The Fibonacci Strategy in Roulette: sequence, example, bankroll

The Fibonacci strategy is a betting system where the size of the next bet is taken from the famous number sequence 1-1-2-3-5-8-13-21. The Fibonacci system in roulette belongs to the negative progressions: the bet grows after a loss and falls after a win, but it does so noticeably more gently than the Martingale. Let's break down the sequence itself, the rule for moving along it, a step-by-step example with a table, what bankroll you need and where the method has its limits. Honestly, up front: no progression removes the house edge. So the Fibonacci is best treated as a way to order your bets and bankroll, not to beat the wheel.

What the Fibonacci sequence is

The Fibonacci sequence is a number series where each next number equals the sum of the two previous ones: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. The series can continue indefinitely, but in practice the first eight to ten values are enough for a player. In a betting system each number of the series is the number of base units staked in the current round. If the base unit equals 1 dollar, the bets along the series will be 1, 1, 2, 3, 5, 8 dollars and so on.

The rule for moving along the sequence

The system works only on even-money bets - red or black, odd or even, high or low. Such bets pay 1 to 1, and the chance of winning on the European wheel of 37 pockets is close to 48.6% because of the zero. The movement rule is simple:

• after a loss you take a step forward along the series - you bet the next number;
• after a win you take two steps back - you return two numbers along the series;
• if you are at the very start of the series and a step back would take you past the first number, the cycle simply begins again from one.

The logic is that a single win rolls you back two positions at once and in theory covers several previous losses. The cycle closes when you return to the start of the series.

Step-by-step example with a table

Let's take a base unit of 1 dollar and follow a run of rounds. L is a loss, W is a win. After a loss we move forward, after a win - two numbers back.

After four losses in a row the bet reached 5 units. Two wins rolled us back from the number 5 to the number 1, and the run closed with a small plus. This is the idea of the method: a short run of losses is recovered by a couple of wins without a sharp rise in the bet.

How the Fibonacci is gentler than the Martingale

In the Martingale the bet doubles after each loss: 1, 2, 4, 8, 16, 32, 64. In the Fibonacci the growth is slower: 1, 1, 2, 3, 5, 8, 13. On the seventh loss in a row the Martingale requires 64 units, while the Fibonacci - only 13. The difference is that the Fibonacci series grows not geometrically but in a gentler progression, so the bankroll is spent more slowly and runs into the table limit less often.

The price for this gentleness is that a single win does not always bring the whole run into the plus - sometimes it only reduces the loss, and full recovery needs several wins. A comparison with the Martingale, D'Alembert and other systems is gathered in the review of roulette strategies, and a general breakdown of the approaches - in the piece on the roulette betting system.

What bankroll you need

The main risk of any negative progression is a long losing streak. The bankroll should be calculated so as to withstand a streak of 8-10 losses in a row without going beyond your money and the table limit. Let's add up the total bet along the series:

• to work through 7 steps (1, 1, 2, 3, 5, 8, 13), 33 units have already been staked in total;
• over 10 steps (up to the number 55) the total exposure exceeds 140 units.

That is why the base unit is chosen small relative to the whole bankroll - usually no more than 1-2% of it. Then a rare but possible long run of bad luck will not zero out the account in one cycle.

Where the method's limits are

The Fibonacci changes only how you distribute your bets over time, but does not affect the maths of the wheel. A few honest limitations:

• the house edge remains. On European roulette the house edge is 2.7%, on American with two zeros - 5.26%. The progression does not cancel it;
• the zero does not go anywhere. When 0 comes up, an even-money bet loses, and the streak lengthens. More on this - in the article on what the zero in roulette is;
• every spin is independent. The wheel does not remember past results, so after ten blacks the probability of red is the same - about 48.6%;
• a long losing streak is dangerous all the same. The bet grows more slowly than in the Martingale, but at 10-12 losses in a row the required amount and the table limit become a real wall.

The reverse Fibonacci

The reverse Fibonacci flips the rule: a step forward along the series is taken after a win, and after a loss you roll back two numbers. This is a positive progression - you raise the bet on a winning streak and lower it quickly as soon as luck leaves. The idea is to risk mainly money already won, but the downside is the same: a single slip at a high bet eats up what was accumulated over several rounds.

Which bets to use it on

The Fibonacci makes sense only on bets that pay 1 to 1, because the whole progression calculation relies on this ratio. There is no point betting along the series on numbers, splits or dozens - the payouts there are different, and the roll-back logic breaks down.

Before testing the system with money, it is useful to look at the real behaviour of even-money chances - how often and how long runs of one colour occur. This is convenient to track in the free roulette statistics tracker, which shows the numbers that have come up, the colours, odd and even on live tables in real time. Statistics do not predict the next spin, but they help you soberly assess how long the runs get and whether your chosen bankroll will withstand them.

The Fibonacci is a way to order your bets and control the pace, not a tool that makes roulette profitable. Play with the money you are ready to lose, and set a loss limit per cycle in advance.