D'Alembert System Calculator
Calculate pyramid betting progressions and analyze risk with this balanced negative progression system
Parameters
Configure your pyramid betting progression to analyze risk and bankroll requirements
Analysis Results
What is the D'Alembert Betting System?
The D'Alembert system is a negative progression betting strategy developed based on the equilibrium theory. Named after 18th-century French mathematician Jean le Rond d'Alembert, this system operates on the principle that wins and losses should eventually balance out over time. It's considered one of the safest negative progression systems because it uses linear increases rather than exponential doubling like the Martingale system.
D'Alembert Betting Rules
After a Loss: Increase bet by 1 unit
After a Win: Decrease bet by 1 unit
Minimum Bet: Never go below base bet
Example: Starting at $10 with $5 units. After loss: bet $15. After win from $15: bet $10. The progression climbs slowly and descends with wins, creating a pyramid pattern.
D'Alembert vs Other Betting Systems
D'Alembert System
Best For: Conservative players seeking balanced risk
Risk Level: Low to Moderate
Pros: Slow progression, manageable bet sizes, lower variance than Martingale
Linear increase makes it sustainable for longer sessions with moderate bankrolls
Martingale System
Best For: Players with large bankrolls
Risk Level: High
Pros: Fast loss recovery, simple to implement
Exponential doubling leads to massive bets quickly - 8 losses can require 256x base bet
Fibonacci System
Best For: Mathematical approach enthusiasts
Risk Level: Moderate
Pros: Slower than Martingale, recovers on sequences
Based on Fibonacci sequence (1,1,2,3,5,8,13...) - moderate progression speed between D'Alembert and Martingale
Critical Limitations & Risks
The Gambler's Fallacy
D'Alembert is based on the false premise that wins and losses must balance out. In reality, each bet is independent. A coin that landed heads 10 times still has 50% chance of heads next flip - there's no "memory" or equilibrium forcing tails.
House Edge Always Wins
No betting system can overcome negative expected value. If a game has 48.6% win probability (like roulette), you lose 2.8% long-term regardless of bet sizing. D'Alembert only manages how fast you lose, not whether you lose.
Slow Loss Recovery
Unlike Martingale which recovers all losses in one win, D'Alembert requires multiple wins to break even after a losing streak. A 6-loss streak needs approximately 6 wins to return to profit, and you must win more than you lose to overcome the house edge.
Table Limits Still Apply
While D'Alembert hits table limits slower than Martingale, long losing streaks can still exceed maximum bet restrictions. A $10 base with $10 units reaches $100 after 9 losses - many table limits cap at 20-40x minimum bet.
Best Practices vs Common Pitfalls
Best Practices
- Use small unit increases (10-20% of base bet)
- Maintain bankroll of 50-100x base bet minimum
- Set maximum bet limit (10x base bet recommended)
- Only play even-money bets near 50% probability
- Set strict session loss limits before playing
- Track all bets to monitor actual performance
Common Pitfalls
- Using large unit increases that escalate too quickly
- Playing with insufficient bankroll for streak length
- Believing the system guarantees eventual profit
- Using on games with high house edge or low win probability
- Chasing losses beyond predetermined stop-loss point
- Ignoring that each bet is statistically independent
Real-World D'Alembert Examples
Example 1: Conservative Roulette Session
Setup: $500 bankroll, $10 base bet, $5 unit increase
Sequence: $10 (L), $15 (L), $20 (W), $15 (W), $10 (W)
Result: Total wagered: $70 | Total lost: $25 | Remaining bankroll: $475
Analysis: Despite 3 wins vs 2 losses, net result is negative due to larger bets on losing outcomes
Example 2: Extended Losing Streak
Setup: $1,000 bankroll, $20 base, $10 unit increase, 8 consecutive losses
Progression: $20, $30, $40, $50, $60, $70, $80, $90
Total Wagered: $440 | Remaining Bankroll: $560
Recovery: Needs 8+ wins to return to profit, assuming perfect alternating wins
Example 3: Maximum Bet Limit Reached
Setup: $10 base, $10 units, table max $200
Limit Hit: After 19 consecutive losses ($10 + 19×$10 = $200)
Total Risk: $1,995 wagered to reach limit
Probability: At 48.6% win rate, 19 loss streak = 0.00037% (extremely rare but possible)
Professional D'Alembert Tips
Small Unit Ratios
Keep your unit increase at 10-25% of your base bet. A $10 base should use $1-2.50 units, not $5-10. This extends your playable streak length and reduces variance significantly.
Set Maximum Bet Caps
Establish a maximum bet limit before starting - typically 10x your base bet. When reached, either reset to base or stop playing. This prevents rare but devastating long losing streaks.
Use Modified Versions
Consider Reverse D'Alembert (increase on wins, decrease on losses) for trending opportunities, or Contra D'Alembert which may preserve capital better during negative expectation games.
Track Win/Loss Patterns
Record every session to identify actual win rates versus expected. If your real win rate is below 47% on even-money bets, no progression system can save you - the house edge is too large.
Combine with Session Limits
Set both time limits (60-90 minutes) and loss limits (20-30% of session bankroll). D'Alembert doesn't prevent losses, it just manages bet sizing - discipline prevents emotional decisions.
Understand the Math
D'Alembert doesn't change expected value. If house edge is 2.7% (European roulette), you lose $2.70 per $100 wagered on average regardless of progression. Only play for entertainment, not profit expectation.
Frequently Asked Questions
What is the D'Alembert betting system?
The D'Alembert system is a negative progression betting strategy where you increase your bet by one unit after a loss and decrease by one unit after a win. Named after 18th-century French mathematician Jean le Rond d'Alembert, it's based on the theory of equilibrium - the idea that wins and losses should eventually balance out.
How does D'Alembert compare to Martingale?
D'Alembert is much safer than Martingale because it uses linear progression (adding units) instead of exponential doubling. While Martingale doubles after each loss, D'Alembert only increases by one unit, requiring less bankroll and reaching table limits more slowly. However, it also recovers losses more slowly than Martingale.
What is the best unit size for D'Alembert?
Most professionals recommend a unit size of 1-2% of your total bankroll, with a base bet of 2-3 units. For example, with a $1,000 bankroll, use $10-20 as your unit size and start with a $20-40 base bet. This ensures you can sustain 10-15 consecutive losses without depleting your bankroll.
Does the D'Alembert system guarantee profits?
No, the D'Alembert system cannot overcome the house edge or negative expected value. While it manages bankroll better than Martingale and can produce short-term profits, the equilibrium theory it's based on is a gambler's fallacy. Past results do not influence future outcomes in independent events like roulette spins.
What games work best with D'Alembert?
D'Alembert works best on even-money bets with approximately 50% win probability, such as roulette red/black, baccarat banker/player, or craps pass/don't pass. Avoid using it on games with high house edge or bets with significantly less than 50% win probability, as the system accelerates losses in such scenarios.
How much bankroll do I need for D'Alembert?
A safe bankroll is at least 50-100 times your base bet. If your base bet is $10, maintain a bankroll of $500-1,000. This provides enough buffer to survive typical losing streaks of 8-12 consecutive losses while keeping your maximum bet reasonable relative to your total funds.