In short: The Fibonacci system raises your even-money roulette stake along the sequence 1, 1, 2, 3, 5, 8 after each loss and steps back two places after a win. It changes how wins and losses are spread, but every bet still carries the 2.70% (single-zero) or 5.26% (double-zero) house edge, and losing runs quickly push stakes towards table limits.
The Fibonacci number sequence
The Fibonacci betting system raises stakes after losses. Its sequence grows more slowly at first than doubling, but still becomes very large. It cannot overcome roulette’s house edge.
Fibonacci’s Liber Abaci was published in 1202. The later betting application is separate from the mathematical sequence: a pattern of numbers does not predict a roulette outcome.
The sequence is designed by starting with 1 and by adding the two prior numbers together. Or, the sequence is cumulative in its nature, which means every number that follows equals the sum of the previous two numbers. Thus, the first 15 numbers in the sequence will be as follows:
1 – 1 – 2 – 3 – 5 – 8 – 13 – 21 – 34 – 55 – 89 – 144 – 233 – 377 – 610
Using the Fibonacci sequence in Roulette
It is important to note that the number sequence is appropriate to use when placing even-money outside bets (red/black, even/odd, high numbers/low numbers).
Start at the first 1. After a loss, move one position forward; after a win, move two positions back, stopping at the first position if fewer than two are available. The examples below use this rule, not a reset after every win.
The further the player goes through the sequence, the greater his/her losses will be. A win on the first bet is considered as the best scenario, while a win on the second or the third bet will lead the player to breakeven.
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These selected outcomes show how stakes and balances change. They are examples, not forecasts:
| Bet Number | Unit(s) | Outcome |
|---|---|---|
| 1 | 1 | loss |
| 2 | 1 | loss |
| 3 | 2 | loss |
| 4 | 3 | loss |
| 5 | 5 | loss |
| 6 | 8 | loss |
| 7 | 13 | loss |
| 8 | 21 | loss |
| 9 | 34 | loss |
| 10 | 55 | win |
A win has finally occurred on the 10th bet. What the player needs to do next is to move two numbers back in the Fibonacci sequence and place the respective number as the 11th bet. Thus, he/she will next bet 21 units. This step is to be repeated again and again until the player reaches the beginning of the sequence. So, after each win, he/she needs to move two numbers back, while after each loss, he/she needs to move one number forward. Now, let us extend the above-mentioned betting process:
| Bet Number | Unit(s) | Outcome |
|---|---|---|
| 1 | 1 | loss |
| 2 | 1 | loss |
| 3 | 2. | loss |
| 4 | 3 | loss |
| 5 | 5 | loss |
| 6 | 8 | loss |
| 7 | 13 | loss |
| 8 | 21 | loss |
| 9 | 34 | loss |
| 10 | 55 | win |
| 11 | 21 | win |
| 12 | 8 | win |
| 13 | 3 | loss |
| 14 | 5 | win |
| 15 | 2 | loss |
| 16 | 3 | loss |
| 17 | 5 | win |
| 18 | 2 | win |
| 19 | 1 | win |
It became evident that the player reached the very beginning of the number sequence and scored a profit of 1 unit, despite the fact there have been 12 losses and only 7 wins.
Different outcomes can prevent recovery altogether. Nine initial losses cost 88 units; a 55-unit winner still leaves a 33-unit loss. A single win does not necessarily clear the accumulated loss.
Limiting the losses is critical
Long losing runs can exhaust the budget or reach a table maximum. Set an affordable cash limit beforehand; no universal six- or seven-step cutoff makes this safe. Stop at the limit even if the sequence is unfinished.
Fibonacci is not a route to consistent profit or a reliably “medium-risk” strategy. Actual risk depends on unit size, available funds, limits and outcomes. Increasing stakes changes volatility while the house advantage remains.
Further reading: Gambling Commission explanation of house edge.
