Key facts
- The Labouchere betting system bets the first plus the last number of a written line. A win crosses both off; a loss adds the amount lost to the end of the line.
- Because a win removes two numbers and a loss adds only one, a line can finish even if you win only about a third of your bets.
- In our simulation of 1,000,000 lines, a 1-2-3-4 line ($50 target at $5 units) finished 93.03% of the time with a $1,000 bankroll, and the failures lost $858.50 on average.
- The chance of finishing 10 lines in a row was 48.6%, and 50 in a row 2.7%, in our calculation from the same figures.
- Longer lines aim higher and fail more often: a 1-2-3-4-5-6 line finished 86.52% of the time. Each line lost about 2.70% of everything it bet.
How the Labouchere betting system works
The Labouchere betting system turns a profit target into a written line of numbers and bets them off two at a time. It is also called the cancellation system, because winning bets cancel numbers from the line.
- Choose a target and write it as a line. A common starting line is 1, 2, 3, 4, which totals 10 units.
- Your bet is the first number plus the last number (1 + 4 = 5 units).
- Win: cross off both numbers you just used.
- Lose: write the amount you just lost at the end of the line.
- When one number is left, bet that number. When the line is empty, you are up by the target, and you start a new line.
It is played on even-money bets such as red or black. On a single zero wheel each of those wins 18 spins in 37.
A worked Labouchere line at $5 a unit
Starting line 1, 2, 3, 4, target 10 units ($50). The results run loss, win, loss, loss, win, win, win:
| Spin | Line before the bet | Bet | Result | Running total |
|---|---|---|---|---|
| 1 | 1 2 3 4 | 5 units ($25) | Loss | -$25 |
| 2 | 1 2 3 4 5 | 6 units ($30) | Win | +$5 |
| 3 | 2 3 4 | 6 units ($30) | Loss | -$25 |
| 4 | 2 3 4 6 | 8 units ($40) | Loss | -$65 |
| 5 | 2 3 4 6 8 | 10 units ($50) | Win | -$15 |
| 6 | 3 4 6 | 9 units ($45) | Win | +$30 |
| 7 | 4 | 4 units ($20) | Win | +$50 |
Four wins and three losses, and the line is finished $50 up. Notice the bets: a $50 target needed a $50 stake at spin 5. That is the Labouchere's pattern. The target stays fixed while the bets drift upward after every loss.
Why the line usually finishes
Each win removes two numbers; each loss adds one. Roughly, a line of four numbers is cleared once twice your wins exceed four plus your losses. You do not need to win half your bets for that; somewhere near a third will do over a long line. Red wins 48.6% of the time, so most lines do get cleared. The ones that do not are the ones where the size of the bets catches up with your bankroll or the table limit first.
How often it breaks: simulated lines
We simulated 1,000,000 lines of 1, 2, 3, 4 at $5 units on a single zero wheel. A line fails when the next bet is more than the money you have left.
| Bankroll | Line finishes (+$50) | Line fails | Average loss when it fails | Bet of $100 or more needed | Bet of $150 or more needed |
|---|---|---|---|---|---|
| $500 | 87.32% | 12.68% | $419.50 | 19.4% | 5.3% |
| $1,000 | 93.03% | 6.97% | $858.50 | 20.7% | 13.6% |
Doubling the bankroll halves the failure rate but doubles the failure bill. One line in five needs a single bet of $100 or more to finish, and the line that does fail usually costs close to the full bankroll, because by then the bets are large.
Strings of lines are where it shows. With a $1,000 bankroll, the chance of finishing 10 lines in a row is 0.9303 to the power 10, or 48.6%; finishing 50 in a row is 2.7%, in our calculation.
Choosing a line
The line sets your target, not your risk. With the same $1,000 bankroll ($5 units):
| Starting line | Target | Finishes | Average loss when it fails |
|---|---|---|---|
| 1 1 1 1 | 4 units ($20) | 96.84% | $865 |
| 1 2 3 4 | 10 units ($50) | 93.03% | $858.50 |
| 1 2 3 4 5 6 | 21 units ($105) | 86.52% | $849 |
A bigger target fails more often, and the loss on failure barely changes. In all three lines the average result came to close to 2.70% of the amount bet: a 1-2-3-4 line lost 2.67 units on 98.71 units bet, in our simulation.
Pundit tip: if you play a Labouchere, write your stop on the same piece of paper as the line, as a maximum single bet. When the next bet would pass it, the line has failed, and pretending otherwise is how a $50 target becomes a $1,000 loss.
Table limits break lines too
Every roulette table in an Australian casino displays a minimum and maximum bet, and approved rules settle oversized bets only up to the maximum. A limit cuts the ladder off early. In our simulation, adding a $200 maximum bet to the $1,000 bankroll cut the finishing rate from 93.03% to 89.99%, and Tasmania's rules also forbid partnerships aimed at exceeding the maximum.
Labouchere against the other systems
The Labouchere shares its shape with the Martingale strategy: frequent small successes, rare large failures. It grows bets more slowly, by adding the last loss rather than doubling. The Fibonacci betting system and the d'Alembert betting system are slower still. Oscar's Grind also targets a fixed profit per series but only raises bets after wins, and the Paroli betting system turns the whole idea around.
None of them changes the 1 in 37 edge on each bet. Try a doubling ladder in the Martingale calculator to see how quickly bet sizes run away. If you keep chasing a line you meant to abandon, our gambling help page lists free support.
Online, roulette is one of the casino games that cannot legally be offered to people in Australia. Our online roulette Australia page sets out the law and where roulette can be played in person.
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Frequently asked questions
How does the Labouchere betting system work?
Write a line of numbers such as 1, 2, 3, 4; their total is your target in units. Bet the first number plus the last. If you win, cross both off. If you lose, write the amount you lost at the end of the line. Keep going until every number is crossed off, at which point you are ahead by the target.
Why is the Labouchere called the cancellation system?
Because each win cancels numbers from the line. It is the cancelling, two numbers per win against one added per loss, that lets a line finish even through a run of mostly losing spins.
How often does a Labouchere line fail?
It depends on your bankroll and the table limit. In our simulation a 1-2-3-4 line at $5 units failed 12.68% of the time with $500 behind it and 6.97% with $1,000. A $200 table maximum pushed the failure rate from 6.97% to 10.01%.
Does the Labouchere beat roulette?
No. A finished line wins the target and a failed line loses close to the whole bankroll. In our simulation those balanced out to a loss of about 2.70% of the total amount bet, the same as betting flat.
What is a good Labouchere line?
Shorter, smaller lines finish more often but win less: in our simulation 1-1-1-1 finished 96.84% of the time for a 4-unit target, and 1-2-3-4-5-6 finished 86.52% for 21 units. The failure cost is similar in every case, because it is set by your bankroll.
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