Fibonacci roulette system

How the Fibonacci roulette system works

The Fibonacci sequence starts 1, 1 and builds each new number by adding the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on. As a roulette staking plan, each number is a multiple of your base unit. You start at the first 1, go up one place every time you lose, and come back two places every time you win.

It's a negative progression, like the Martingale: stakes rise after losses in the hope that a win will claw them back. The difference is speed. The Martingale doubles; the Fibonacci grows by roughly 1.6 times per step once the numbers get going, so it takes longer to reach frightening bets.

Wizard of Odds' page on the Fibonacci betting system (opens in a new tab) describes the same rules and tests them in simulation. Its conclusion is the one every system reaches: the ratio of money won to money bet comes out at −0.0270 on single-zero even-money roulette and −0.0526 on double zero, which are simply the house edges of those wheels.

The Fibonacci sequence as a roulette betting ladder

Here's what the ladder looks like with a £2 unit on an even-money bet such as red or black. The right-hand column is what you'd be down in total if you had lost every bet up to and including that step.

The early steps feel harmless. By step ten, though, a £2 player is staking £110 on a single spin, having already lost £176 getting there. That's the bankroll problem every negative progression shares.

How to use the Fibonacci roulette system, step by step

1. Set a session budget and a unit size. Check that your budget could cover the stakes up to at least step eight or nine.
2. Choose a single-zero table and an even-money bet: red or black, odd or even, or 1–18 or 19–36.
3. Bet one unit (step 1).
4. After a loss, move up one step and bet that number of units.
5. After a win, move back two steps. If that takes you below step 1, start again at step 1.
6. A sequence is finished when a win brings you back to the start. Begin a new one or stop.
7. Stop at once if the next stake would break your budget or the table maximum. Don't add money to keep the sequence going.

Worked example: a Fibonacci run with £2 units

Suppose you back black at £2 a unit and the first four spins lose, followed by three wins.

This is the bit that surprises people. A win doesn't wipe out the whole losing run, as it would with the Martingale. Because you only step back two places, the £10 win on spin five recovers £10 of the £14 lost. It takes a second win to get level and a third to finish one unit (£2) ahead.

In other words, the Fibonacci only works out when wins come along at a decent rate. With 18 winning pockets out of 37, wins arrive slightly less than half the time on average, and the zero means slightly fewer wins than losses over the long run.

Losing runs: the Fibonacci system's real risk

On an even-money bet, a spin loses 19 times in 37 (18 pockets of the other colour plus zero). The chance that the next few spins all lose is that figure multiplied by itself:

Those look like long odds, but they're the chances for one particular stretch of spins. Over a whole session there are many stretches. Standard probability maths gives the chance of seeing at least one run of eight or more losses somewhere in 300 even-money spins at about 51%. For a run of ten or more in 500 spins, it's about 26%. A run of six or more in just 100 spins happens about 60% of the time.

So long runs aren't freak events; in a long enough session they're expected. This is the gambler's ruin in action: with a finite budget and a negative-edge game, any progression eventually meets a run it can't survive. Our risk of ruin page explains the idea in more depth.

Fibonacci roulette odds and the house edge

No matter how the stakes move, each individual bet on a single-zero wheel has an expected loss of 2.70% of its size. A £2 bet loses about 5.4p on average; a £42 bet loses about £1.13. Add them up and the session's expected loss is 2.70% of everything staked.

The Fibonacci actually tends to raise your expected loss compared with flat betting at one unit, simply because it puts more money through the wheel. If a session of Fibonacci bets totals £400 in stakes, the average cost is about £10.80 on single zero and £21.04 on double zero. Wizard of Odds' broader study of betting systems (opens in a new tab) makes the same point: systems change the pattern of results, never the long-run ratio.

To compare that with other ways to play, see our house edge by game table, or read why American roulette nearly doubles the cost.

Table limits and the Fibonacci ceiling

Every roulette table has a maximum bet, and it puts a hard ceiling on any negative progression. Take a £5 unit and an imagined £500 table maximum. The stakes run £5, £5, £10, £15, £25, £40, £65, £105, £170, £275, £445, and then £720 at step 12, which the table won't accept.

By the time you hit that wall you'd have lost £1,160 across eleven straight losses. At that point the sequence can't recover, because the bet needed is simply not allowed. Check the table limit in the game's help screen before you start; limits vary from table to table.

Fibonacci vs Martingale: how fast the stakes climb

The gentler climb is the Fibonacci's main selling point. Here's the comparison at a £5 base.

The Fibonacci survives longer runs on the same budget, but the price is slower recovery: one win after a long run doesn't get you back level. Both cost the same per pound staked. For another gentle system, compare the D'Alembert, which adds just one unit after each loss.

Fibonacci roulette strategy myths and mistakes

• "The golden ratio gives it an edge." The sequence is elegant maths, but a roulette wheel has no idea what numbers you're betting.
• "After a long losing run, red is due." Every spin is an independent event; the wheel has no memory.
• Starting a fresh sequence mid-run to "reset" losses. The losses are still real; you've just stopped counting them.
• Raising the unit after a good session. That pushes the ceiling closer and increases the hourly cost.
• Using it on inside bets. Wins on a straight-up bet are so rare that the sequence races up the ladder.

Playing the Fibonacci system online in the UK

The system runs the same way on RNG and live roulette. The UK rules that matter: autoplay has been banned on all online casino games since 17 January 2025, so every step must be placed manually; table and live games must allow at least 5 seconds per game cycle; and casinos must show your net spend and time played in real time. The slot stake caps of £5 and £2 don't apply to roulette, so nothing but the table maximum stops a progression from climbing.

That makes your own limits important. UK casinos must prompt you to set a financial limit before your first deposit, and they'll offer time-outs and reality checks. Raising stakes after losses is close to chasing losses, one of the warning signs of harmful gambling. The NHS gambling addiction pages (opens in a new tab) and the National Gambling Helpline (0808 8020 133) offer free support.

Where to play roulette: our partner offers

None of our partner offers is a roulette bonus, and none changes how the Fibonacci performs. Roulette and other table games are often excluded from wagering or count for less, so check the terms and the table game lobby first. 18+ and terms apply.

Casumo: a 50% bonus up to £100 for new customers who opt in, on a first deposit of £20 or more; wager the bonus 10x within 7 days, £5 maximum bet while it's active, game, play and payment restrictions apply. 10bet: new UK customers who choose the casino welcome bonus at sign-up and deposit within 7 days get a 100% match up to £25, wagered 10x on slots within 3 days, with maximum bonus winnings of £1,000 and Skrill and Neteller deposits excluded. Coral: deposit (certain types excluded) and bet £10 on slots to get 100 free spins at 10p each on selected games, accepted within 48 hours and valid for 7 days, with no wagering on free spin winnings.

For more on each casino's tables, see Casumo blackjack and roulette, and for every other bet and system, head back to the roulette guide.

18+. Every casino game has a built-in house edge, so over time you should expect to lose what you stake. Set a budget before you play and stop when it’s gone: safer gambling tools and support. Free, confidential help: National Gambling Helpline 0808 8020 133.