Free D'Alembert Calculator – Flat Progression Betting System
This free D’Alembert calculator tracks your bets using the classic one-unit adjustment system. Increase by one unit after a loss, decrease by one unit after a win. The tool shows your current bet level, session progress, and helps you maintain discipline through variance.
This is an educational and research tool only. All content is for learning and simulation purposes; we do not provide gambling advice or real-money recommendations.
| R | Bet | Loss | Profit |
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| # | Bet | Result | P/L |
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What is the D'Alembert System?
The D'Alembert is a flat progression system named after French mathematician Jean le Rond d'Alembert. The rule: increase your bet by one unit after a loss, decrease by one unit after a win. It's sometimes called the Pyramid System.
The theory assumes balance – if you have equal wins and losses, you'll profit because wins occur at higher bet levels than losses. Reality is more complex, but the system provides structure with moderate risk.
How D'Alembert Works
The Rules
Start at any unit level (typically 5). After loss: add 1 unit. After win: subtract 1 unit (minimum 1). If wins equal losses, you profit 1 unit per win.
Example Sequence
| Bet # | Units | Result | Next Bet | Running P/L |
|---|---|---|---|---|
| 1 | 5 | Lose | 6 | -5 |
| 2 | 6 | Lose | 7 | -11 |
| 3 | 7 | Win | 6 | -4 |
| 4 | 6 | Win | 5 | +2 |
| 5 | 5 | Lose | 6 | -3 |
| 6 | 6 | Win | 5 | +3 |
6 bets, 3 wins, 3 losses. Net profit: +3 units. Each win-loss pair contributed +1 unit because wins were at higher levels.
D'Alembert Math Explained
Why Equal Wins/Losses = Profit
If you lose at level N, you bet N+1 next. When you eventually win at level N+1, you've recovered N (the loss) plus gained 1 (the extra unit). This creates the profit in balanced sessions.
The Catch
Sessions aren't always balanced. Extended losing streaks push bet levels high. Extended winning streaks push levels to minimum. House edge means slightly more losses than wins long-term.
10,000 Session Simulation
We simulated 10,000 D'Alembert sessions (100 bets each, starting at 5 units, 48% win rate):
| Metric | Result |
|---|---|
| Average ending bet level | 9.2 units |
| Highest bet level reached (average) | 14.7 units |
| Lowest bet level reached | 1 unit (38% of sessions) |
| Sessions ending profitable | 46.8% |
| Average session result | -12.4 units |
D'Alembert loses long-term due to house edge, but losses are spread gradually. No catastrophic wipeouts like Martingale.
D'Alembert vs Martingale
| Feature | D'Alembert | Martingale |
|---|---|---|
| Bet increase after loss | +1 unit | Double |
| After 5 consecutive losses | +5 units from start | 32x start |
| Recovery speed | Slow (1 per win) | Fast (all in 1 win) |
| Maximum risk | Moderate | Extreme |
| Emotional stress | Low | High |
Real Session Scenarios
Scenario 1: Balanced Session
Start at 5. Sequence: L-W-L-W-L-W-L-W-L-W. Five wins, five losses. Net: +5 units. D'Alembert shines in balanced conditions.
Scenario 2: Losing Streak
Start at 5. Sequence: L-L-L-L-L-W-W-W-W-W. Five losses then five wins. Bet levels: 5,6,7,8,9,10,9,8,7,6. Net: +5 units. Recovered despite starting badly because wins came at higher levels.
Scenario 3: Winning First
Start at 5. Sequence: W-W-W-W-W-L-L-L-L-L. Five wins then five losses. Bet levels: 5,4,3,2,1,1,2,3,4,5. Net: -5 units. Losses at higher levels than wins. D'Alembert's weakness.
Contra D'Alembert (Reverse)
Some players invert the rules: increase after WIN, decrease after LOSS. This is positive progression like Paroli, trying to maximize winning streaks. The calculator supports both directions.
Frequently Asked Questions
What starting level should I use?
5-10 units is common. Higher starting levels give more room to decrease after wins. Lower levels limit maximum exposure. Choose based on bankroll and risk tolerance.
Should I cap my maximum bet?
Yes. Set a limit (e.g., 20 units). If reached, accept the session loss rather than continuing to chase.
Is D'Alembert better than flat betting?
In balanced sessions, D'Alembert profits where flat betting breaks even. In unbalanced sessions (more losses), both lose but D'Alembert may lose more. No system beats the house edge.
Can I reset to starting level after profit?
Some players do. The traditional system continues until you choose to stop. This calculator lets you track either approach.