing sequences while playing roulette is between 75% and 95%. The smaller the individual unit in a sequence is, the higher this chance becomes.

However, long losing streaks can quickly lead to escalating costs that require you to put up more and more money.

The bright side is that long losing streaks are not very likely. The odds of a losing streak can be calculated using the following formula:

(19/37)k(19/37)^k(19/37)k

Where k is the number of consecutive losses.

To illustrate, here are the odds of hitting a losing streak in both American and European roulette:

Other Considerations

• Risk of Ruin: The risk of ruin of any betting strategy tells you the probability of you losing your entire bankroll. The exact point of “ruin” depends on the size of your bankroll, the size of a betting unit, and other factors. You can use our RoR calculator tool to help you understand and manage the risks involved.
• Table Limits: Spending your entire bankroll is not the only risk concern. All roulette tables have pre-set betting limits. A long streak of losses can cause your stake to skyrocket, potentially going beyond the table’s maximum wager.
• Gambler’s Fallacy: Since this strategy revolves around making repeated bets, remember that the results of previous rounds do not impact future outcomes in any way. That means that a Red result is not “due” just because you hit a few Blacks in a row. The probability of an even money bet winning in roulette is 48.60% every time, no matter what the previous outcomes are.

What the Big Simulations Say (evidence, not vibes)

The risks, effectiveness, and usefulness of the Labouchere can all be tested through simulations. For example, the good old Wizard of Odds has already performed a series of tests that involve millions of simulated bets with a profit goal of 10 units.

We’ll summarise his results below.

• Single-zero roulette: As the bankroll increases, the probability of hitting the winning goal increases, going from 79.52% with 50 units to 99.26% with 2,500 units. However, the average bet reaches upwards of 22 units, which can be a big strain on most budgets. Additionally, the percentage of money lost compared to money one is around 2.7% with very little variation, highlighting that the Labouchere does not decrease house edge.
• Double-zero roulette: Largely the same pattern, but with a 1-4% lower probability of reaching the profit goal. Slightly higher average bet at 18-24 units, and consistently higher house edge at 5.26%.
• Baccarat: Profit goal probability is largely the same as single-zero roulette, ranging from 81.47% to 99.45% as the bankroll increases. The average bet ranges from 17.8 to 21.5, indicating slightly less risk exposure. The ratio of money lost to money bet remains the same as the house edge (1.05-1.23%).

The chart below highlights the session win rate compared to the bankroll. Again, the profit goal is 10 units, and a session is considered successful once it hits that goal.

EV tracks house edge; system does not create advantage.