Labouchère Calculator: The Cancellation System

The Labouchère (cancellation) system uses a custom number sequence where you bet the sum of first and last numbers. Win and cancel both; lose and add the loss to the sequence. Our calculator tracks your sequence, calculates next bets, and reveals why customization doesn't change the house edge.

What Is the Labouchère System?

The Labouchère (also called cancellation or split Martingale) is a negative progression where you create a sequence of numbers representing your target profit. You bet the sum of the first and last numbers. Wins cancel those numbers; losses add the bet amount to the sequence end.

Quick Answer: Labouchère = create number sequence (e.g., 1-2-3-4-5 = 15 unit goal). Bet = first + last (1+5 = 6). WIN: Cross off both ends. LOSE: Add bet to end. Cycle complete when sequence cleared. Flexible progression. Customizable risk. Same house edge. More complex than Martingale but similar outcome.

How to Use Our Calculator

Use the Labouchère Calculator →

Calculate sequence progression and bet sizing.

Step-by-Step Instructions

1. Enter Sequence: Your number string

2. Track Result: Win or loss

3. View Next Bet: First + last

4. Watch Sequence: Numbers remaining

5. Calculate Progress: Target status

Input Fields Explained

Field	Description	Example
Initial Sequence	Starting numbers	1-2-3-4-5
Target Profit	Sequence sum	15 units
Current Sequence	Active numbers	2-3-4-6
Next Bet	First + last	8 units
Session P/L	Current status	-3 units

How Labouchère Works

Setting Up

Creating your sequence:

Choose numbers that sum to target profit
Example: Want to win 10 units

Options:
1-2-3-4 (sums to 10)
2-2-2-2-2 (sums to 10)
1-1-1-1-1-1-1-1-1-1 (sums to 10)

Longer = smaller bets, more cycles
Shorter = larger bets, fewer cycles

The Betting Process

Sequence: 1-2-3-4

Bet: 1 + 4 = 5 units
WIN: Cross off 1 and 4
New sequence: 2-3

Bet: 2 + 3 = 5 units
WIN: Cross off 2 and 3
Sequence empty = DONE
Won 10 units total (1+2+3+4)

Handling Losses

Sequence: 1-2-3-4

Bet: 1 + 4 = 5 units
LOSE: Add 5 to end
New sequence: 1-2-3-4-5

Bet: 1 + 5 = 6 units
LOSE: Add 6 to end
New sequence: 1-2-3-4-5-6

Sequence grows with losses

Single Number Case

If sequence has one number:

Sequence: 3
Bet = 3 (just that number)

WIN: Sequence cleared
LOSE: Sequence becomes 3-3

Continue normally

Sequence Strategy

Aggressive Sequence

Short, large numbers:

5-5-5-5 (20 unit target)
Bets: 10, 10, 10...

Faster progression
Higher variance
Bigger swings

Conservative Sequence

Long, small numbers:

1-1-1-1-1-1-1-1-1-1 (10 unit target)
Bets: 2, 2, 2...

Slower progression
Lower variance
More grinding

Balanced Approach

Moderate sequence:

1-2-3-2-1 (9 unit target)
Bets: 2, 4, 3...

Middle ground
Reasonable bets
Flexible play

Mathematical Analysis

Why It "Works"

The cancellation logic:

Each win cancels 2 numbers
Each loss adds 1 number

If wins = losses:
Canceled: 2 per win
Added: 1 per loss
Net: Shrinking sequence

Seems to favor player

Why It Doesn't

The flaw:

Wins ≠ losses in house games
Expected wins: 48.65% (roulette)
Expected losses: 51.35%

More losses than wins
Sequence grows over time
Eventually: bust or table limit

Expected Value

Labouchère EV:

Same as flat betting
House edge unchanged

$10 average bet, 2.7% edge:
Expected loss: $0.27/bet

Custom sequences don't change math
Only change bet sizing pattern

Real-World Examples

Example 1: Clean Win

Perfect scenario:

Sequence: 1-2-3-4 ($10 unit)

Bet $50, WIN → 2-3
Bet $50, WIN → empty

Won: $100 (10 units)
Total wagered: $100
Clean completion

Example 2: Mixed Results

Typical play:

Sequence: 1-2-3-4 ($10)

Bet $50, LOSE → 1-2-3-4-5
Bet $60, WIN → 2-3-4
Bet $60, WIN → 3
Bet $30, WIN → empty

Won: $150, Lost: $50
Net: +$100 (10 units)
Sequence cleared successfully

Example 3: Growing Sequence

Losing streak:

Sequence: 1-2-3-4 ($10)

Bet $50, LOSE → 1-2-3-4-5
Bet $60, LOSE → 1-2-3-4-5-6
Bet $70, LOSE → 1-2-3-4-5-6-7
Bet $80, LOSE → 1-2-3-4-5-6-7-8

Lost: $260
Target: $100
Need many wins to recover

Example 4: Session Analysis

100 bets at roulette:

1-2-3-4 sequence ($10 unit)

Expected wins: 48-49
Expected losses: 51-52

Starting each cycle at 10 units
Some cycles complete
Some grow dangerously

Long-term: Same as flat betting
Just different experience

Variations

Reverse Labouchère

Opposite rules:

WIN: Add bet to sequence
LOSE: Cancel first + last

Rides winning streaks
Cuts losing streaks fast
Different variance profile

Modified Sequences

Custom approaches:

Restart if sequence doubles
Cap maximum bet size
Reset after X losses

All modifications = same edge
Just different experiences

Common Mistakes

1. Wrong Cancellation

Mistake: Canceling wrong ends Problem: Breaks the math Fix: Always first + last, exactly

2. Forgetting Additions

Mistake: Not adding losses to end Problem: Incomplete sequence Fix: Track every loss carefully

3. Too Aggressive Sequence

Mistake: 10-10-10-10 start Problem: Huge bets, fast bust Fix: Start conservative

4. No Limits Set

Mistake: Playing until clear Problem: Sequence can grow forever Fix: Set max sequence length

Frequently Asked Questions

Is Labouchère better than Martingale?

Different, not better. Labouchère is more flexible but still can't beat the house edge. Bets grow slower but recovery is more complex.

Can I customize my sequence?

Yes—that's the system's appeal. But customization affects variance, not expected value. All sequences face the same edge.

What's the best starting sequence?

No sequence is mathematically better. Longer sequences = lower variance. Shorter = higher variance. Choose based on preference.

How do I handle growing sequences?

Set limits: max sequence length, max bet size, or loss limit. Abandon if thresholds exceeded rather than chasing.

Does the cancellation math guarantee profit?

Only if wins exactly equal losses—which they won't on average. The house edge means more losses than wins expected.

Why is it called "split Martingale"?

It splits the recovery across multiple bets rather than one double-or-nothing bet. Less immediately dangerous, same long-term result.

Pro Tips

• Start conservative: Small numbers, longer sequence

• Track carefully: Errors compound quickly

• Set limits: Max sequence length

• Same edge: Customization doesn't help

• First + last: Always, no exceptions

Related Calculators

• Martingale Calculator - Compare systems
• D'Alembert Calculator - Simpler progression
• Fibonacci Calculator - Sequence betting
• Roulette Odds Calculator - Base game
• Expected Value Calculator - True EV

Conclusion

The Labouchère system offers the most customizable progression—create any number sequence, bet first plus last, cancel on wins, add on losses. Our calculator tracks your sequence, shows next bets, and proves why even this flexible approach cannot overcome the mathematical house edge.

Calculate Labouchère Sequence Now →

Your 1-2-3-4 sequence seems destined to clear—until three losses turn it into 1-2-3-4-5-6-7. Our calculator shows how quickly sequences grow and why the cancellation logic doesn't cancel the house edge.