The Labouchère, sometimes called the cancellation system or the split Martingale, is the most involved progression most players will meet. It comes with pen and paper, a written target, and a satisfying ritual of crossing numbers off a line. It is also, like every negative progression, unable to change the odds.
How the Labouchère system works
Start by writing a line of numbers — say 1-2-3-4. Their sum, 10, is your profit target in units. Each bet is the sum of the first and last numbers of the line. So your opening bet is 1 + 4 = 5 units. If you win, cross off both end numbers. The line becomes 2-3, and your next bet is 2 + 3 = 5. If you lose, add the amount you just lost to the end of the line. Lose that 5 and the line becomes 1-2-3-4-5, next bet 1 + 5 = 6. You keep going until every number is crossed off — at which point you have booked your target profit.
Why the ritual is seductive
The Labouchère gives structure and a clear finish line, which is exactly why it feels controlled. Wins remove two numbers at a time, so a decent run clears the line quickly and banks the target. On paper the cancellation system looks like a plan with an end state, unlike the open-ended Martingale.
Where it breaks
The flaw is the same one every negative progression shares. Losses lengthen the line, and a lengthening line means rising stakes with no ceiling but the table maximum and your bankroll. A bad run can leave you with a long line of large numbers you cannot realistically clear. Each spin remains independent, the 2.70% edge is charged throughout, and no amount of crossing-off changes the expected result. The Labouchère is an engaging way to structure a session for entertainment; it is not a way to beat roulette.
A losing line, spin by spin
The danger is easiest to feel by watching a line grow. Start with 1-2-3-4, a target of 10 units, on a $1 unit. The table below follows a rough patch — more losses than wins — and shows how quickly the stakes climb even though the target never moved.
| Spin | Line before | Bet (ends) | Result | Line after |
|---|---|---|---|---|
| 1 | 1-2-3-4 | 5 | Loss | 1-2-3-4-5 |
| 2 | 1-2-3-4-5 | 6 | Loss | 1-2-3-4-5-6 |
| 3 | 1-2-3-4-5-6 | 7 | Win | 2-3-4-5 |
| 4 | 2-3-4-5 | 7 | Loss | 2-3-4-5-7 |
| 5 | 2-3-4-5-7 | 9 | Loss | 2-3-4-5-7-9 |
| 6 | 2-3-4-5-7-9 | 11 | Loss | 2-3-4-5-7-9-11 |
Six spins in, three of them losses, and the bet has grown from 5 units to 11 while the line has stretched to seven numbers. Clearing it now needs a string of wins, each of which only removes two numbers. That asymmetry — losses add one number, wins remove two — is what makes a bad run so hard to claw back, and why the Labouchère system carries a higher streak risk than a gentle progression like the D’Alembert.
The Reverse Labouchère
Flip the rules and you get the Reverse Labouchère: cross numbers off after a loss, add the amount won to the line after a win. Instead of grinding toward a fixed profit, you are trying to ride a hot streak until you hit the table limit, capping your losses at the length of the starting line. It behaves like a positive progression, closer in spirit to the Reverse Martingale, and it trades the classic version’s rare catastrophic run for many small losing sessions and the occasional large winning one. Neither direction changes the edge; they simply move the risk to opposite ends of the outcome curve.
Who it suits, and the mistakes that hurt
The Labouchère rewards players who enjoy the bookkeeping — the written line turns a session into a project with a visible finish, which for some people is genuinely more absorbing than staring at a wheel. It suits a patient bankroll and even-money bets, and it punishes three habits. The first is starting with an ambitious line: a target of 30 or 40 units means longer lines and bigger bets when a streak turns. The second is ignoring the table maximum, which can strand you mid-line with a required bet the table will not accept. The third is the belief that a long line is “due” to clear — it is not, because the wheel does not read your paper.
European versus American wheels
As with every system here, the wheel matters more than the staking plan laid on top of it. On a single-zero European wheel the even-money bets the Labouchère relies on win about 48.6% of the time and the house edge is 2.70%. On an American wheel the second green pocket drops that win chance to 47.4% and nearly doubles the edge to 5.26%, so lines lengthen faster and clear more slowly. Where French tables offer la partage, the even-money edge falls to 1.35%, which is the friendliest home a cancellation system will find. See roulette house edge explained for why that gap exists.
Compare its risk with the gentler D’Alembert and the full systems line-up.
Frequently asked questions
How does the Labouchère system work?
You write a line of numbers whose sum is your target profit. Each bet is the sum of the two end numbers. Win and you cross both off; lose and you append the lost amount. Clear the line and you have hit your target.
Is the Labouchère risky?
Moderately to high. A losing streak keeps lengthening the line and raising the stakes, and there is no guarantee you clear it before hitting the table limit or your bankroll.
Can I choose any line?
Yes. A longer line or larger numbers means a bigger target but bigger swings. A short line like 1-2-3 is gentler.
Does it beat roulette?
No. Like every negative progression it leaves the house edge untouched and relies on avoiding a long losing run, which the maths does not let you do reliably.