The Fibonacci System
The Fibonacci system is a negative progression roulette strategy based on one of the most famous number sequences in mathematics. Each bet is the sum of the two previous bets — creating a slower, safer progression than the Martingale while still offering a structured path back to profit after losses.
What Is the Fibonacci System?
The Fibonacci system applies a mathematical sequence — originally described by the Italian mathematician Leonardo of Pisa (Fibonacci) in 1202 — to roulette betting. The core rule: each number is the sum of the two numbers before it. In roulette, each number represents your bet size in units.
Unlike the Martingale which doubles after every loss, the Fibonacci increases bets more gradually. After a win, you move back two steps in the sequence instead of resetting completely. This creates a more forgiving progression that doesn’t escalate as aggressively.
The Fibonacci Sequence
The sequence starts at 1 and each subsequent number is the sum of the two before it:
In practice, you rarely need to go beyond 34 or 55. If you reach that point, the bets are getting large and you should consider your stop-loss limit. The beauty of the sequence is that it grows much slower than doubling — after 8 losses, a Fibonacci bet is 21 units while a Martingale bet would be 256 units.
| Step | Fibonacci Bet | Martingale Bet | Difference |
|---|---|---|---|
| 1 | 1 | 1 | Same |
| 2 | 1 | 2 | Fibonacci is lower |
| 3 | 2 | 4 | Half the Martingale |
| 5 | 5 | 16 | 3x lower |
| 8 | 21 | 128 | 6x lower |
| 10 | 55 | 512 | 9x lower |
How to Use It at the Roulette Table
The Fibonacci system works on even-money bets only: red/black, odd/even, or low/high on a European or French roulette table.
| Situation | Action | Example |
|---|---|---|
| Start | Bet 1 unit | Bet €5 |
| After a loss | Move one step forward in the sequence | Next bet: €5 (still 1) |
| After another loss | Continue forward: bet the sum of the two previous | Next bet: €10 (1+1=2 units) |
| After a win | Move two steps back in the sequence | Go back two positions |
| Back at start? | You are in profit — cycle complete | Restart at €5 |
Full Game Example
Starting bankroll: €200. Unit size: €5. Betting on Red.
| Spin | Sequence Position | Bet | Result | Action | Bankroll |
|---|---|---|---|---|---|
| 1 | 1 | €5 | Loss | Move forward | €195 |
| 2 | 1 | €5 | Loss | Move forward | €190 |
| 3 | 2 | €10 | Loss | Move forward | €180 |
| 4 | 3 | €15 | Loss | Move forward | €165 |
| 5 | 5 | €25 | Win | Move back 2 | €190 |
| 6 | 2 | €10 | Win | Move back 2 | €200 |
| 7 | 1 (start) | €5 | Win | Cycle complete | €205 |
Result: 4 losses and 3 wins — yet a net profit of €5. The system recovered all losses and produced a profit with fewer wins than losses. This is the core strength of the Fibonacci: you don’t need a 50% win rate to recover.
Fibonacci vs Martingale
| Feature | Fibonacci | Martingale |
|---|---|---|
| Progression type | Sum of two previous bets | Double after every loss |
| Bet after 8 losses (€5 base) | €105 (21 units) | €1,280 (256 units) |
| Recovery after win | Move back 2 steps | Full reset to base |
| Wins needed to recover | Multiple small wins | One single win |
| Table limit risk | Low — slow growth | High — exponential growth |
| Best for | Patient players, longer sessions | Short sessions, aggressive play |
Learn more: Martingale guide · D’Alembert guide · Labouchère guide
Advantages & Risks
| Advantages | Risks |
|---|---|
| Much slower bet growth than Martingale | Long losing streaks still create large bets |
| Can recover with fewer wins than losses | Does not change the 2.70% house edge |
| Simple to follow — just add two numbers | Requires patience — recovery takes multiple wins |
| Works within most table limits | No guaranteed profit — streaks are unpredictable |
| Lower emotional stress than aggressive systems | Tracking required — easy to lose your place |
When to Use the Fibonacci System
Medium-risk players — the Fibonacci sits between the conservative D’Alembert and the aggressive Martingale. It is ideal if you want structure without extreme risk.
Longer sessions — because bets grow slowly, the Fibonacci supports extended play. Set a target (e.g., return to position 1 three times) and stop.
European tables only — always play on a single zero wheel for better odds. On a French table with La Partage, your even-money bets have just 1.35% house edge.
Explore more systems: Martingale · Paroli · D’Alembert · Labouchère · All strategies