Labouchere (cancellation) system: 100,000 sessions simulated
The Labouchere cancellation system writes a line of numbers and bets the ends. See what 100,000 simulated single zero roulette sessions reveal about its win rate and how often it empties a bankroll.
What it is and how it works
You write down a short line of numbers, for example 1, 2, 3, 4. Each bet is the first number plus the last. If it wins, you cross both off. If it loses, you add the amount you just lost to the end of the line.
The line is finished when every number is crossed off, at which point you have won the total of the line you started with. The catch is that a losing run makes the line longer and the bets larger at the same time.
A simple example at a base bet of 5
- Line 1, 2, 3, 4. Bet the ends: 1 + 4 = 5 units, which is 25 at a base of 5. It loses.
- The line becomes 1, 2, 3, 4, 5. The next bet is 1 + 5 = 6 units, or 30.
- That wins, so the ends come off and the line becomes 2, 3, 4.
- The next bet is 2 + 4 = 6 units, or 30.
What our simulation shows
We ran 100,000 sessions of this system against a fair single zero wheel, each session lasting up to 100 spins, starting with 500 virtual points and a base bet of 5. Those are the same defaults the app's Lab starts with. A session ends early if the bankroll can no longer cover the next required bet.
| Sessions simulated | 100,000 |
|---|---|
| Sessions that finished ahead | 31.3% |
| Sessions that finished level | 0.0% |
| Sessions that finished behind | 68.7% |
| Sessions that ran out of money | 67.8% |
| Average result per session | -84.2 points |
| Typical (median) result | -360 points |
| Average total staked in a session | 3,159.5 points |
| Loss predicted by the house edge | 85.4 points |
| Best session seen | +1,300 points |
| Worst session seen | -500 points |
| Average longest run of losing spins | 5.3 |
| Longest run of losing spins seen | 18 |
Read that table slowly. The share of sessions finishing ahead is often the number that sells a system, and on its own it is misleading: what matters is the average result, which includes the sessions that went badly.
Why this system cannot overcome the house edge
A single zero wheel has 37 pockets. An even money bet such as red wins on 18 of them and loses on 19, so every point you stake returns 36 of 37 points on average. That is a loss of 2.7027% of everything staked, and it applies to every single bet no matter what size it is or what order the bets come in.
Our simulation shows this directly. Across 100,000 sessions this system staked an average of 3,159.5 points per session. Applying the edge to that amount predicts a loss of 85.4 points. The simulation actually produced an average of -84.2 points.
The staking pattern changed how the wins and losses were spread out. It did not change the total. That is the whole story of every betting system: they move risk around, and nothing more.
Strengths and weaknesses
Strengths
- It has a defined finish line, so a completed cycle has a clear target profit.
- A single win removes two numbers, so a good run finishes the line quickly.
Weaknesses
- Losses lengthen the line and raise the bet at once, so a bad run compounds in two directions.
- Even the opening bet is several units, so it stakes much more than a flat stake from the first spin.
- It requires bookkeeping that is easy to get wrong away from a screen.
Who it might suit
The Labouchere suits players who enjoy the structure of working through a written line and who accept that a bad run makes the line grow faster than it shrinks.
Common questions
Does the Labouchere system work?
It completes its line often enough to feel effective, but in our 100,000 session simulation the sessions where the line ran away emptied the bankroll frequently, and the average result was a loss consistent with the house edge.
Why does the Labouchere stake so much?
Its opening bet is the sum of two numbers in the line rather than a single unit, and losses append to the line. Over 100 spins it stakes far more in total than a flat stake, so the same edge percentage applies to a much larger amount.
Test it yourself
Open the Lab in the app with Labouchere already selected, set your own budget, base bet, and number of rounds, and watch it play out spin by spin with virtual points.