# Fibonacci Betting System

The Fibonacci betting system is popular for the even money bets in roulette. It is based on the Fibonacci sequence, a famous numerical series introduced in the Western world by the 13th century mathematician Fibonacci. In addition to roulette, this number sequence has many different applications, such as:

- It has many uses in computer science and mathematical analysis.
- It appears in most of the fine arts: architecture, sculpting, painting, music, etc.
- It is used in financial markets to help determine likely price drops and increases, depending on past activity.
- It is strongly related to the Golden Ratio, and found very often in nature, in the leaf patterns of a plant, spiralling seashells, etc.

## Origin of the Fibonacci Series

**Leonardo Pisano Bigollo**, also known as Leonardo of Pisa and **Leonardo Fibonacci** (1170-1250), was the son of an Italian merchant and, as such, travelled a lot through both Europe and the Arabian world. This gave him the opportunity to learn the Arabic number system and popularize it in Middle Age Italy and beyond, which up until then still used Roman numerals in their calculations. In addition to this, he came across a sequence of numbers which he published in his book *Liber Abaci* that later came to be known as the Fibonacci sequence. This series was already known at the time in India, and it was not Fibonacci who discovered it. Fibonacci was, however, the first person to introduce it in the West.

He demonstrated the utility of the number series by using it to solve problems in animal husbandry, using an example with rabbits. If a pair of rabbits always gives birth to two baby rabbits, and wait with birthing again until their young have reached sexual maturity, the Fibonacci sequence predicts exactly how many rabbits there will be at any given time.

## The Fibonacci Series

The series of Fibonacci numbers satisfies the condition that any number in the sequence is the sum of the two previous ones. The first two numbers are given to be 1, and this decides the full series:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …

This sequence of numbers has a number of special properties that are unique to the Fibonacci numbers:

- The most important is that the ratio between two consecutive numbers, while constantly changing, tends, as the series progresses, toward the Golden Ratio φ = 1.6180339… This is a constant that is found throughout nature in very many natural processes and phenomena.
- The square of each number is one less or one more than the product of the number to either side in the sequence (for instance, 3
^{2}= 2 × 5**-1**). - For every four consecutive Fibonacci numbers A, B, C, D it holds that

C^{2}– B^{2}= A×D

And much, much more!

## Using the Fibonacci System

This system uses the numbers of the Fibonacci system as bets. It is a **negative progression** system, where we increase the betted amount whenever we lose. The progression of the bets is geometric, which means losses can increase **very quickly** with a losing streak.

### How it works

- Start by betting a number of the Fibonacci sequence on an even money bet (Red, Odd, 19-36, etc.).
- Whenever we lose, increase the bet to the next number in the series.
- Whenever we win, decrease the bet to two numbers earlier in the series.
- As soon as we have a net profit of 0 chips, bet the initial number again. If we win, the series ends. This gives us a profit equal to that first bet.

### An example…

We will consider what happens when we start with betting 1 chip (the first number in the series), and we have a sequence of Wins (W) and Losses (L): LLLLWLWWW. This is how the Fibonacci system works in this case:

- We bet 1 chip. We lose.

Net: -1 - We lost, so our bet is the next number in the series, which is also 1. We lose again.

Net: -1-1 = -2 - Lost again, so we bet the next number, that’s 2 chips. We lose.

Net: -1-1-2 = -4 - Lost, so we increase the bet to 3. We lose again.

Net: -1-1-2-3 = -7 - Another loss. Increase the bet to 5. We win!

Net: -1-1-2-3+5 = -2 - We won, so we go back two steps in the series, and decrease the bet to 2. We lose…

Net: -1-1-2-3+5-2 = -4 - We lost, so we increase the bet to 3. We win!

Net: -1-1-2-3+5-2+3 = -1 - After the win, we go back two places, and decrease the bet to 1. We win!

Net: -1-1-2-3+5-2+3+1 = 0 - Our net profit is 0, that means we’re back where we started. We bet our initial bet of 1 chip again and win! With a net profit of 1, the system ends.

### Pros and Cons

When we win a Fibonacci series (coming back to where we started and winning), we win only our initial bet. The system is based on recovering losses by wins in such a way that a winning spin repays us the previous two losses. This way we only need half as many wins as there are losses (plus sometimes one extra) in order to make a profit.

As with all betting systems, it is important to set limits before playing. Although the Fibonacci system does not increase as quickly as the Martingale system, its progression is still very rapid and losses can get out of hand easily, to the point where you will not be able to recover them with your bankroll.

## Reverse Fibonacci

As with almost all systems, the Fibonacci also has a "Reverse" variant, that uses positive progression, which means the bets are increased after wins instead of losses. The idea here is to try to take advantage of winning streaks while minimizing losses during streaks of losing bets.

### Using Reverse Fibonacci

Start by betting a number in the series. Bet the next number on a win, go back two numbers on a loss. This means that in the course of a long streak of losses, you end up betting a minimum each spin, until you start winning again.

When you hit a winning streak this can earn you more than the regular Fibonacci system, but recovering losses requires on average more wins.