Roulette Labouchère Calculator: The Cancellation Method

The Labouchère system uses a number sequence to determine bet sizes—crossing off numbers when you win, adding when you lose. Our calculator tracks your sequence and shows why this elegant system, like all betting progressions, cannot overcome the mathematical house edge.

What Is the Labouchère System?

Also called the cancellation system or split Martingale, Labouchère uses a sequence of numbers. Each bet equals the sum of the first and last numbers. Wins cross off both ends; losses add the lost amount to the end. Complete the sequence to achieve your target profit.

Quick Answer: Start with a sequence like 1-2-3-4 (total = target profit of 10 units). Bet first + last (1+4 = 5 units). Win = cross off both ends (sequence becomes 2-3). Lose = add bet to end (sequence becomes 1-2-3-4-5). Complete sequence = target achieved. But house edge still applies: expected loss = total wagered × 2.70%. Labouchère gives structure but doesn't change the math.

How to Use Our Calculator

Use the Labouchère Calculator →

Enter your sequence to track progression and outcomes.

Step-by-Step Instructions

1. Set Initial Sequence: Your starting numbers

2. Enter Bet Result: Win or Loss

3. View Current Sequence: Updated numbers

4. See Next Bet: First + last sum

5. Track Progress: Toward target or expansion

Input Fields Explained

Field	Description	Example
Initial Sequence	Starting numbers	1-2-3-4-5
Current Sequence	Active numbers	2-3-4-6
Next Bet	First + last	8 units
Target Profit	If completed	15 units
Current P/L	Running total	-12 units

The Labouchère Method

Basic Rules

1. Create sequence (e.g., 1-2-3-4)
2. Bet = First number + Last number
3. WIN: Cross off first AND last numbers
4. LOSE: Add bet amount to END of sequence
5. Repeat until sequence is empty
6. Empty sequence = target profit achieved

Example Sequence

Starting: 1-2-3-4 (target: 10 units)

Round	Sequence	Bet	Result	New Sequence
1	1-2-3-4	5	WIN	2-3
2	2-3	5	LOSE	2-3-5
3	2-3-5	7	WIN	3
4	3	3	WIN	(empty)

Result: Sequence complete, +10 units profit

Target Profit Calculation

Target profit = Sum of initial sequence

1-2-3-4 = 1+2+3+4 = 10 units
1-1-1-1-1 = 5 units
2-3-4-5-6 = 20 units

Each crossed pair contributes its sum
Complete sequence = full target achieved

Why Labouchère Seems to Work

The Appeal

Structured approach to betting
Clear target profit
Wins cross two numbers
Losses add only one
Feels mathematically sound

The Illusion

Winning sessions are common:
Complete sequence = profit
Looks like "winning system"

But losing sessions are severe:
Sequence can grow very long
Bets can become very large
One bad run = large loss

Mathematical Reality

Expected Value

Every roulette bet: -2.70% EV

Labouchère total wagered varies:
If you bet 100 total units:
Expected loss: 2.7 units

No matter how bets are sized
House edge applies to all

Win Rate vs Profit

Labouchère might complete 60% of sessions
Each completion: +10 units (example)
Each failure: -50 to -200+ units

60% × +10 = +6 units
40% × -50 = -20 units
Net: -14 units

Wins are frequent but small
Losses are rare but large

Real-World Examples

Example 1: Successful Completion

Sequence: 1-1-2-2-3 (target: 9 units)

Start: 1-1-2-2-3, bet 4, WIN → 1-2-2
Bet: 3, LOSE → 1-2-2-3
Bet: 4, WIN → 2-2
Bet: 4, WIN → (empty)

Total wagered: 4+3+4+4 = 15 units
Net result: +9 units
Completion achieved

Example 2: Growing Sequence

Sequence: 1-2-3 (target: 6 units)

Start: 1-2-3, bet 4, LOSE → 1-2-3-4
Bet: 5, LOSE → 1-2-3-4-5
Bet: 6, LOSE → 1-2-3-4-5-6
Bet: 7, LOSE → 1-2-3-4-5-6-7

After 4 losses:
Sequence sum: 28 units
Next bet: 8 units
Already 4× original target

Example 3: Long Session

100 spins, $5 base, 1-1-2-2-3 sequence

Simulation:

Completed 3 times: +$45
Failed once (table limit): -$200
Net: -$155

Sessions looked good until failure
One bad sequence destroyed profit

Example 4: Recovery Math

Sequence grown to: 2-3-5-7-9-11

Analysis:

Sum: 37 units (you're down 37)
Next bet: 13 units
Need 3 wins to complete:
13+12+11 = 36 units of bets

If all win: Recover +37 units
If any lose: Sequence grows more

Recovery possible but not guaranteed

Labouchère Variations

Aggressive Start

Standard: 1-2-3-4-5 (15 target)
Aggressive: 3-4-5-6-7 (25 target)

Higher targets = larger initial bets
Faster profits if successful
Bigger losses if sequence grows

Conservative Approach

Standard: 1-2-3-4
Conservative: 1-1-1-1 (target: 4 units)

Smaller bets, slower growth
Lower variance
Still can't beat house edge

Reverse Labouchère

Opposite rules:
WIN: Add bet to end
LOSE: Cross off both ends

Attempts to capitalize on streaks
Same expected value
Different volatility pattern

Comparison to Other Systems

vs Martingale

Feature	Labouchère	Martingale
Bet growth	Moderate	Exponential
Recovery	Gradual	All-at-once
Table limit risk	Lower	Higher
Sequence tracking	Required	Not needed
Expected value	Same	Same

vs D'Alembert

Feature	Labouchère	D'Alembert
Bet sizing	Sum of ends	+1/-1 unit
Complexity	Higher	Lower
Flexibility	More	Less
Tracking	Requires paper	Simple count

vs Flat Betting

Feature	Labouchère	Flat
Bet size	Varies	Constant
Variance	Higher	Lower
Expected loss	Same rate	Same rate
Excitement	More	Less

Managing the System

Sequence Selection

Short sequences:
- Complete faster
- Lower targets
- Less risk

Long sequences:
- Higher targets
- More risk
- Larger potential growth

Bankroll Requirements

Conservative estimate:
20× initial sequence sum

Example: 1-2-3-4-5 (sum: 15)
Bankroll: 300 units

Accounts for sequence growth
Losing streaks happen

Stop Conditions

Set limits before playing:
- Max sequence length (e.g., 10 numbers)
- Max bet size (e.g., 50 units)
- Session loss limit (e.g., 100 units)

Prevents catastrophic losses

Common Mistakes

1. No Maximum Limits

Mistake: Follow system indefinitely Problem: Sequences can grow forever Fix: Set hard caps on bet size and sequence length

2. Starting Too Aggressive

Mistake: High-value starting sequence Problem: Faster growth when losing Fix: Start conservative, accept smaller targets

3. Not Tracking Properly

Mistake: Mental tracking Problem: Errors compound, wrong bets Fix: Use paper or calculator app

4. Thinking System Beats House

Mistake: Believe structure = advantage Problem: Expected value unchanged Fix: Use for entertainment, not profit expectation

Frequently Asked Questions

Does Labouchère work long-term?

No system beats the house edge. Labouchère structures your betting but expected loss still equals total wagered × house edge.

How do I choose my sequence?

Sum equals target profit. Shorter sequences complete faster with lower risk. Longer sequences target more but risk larger losses.

What if my sequence gets too long?

Set a maximum sequence length. If exceeded, either accept the loss and restart, or set a loss limit before playing.

Is Labouchère better than Martingale?

Different, not better. Labouchère grows slower (lower table-limit risk) but requires tracking. Same expected value long-term.

Can I use Labouchère online?

Yes. Easier to track with paper/calculator nearby. Same math applies to online and live roulette.

What's the best starting sequence?

There's no "best." 1-1-2-2-3-3 is popular (target: 12 units, moderate bets). Adjust to your bankroll and risk tolerance.

Pro Tips

• Track on paper: Don't rely on memory

• Set stop-losses: Maximum bet and sequence length

• Start small: 1-1-1-2-2 type sequences

• Know your limits: Bankroll should handle growth

• Accept the math: Entertainment value, not profit strategy

Related Calculators

• Roulette D'Alembert Calculator - Gentler system
• Roulette Martingale Calculator - Aggressive system
• Roulette Odds Calculator - Bet probabilities
• Gambling Bankroll Calculator - Session sizing
• Expected Value Calculator - EV analysis

Conclusion

Labouchère offers an elegant structure for betting—target profits, systematic progression, and the satisfaction of completing sequences. Our calculator tracks your sequence and shows the math behind each bet, helping you use the system correctly while understanding its limitations.

Calculate Labouchère Sequence Now →

The cancellation system appeals because it feels mathematical and controlled. But controlled betting doesn't mean controlled outcomes. Use Labouchère if you enjoy the structure, but set firm limits and accept that the house edge applies to every spin regardless of your sequence.