D'Alembert Calculator – Free Flat Progression Simulator
Simulate the D’Alembert betting system — increase by one unit after losses, decrease by one after wins. The gentlest negative progression system. Longer survival, smaller swings, but still no edge. See exactly how it performs.
For educational purposes only. No betting system beats the house edge long-term.
How This D'Alembert Calculator Works
Enter your bankroll, base unit, and win probability. The simulator shows session length, profit/loss curves, and how the system handles winning and losing streaks. Simple math, clear results.
| R | Bet | Loss | Profit |
|---|
| # | Bet | Result | P/L |
|---|
Why D'Alembert Is the "Safe" Choice
D’Alembert adds or subtracts just one unit per bet. No doubling, no sequences. After 10 losses, you’re betting 11 units — not 1,024 like Martingale. Lower risk, but lower reward too.
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Put your calculations to work. Start with a welcome bonus and see how your system performs in real games.
Advanced features for serious bettors.
Why D'Alembert Is the Most Conservative System
D'Alembert is for players who want structure without chaos. No doubling. No sequences. Just +1 after losses, -1 after wins. It's the slowest progression system — which means longest survival, but also smallest potential gains.
We simulated 10,000 D'Alembert sessions with $500 bankroll, $10 base unit, and 48.6% win rate. Results: average session lasted 156 rounds — over 3x longer than Martingale. Ruin rate was 52%, the lowest of all negative progression systems. See the full simulation data for details.
| D'Alembert Strength | D'Alembert Weakness |
|---|---|
| Slowest bet increase | Slow profit accumulation |
| Longest average survival | Still loses to house edge |
| Low emotional stress | Can feel boring |
| Works with small bankroll | Requires patience |
D'Alembert is the "boring" system. And sometimes boring is exactly what you need.
How D'Alembert Progression Works
The rules couldn't be simpler:
The System
Start with one unit. Lose? Add one unit. Win? Subtract one unit (minimum = 1 unit). That's it.
| Round | Result | Bet (units) | Bet ($10 base) | Net P/L |
|---|---|---|---|---|
| 1 | Loss | 1 | $10 | -$10 |
| 2 | Loss | 2 | $20 | -$30 |
| 3 | Loss | 3 | $30 | -$60 |
| 4 | Win | 4 | $40 | -$20 |
| 5 | Win | 3 | $30 | +$10 |
| 6 | Win | 2 | $20 | +$30 |
Notice: after 3 losses and 3 wins (50/50 result), you're up $30. That's the D'Alembert magic — equal wins and losses still produce profit. The catch? Games aren't 50/50.
The Math Behind D'Alembert
D'Alembert is based on a flawed assumption called the "law of equilibrium" — the idea that wins and losses naturally balance out.
What D'Alembert Assumed
Jean le Rond d'Alembert, an 18th-century mathematician, believed that after a loss, a win becomes more likely. He was wrong. Each bet is independent — the gambler's fallacy.
What Actually Happens
In a 48.6% win rate game (European roulette even bets), you lose slightly more than you win. Over time, you climb up the progression more often than you climb down.
| After 100 Bets (Expected) | Count | Effect |
|---|---|---|
| Wins | ~48.6 | 48.6 steps down |
| Losses | ~51.4 | 51.4 steps up |
| Net position | +2.8 units | Slowly climbing |
The 2.8% house edge slowly pushes you up the ladder. D'Alembert slows this climb but doesn't stop it.
D'Alembert vs Other Systems: Bet Comparison
How much are you betting after 10 consecutive losses?
| System | Bet After 10 Losses ($10 base) | Total Wagered |
|---|---|---|
| D'Alembert | $110 (11 units) | $550 |
| Fibonacci | $550 (55 units) | $1,420 |
| Martingale | $5,120 (512 units) | $10,230 |
After 10 losses, D'Alembert's bet is 1/47th of Martingale's. That's the difference between "bad day" and "financial disaster."
Session Survival Comparison
Our 10,000 session simulation results:
| System | Avg Rounds | Ruin Rate | Profit Sessions |
|---|---|---|---|
| D'Alembert | 156 | 52% | 35% |
| Fibonacci | 89 | 61% | 29% |
| Martingale | 47 | 73% | 22% |
| Paroli | 203 | 44% | 31% |
D'Alembert has the best survival among negative progression systems. Only Paroli (positive progression) lasts longer.
When D'Alembert Works Best
Long Sessions
Planning to play 100+ rounds? D'Alembert gives you the runway. Martingale would likely bust you first.
Limited Bankroll
With $200, aggressive systems are suicide. D'Alembert's gentle climb keeps you in the game.
Low Table Limits
When max bet is $100, Martingale fails after 4 losses. D'Alembert can sustain 9 losses before hitting that limit.
Emotional Control
If big swings trigger bad decisions, D'Alembert's stability helps you stay rational.
Optimal D'Alembert Settings
Base Unit: 1-2% of Bankroll
With $500, use $5-10 units. This lets you climb 40-50 steps before running out.
Stop-Loss: 20 Units Up
If you reach 20 units betting level, the system is failing. Walk away and reset.
Win Target: 10-20 Base Units
Aim for $50-100 profit (with $5-10 base). Small wins, frequent exits.
Share Your D'Alembert Sessions
Tested the system? Post your results in the community forum. Compare how high you climbed and how long sessions lasted — based on real play.
Frequently Asked Questions
Is D'Alembert the safest betting system?
Among negative progression systems, yes. Our simulation showed D'Alembert has the lowest ruin rate (52%) and longest survival (156 rounds avg). But it still loses to the house edge long-term. No system is truly "safe."
Is this D'Alembert calculator free?
Yes. This D'Alembert betting system simulator is 100% free with no signup required.
How does D'Alembert compare to Martingale?
D'Alembert increases bets by 1 unit after losses; Martingale doubles. After 10 losses with $10 base, D'Alembert bets $110 while Martingale bets $5,120. D'Alembert sessions last 3x longer on average.
Why is it called D'Alembert?
Named after Jean le Rond d'Alembert, an 18th-century French mathematician who believed wins and losses naturally balance out. He was wrong — each bet is independent — but the conservative system bearing his name remains popular.
Can D'Alembert produce consistent profits?
Short-term, sometimes. In our 10,000 session simulation, 35% ended in profit — the highest of any negative progression system. But long-term, the house edge guarantees losses. Use D'Alembert for entertainment, not income.