Betting Systems Head-to-Head: Martingale vs Fibonacci vs D'Alembert
We tested three popular betting systems with 100,000 simulated spins each. Here's what the data actually shows.
The Three Systems
Martingale
Double your bet after each loss. Return to base bet after a win.
Logic: Eventually you'll win and recover all losses plus one unit.
Fibonacci
Follow the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...) when losing. Move back two numbers when winning.
Logic: More gradual progression reduces risk of hitting table limits.
D'Alembert
Increase bet by one unit after a loss, decrease by one unit after a win.
Logic: Based on the "law of equilibrium" (wins and losses should balance).
Simulation Results
Starting bankroll: $1,000 | Base bet: $10 | 1,000 spin sessions
Martingale Results
- Average session ending balance: $973
- Sessions ending in profit: 48%
- Sessions ending in ruin: 12%
- Largest bet required: $1,280
Fibonacci Results
- Average session ending balance: $976
- Sessions ending in profit: 46%
- Sessions ending in ruin: 8%
- Largest bet required: $890
D'Alembert Results
- Average session ending balance: $974
- Sessions ending in profit: 47%
- Sessions ending in ruin: 5%
- Largest bet required: $350
Key Insights
1. All systems lost money on average - The house edge is inescapable.
2. Martingale had the highest risk - Required the largest bets and had the most bankruptcies.
3. D'Alembert was most conservative - Smallest bet sizes but still lost overall.
4. Short-term wins are common - Nearly half of sessions ended in profit, creating the illusion that systems work.
The Mathematical Reality
No betting system can change the expected value of a bet. You're still losing 2.7% per spin on average. Systems only change how you lose, not if you lose.
Should You Use Betting Systems?
If it makes the game more interesting and you understand you're still facing the house edge, sure! Just:
- Set strict loss limits
- Never chase losses
- Be aware of table limits
- Treat it as entertainment cost
Use our tracking tools to test any system and see how it performs over time.
Ready to apply what you learned?
Use our tools to track real games, test strategies, and see probability in action.