Fibonacci Roulette Strategy
Fibonacci is a negative progression strategy that uses the famous 1, 1, 2, 3, 5, 8, 13… sequence to size bets. After a loss you move forward in the sequence. After a win you move back two steps. It is slower and slightly less aggressive than Martingale.
Fibonacci changes the shape of the recovery curve. It does not change the long-run house edge.
The Fibonacci sequence
Each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
Your current bet equals the sequence number at your current index multiplied by a base unit (say $10). After a loss, advance one index. After a win, retreat two indices, but never below index 0.
Example progression
| Spin | Index | Bet | Result | Next index |
|---|---|---|---|---|
| 1 | 0 | $10 | Loss | 1 |
| 2 | 1 | $10 | Loss | 2 |
| 3 | 2 | $20 | Loss | 3 |
| 4 | 3 | $30 | Win | 1 |
| 5 | 1 | $10 | Loss | 2 |
| 6 | 2 | $20 | Win | 0 |
Recovery behaviour
Because a win moves you back two indices, two consecutive wins from a deep negative cycle clear most of the lost ground. The system is built around the property that any win pair recovers more than the corresponding loss pair lost.
On paper, completing a full down-and-back cycle from index 0 to index N and back to index 0 yields a small net profit equal to the base unit. In practice, losing streaks lock you at high indices long enough for the bankroll to run out.
Bankroll requirements
Bankroll needed to absorb n consecutive losses with $10 base unit:
| Losses absorbed | Total wagered | Comparison to Martingale |
|---|---|---|
| 5 (idx 4, $50) | $110 | $310 |
| 7 (idx 6, $130) | $340 | $1,270 |
| 9 (idx 8, $340) | $890 | $5,110 |
| 12 (idx 11, $1,440) | $3,770 | $40,950 |
Fibonacci is dramatically cheaper than Martingale at the same loss count. But it still grows fast enough that a 14-15 streak ends most realistic bankrolls.
Comparison to Martingale
- Slower escalation - bets grow at ratio ~1.618 (golden ratio) per loss versus 2.0 for Martingale.
- Smaller bankroll requirement for the same number of absorbed losses.
- Recovery requires multiple wins, not just one.
- Lower bust rate over similar session lengths.
- Same long-run expected return: minus the house edge times total wagered.
Test results
Across 200 spins of $10 Fibonacci on $1,000 bankroll on European:
- ~80% of sessions end profitable or near break-even.
- ~15% end with a moderate loss ($100-$400).
- ~5% bust during a deep losing streak.
- Average final bankroll lands near the expected loss (~−$65 over 200 spins).
Where Fibonacci fits in
Fibonacci is the system to test if you want progression behaviour but cannot stomach Martingale's bankroll demands. The sequences are gentler and the swings are smaller. The long-run math is identical.
Run flat, Martingale and Fibonacci on the same setup in the tester. The differences are easier to see than to describe.