D'Alembert adds one base unit to the stake after a loss and removes one after a win. It rests on the idea that wins and losses balance out, but on a wheel with a zero they do not: 19 of 37 pockets lose an even-money bet.
Use the calculator to see how far the stake climbs during an unlucky stretch and how the drawdown compares with the expected loss line. The comparison table below runs the same seeds for every progression.
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: 373 went bankrupt (93.3%). The median session ended at 0 coins.
D'Alembert never raises its stake after a loss, so the table maximum is never the binding constraint. Its risk comes from the house edge alone.
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 |
It is the flattest of the classic progressions, so swings are smaller, but the expected loss is still 2.70% of everything wagered on a European wheel. Because stakes rise during losing runs, total wagered and therefore expected loss are higher than with flat betting.
One unit per net loss. After 30 more losses than wins the stake is 31 units. The table below shows how often sessions reach that kind of depth.
Yes. Pick a base bet, bankroll and number of spins. The URL updates so the setup can be shared.
No. It is a simulator with virtual coins. No real money, 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.