Labouchere System Simulator
The cancellation system—sophisticated bookkeeping that cannot outsmart mathematics.
Why This System Cannot Work
The Labouchere system is mathematically guaranteed to fail. No amount of clever sequence manipulation can overcome negative expected value. Here is why:
- The house edge never changes: Each bet still has negative expected value regardless of where it appears in your sequence. Crossing out numbers does not create value.
- Losses grow the sequence exponentially: Bad streaks make the sequence longer and bets larger, just like Martingale. The arithmetic disguises geometric growth.
- Complexity does not equal effectiveness: Sophisticated bookkeeping creates the illusion of strategy, but the math is against you on every single bet.
- Table limits guarantee failure: As the sequence grows, bets eventually exceed table limits, stranding you with unrecoverable losses.
Quick Examples
System Parameters
Starting amount
Base unit (multiplies sequence)
Maximum bet allowed
Goal for each cycle
e.g., 48.65% for roulette
e.g., 1 for even money
Experience the Labouchere (Cancellation) system firsthand. Click to place each bet and watch how the sequence evolves. Win to cancel numbers, lose to add them.
How It Works
Understanding the Labouchere System
The Labouchere system, invented by British politician Henry Labouchere in the 19th century, is one of the most sophisticated negative progression betting systems. Also known as the Cancellation System or Split Martingale, it uses a sequence of numbers to determine bet sizes and track progress toward a profit goal.
How the System Works
Unlike the Martingale which simply doubles bets, the Labouchere uses a customizable sequence. Here is a complete example:
- Create a sequence: Decide on a target profit (say, $20) and divide it into a sequence. For example: [2-2-2-2-2-2-2-2-2-2]. The sum must equal your target.
- Bet first + last: Your bet is the sum of the first and last numbers. In this case, 2 + 2 = $4 (assuming $1 base unit).
- If you win: Cancel (cross out) the first and last numbers. Your sequence becomes [2-2-2-2-2-2-2-2].
- If you lose: Add the bet amount to the end. Your sequence becomes [2-2-2-2-2-2-2-2-2-2-4].
- Repeat: Continue until all numbers are cancelled (you hit your target) or you hit table limits / run out of money.
The Appeal: Perceived Control
The Labouchere is appealing because it gives players a sense of control and sophistication:
- You choose your own sequence and profit target
- The progression is less aggressive than doubling (at first)
- Crossing out numbers feels like making progress
- The system appears mathematical and strategic
The Reality: Exponential Sequence Growth
Despite its sophistication, the Labouchere suffers from the same fatal flaw as all negative progression systems: losing streaks cause exponential growth.
Example: Starting with [2-2-2-2-2] (target: $10), observe what happens with five consecutive losses:
- Bet 1: $4 (2+2) LOSS → [2-2-2-2-2-4]
- Bet 2: $6 (2+4) LOSS → [2-2-2-2-2-4-6]
- Bet 3: $8 (2+6) LOSS → [2-2-2-2-2-4-6-8]
- Bet 4: $10 (2+8) LOSS → [2-2-2-2-2-4-6-8-10]
- Bet 5: $12 (2+10) LOSS → [2-2-2-2-2-4-6-8-10-12]
After just five losses, your sequence has nearly doubled in length, and your next bet is $14—triple your starting bet. You have lost $40 trying to win $10. The sequence manipulation did not prevent the exponential growth; it only disguised it with arithmetic instead of geometric progression.
Try It Yourself
Use the Manual Play mode below to experience the Labouchere firsthand. Watch your sequence grow and shrink with each bet. Notice how wins feel satisfying as you cancel numbers, but a bad streak grows the sequence beyond control.
Then switch to Multi-Simulation mode to run 100 trials. See the ruin rate, observe the profit/loss trajectories, and understand the statistical reality: sophisticated bookkeeping cannot overcome negative expected value.
The Bottom Line: The Labouchere system is mathematically equivalent to the Martingale. Both chase losses with escalating bets. Both hit table limits. Both face negative expected value on every wager. The only difference is packaging—the Labouchere uses addition where Martingale uses multiplication. The house edge always wins.
Frequently Asked Questions
Learn More: Guides
Why Betting Systems Always Fail
Mathematical proof of why the Martingale, Fibonacci, Labouchere, and Oscar's Grind cannot overcome the house edge.
Kelly Criterion & Flat Betting Guide
The only approaches with a mathematical foundation — flat betting as the honest baseline and Kelly for genuine positive EV.
Related Calculators
Martingale Simulator
Compare Labouchere to the classic doubling system—different mechanics, same inevitable failure.
Fibonacci Simulator
Another sequence-based progression system that cannot overcome house edge.
Flat Betting Calculator
The simplest approach: same negative EV without the catastrophic loss risk.
Risk of Ruin Calculator
Calculate your probability of bankruptcy with any betting strategy.
Educational Disclaimer
This calculator is provided for educational purposes only. It demonstrates mathematical principles and does not constitute betting advice or encouragement to gamble. All casino games have negative expected value—the house always wins in the long run. See our full disclaimer.