The Fibonacci progression moves one step up the sequence 1, 1, 2, 3, 5, 8, 13 after a loss and two steps back after a win. Stakes grow more slowly than with Martingale, so ruin arrives later, but the house edge on every coin is unchanged.
Compare the balance line with the EV line over 1,000 spins, then rerun with new seeds. Long sequences of alternating results keep the progression high for a long time, which is where the deep drawdowns come from.
Open this experiment in the lab ↑All numbers below were computed by the same simulator and models that run in the lab above, when this page was built.
Every bet in roulette has a negative expectation. A betting system changes how stakes are distributed over time, not the edge per coin wagered.
400 simulated sessions of 1,000 spins with a 1,000-coin bankroll and a 10-coin base unit: 301 went bankrupt (75.3%). The median session ended at 0 coins.
With a 10-coin base unit and a 5,000-coin table maximum, Fibonacci needs a bet above the limit after 14 consecutive losses. By then 9,860 coins have been staked on the streak. Chance that a 1,000-spin session contains at least one streak of 14 losses: 4.2%.
400 sessions per strategy, 1,000 spins each, 1,000-coin bankroll, 10-coin base unit, 5,000-coin table maximum, European wheel (2.70%). The same 400 seeds are used for every strategy.
| Strategy | Survived | Median final | Mean final | Avg wagered | Expected loss | Observed loss | Avg longest losing streak |
|---|---|---|---|---|---|---|---|
| Flat bet | 98% | 740 | 724 | 9,980 | 270 | 276 | 9.6 |
| Martingale | 14% | 0 | 670 | 13,510 | 365 | 330 | 7.7 |
| Fibonacci | 25% | 0 | 659 | 13,957 | 377 | 341 | 8.3 |
| D'Alembert | 7% | 0 | 307 | 25,353 | 685 | 693 | 7.5 |
| Labouchère | 3% | 0 | 335 | 22,497 | 608 | 665 | 6.2 |
| James Bond (7.0 / 2.5 / 0.5) | 100% | 738 | 719 | 10,000 | 270 | 281 | 5.9 |
Bankruptcy usually comes later because stakes grow more slowly, but the expected loss per coin wagered is identical: 2.70% on a European wheel. Over a long session both trend toward the same EV line.
Each Fibonacci number is the sum of the two before it, so stepping back two after a win recovers the last two losing bets of the sequence. A single win does not undo a long climb.
An even-money bet of your choice: red, black, even, odd, 1–18 or 19–36. Each has the same edge.
No. Virtual coins only, no deposits, no prizes, 18+.
Free-to-play entertainment and math education with virtual coins only. No real money, no deposits, no withdrawals, no prizes. 18+. Simulated results do not predict real outcomes.