Paroli vs D'Alembert: 200,000 simulated roulette sessions
Paroli and D'Alembert compared with real numbers: 100,000 simulated sessions each on a single zero wheel. Win rates, bust rates, worst sessions, and why neither beats the house edge.
The two systems in one breath
Paroli: The Paroli is the Martingale turned around. You double the stake after a win and reset to the base stake after a loss, aiming to ride a short hot streak with the table money rather than your own.
D'Alembert: The D'Alembert raises the stake by one base unit after a loss and lowers it by one after a win, never dropping below the base unit. It is a much gentler staircase than the doubling systems.
The numbers side by side
| Paroli | D'Alembert | |
|---|---|---|
| Sessions that finished ahead | 38.4% | 54.6% |
| Sessions that ran out of money | 0.0% | 30.4% |
| Average result per session | -22.9 points | -63.4 points |
| Typical (median) result | -25 points | +50 points |
| Worst session seen | -350 points | -500 points |
| Average total staked | 843.6 points | 2,318.1 points |
| Loss predicted by the edge | 22.8 points | 62.7 points |
The honest verdict
Neither system beats the house edge, and the table shows it twice. Each system's average loss sits next to the loss the edge predicts from its own staking (22.8 points for Paroli, 62.7 points for D'Alembert): the wheel took its 1 in 37 of everything each system staked, and nothing more or less.
What actually differs is the shape of the risk. D'Alembert finished ahead more often (54.6% against 38.4%). D'Alembert emptied its bankroll more often (30.4% against 0.0%). Paroli lost less on average (-22.9 points against -63.4 points), mostly because it staked less in total. Choosing between them is choosing which kind of bad day you prefer, not which one wins.
Common questions
Which is better, Paroli or D'Alembert?
Neither, by expectation: both averaged a loss in line with the house edge applied to what they staked (-22.9 points against -63.4 points per session). They differ in risk shape. D'Alembert finished ahead more often (54.6% against 38.4%), while D'Alembert ran out of money more often (30.4% against 0.0%). Pick, if at all, by which bad day you would rather have.
Can I combine two systems to beat the wheel?
No. Any mix of two systems is still a sequence of bets on a wheel that keeps 1 point in 37 staked, so the combination changes the shape of your results, never their long run average. That is exactly what our side by side numbers show for each system alone.
Run both yourself
The Lab in the app runs either system with your own budget, base bet, and rounds, on virtual points. Watch each one's bad day happen instead of taking our word for it.