The Labouchère system starts with a line of numbers, here 1-2-3-4. Each stake is the sum of the first and last numbers. A win crosses both off; a loss appends the lost stake to the end of the line. Clearing the line wins the sum of the original numbers, 10 units.
Run 1,000 spins and watch the stake column in the spin log. A short line is cleared quickly most of the time, but a run of losses lengthens the line and the stakes grow with it. When the line is cleared, the simulator starts a new 1-2-3-4 line.
Open this experiment in the lab ↑All numbers below were computed by the same simulator and models that run in the lab above, when this page was built.
Every bet in roulette has a negative expectation. A betting system changes how stakes are distributed over time, not the edge per coin wagered.
400 simulated sessions of 1,000 spins with a 1,000-coin bankroll and a 10-coin base unit: 389 went bankrupt (97.3%). The median session ended at 0 coins.
With a 10-coin base unit and a 5,000-coin table maximum, Labouchère needs a bet above the limit after 496 consecutive losses. By then 1,252,400 coins have been staked on the streak. Chance that a 1,000-spin session contains at least one streak of 496 losses: 0.0%.
400 sessions per strategy, 1,000 spins each, 1,000-coin bankroll, 10-coin base unit, 5,000-coin table maximum, European wheel (2.70%). The same 400 seeds are used for every strategy.
| Strategy | Survived | Median final | Mean final | Avg wagered | Expected loss | Observed loss | Avg longest losing streak |
|---|---|---|---|---|---|---|---|
| Flat bet | 98% | 740 | 724 | 9,980 | 270 | 276 | 9.6 |
| Martingale | 14% | 0 | 670 | 13,510 | 365 | 330 | 7.7 |
| Fibonacci | 25% | 0 | 659 | 13,957 | 377 | 341 | 8.3 |
| D'Alembert | 7% | 0 | 307 | 25,353 | 685 | 693 | 7.5 |
| Labouchère | 3% | 0 | 335 | 22,497 | 608 | 665 | 6.2 |
| James Bond (7.0 / 2.5 / 0.5) | 100% | 738 | 719 | 10,000 | 270 | 281 | 5.9 |
You only need to win about one third of the spins to clear the line, because each win removes two numbers and each loss adds one. The catch is stake size: the numbers you append keep growing, so the losses that remain are large.
If first plus last exceeds the table maximum, the bet is capped, so a win no longer clears the numbers it should. The table-limit section below shows when that happens with the default settings.
The simulator uses 1-2-3-4, the most common textbook line. The base bet sets the value of one unit.
No. Virtual coins only, no deposits, no prizes. 18+.
Free-to-play entertainment and math education with virtual coins only. No real money, no deposits, no withdrawals, no prizes. 18+. Simulated results do not predict real outcomes.