# Fibonacci Roulette Strategy

The Fibonacci sequence is a mathematical enigma of nature that was discovered by the Italian mathematician Leonardo of Pisa, who, from the nickname of his father (Bonacci) was also known as Fibonacci (filius Bonacci). He described the numerical succession in his Book of the Abacus (Liber Abaci) in the year 1202. Each successive number is the sum of the two previous ones and as this is a negative betting progression, bets are increased after a loss and decreased after a win.

## How the Fibonacci Strategy Works

Fibonacci analyzed an abstract mathematical problem based on the growth of a family of rabbits over a year. However, five centuries before, the succession was already mentioned in Indian books written by ancient mathematicians and in India it is widely used for metrics in the composition of verses.

Repeatedly, from the study of nature, the universe and the world around us, different people have found the Fibonacci sequence in the most unexpected places. In different plants the leaves are arranged (filotaxis) according to this sequence, which can also be found in sunflower seeds, in the arrangement of pine cones, flowers, petals, in the structure of the spirals of shells, hurricanes, tree branches, spiral galaxies and in many other places in nature. Humans also have features that are formed from this sequence including the length of the phalanges on the fingers and the positioning of the mouth and nose on the face in relation to the distance between the eyes and the chin.

The effect of the application of the Fibonacci sequence on the algorithms was also mentioned by Donald Knuth in his immortal works on programming, in mathematics this succession refers to the relation of linear recurrence.

In order to explain the principle of formation of the Fibonacci sequence as clearly as possible, we will say that each number in the numerical sequence is the result of the sum of the two previous ones. The sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597, 2,584, 4,181, 6,765 and 10,946

Although the end of the sequence is infinite.

When applied to the game of roulette the Fibonacci sequence is used to progressively grow bets. As the first digit of the sequence is zero, it is ignored and bets should be placed on red/black, odd/even, low/high as they have a 1 for 1 payout ratio.

## How to Make Bets with the Fibonacci Sequence

The game starts with a minimum base bet and in the case of a loss, the player makes their next bet according to the next number in the Fibonacci sequence. In case of a win, the player goes back two numbers and makes a bet of the same amount as the corresponding number in the sequence. So if they had bet 8 and won, then the next bet would be 3.

The following table shows the rules of the Fibonacci system with an example:

ROUND | RESULT | BET | BALANCE |

1 | Lose | 1 | -1 |

2 | Lose | 1 | -2 |

3 | Lose | 2 | -4 |

4 | Lose | 3 | -7 |

5 | Lose | 5 | -12 |

6 | Lose | 8 | -20 |

7 | Win | 13 | -7 |

8 | Win | 5 | -2 |

9 | Win | 2 | 0 |

10 | Win | 1 | +1 |

The player does not have to perform any kind of complex calculation, they just have to remember the succession. In the actual game, the amount of numbers in the sequence and the size of the last one depend on the player's balance and, in rare cases, on the bet limits of the table.

The adequacy of the length of the succession and the bank of the player is determined in a simple way. Any number in the sequence is equal to the sum of all the previous numbers up to the previous number, plus 1. So choosing a number in The Fibonacci sequence closest to the total balance of the player and isolating the previous number according to the sequence, will give the player their own version of the Fibonacci sequence according to which the game bank will be guided.

For example, a bankroll of 89 (88) base bets, allows the player to sustain a series of 9 unfortunate spins where they will make bets in the following manner: 1, 1, 2, 3, 5, 8, 13, 21, 34. On the other hand, a bank equivalent to 34 (33) base bets, can ensure only 7 consecutive lost rolls, with the following bets: 1, 1, 2, 3, 5, 8, 13. While one of a size equal to 13 (12) base bets will only allow the player to make 5 increases of the bet up to 5, and so on.

## Fibonacci vs Martingale Strategy

It should also be remembered that theoretically, it is possible that a situation occurs in which the player needs to make a bet that exceeds the maximum limit of the table. However, the real possibilities of this happening are very low. The following table shows the growth of bets according to the Fibonacci system and the Martingale system:

ROUND | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

FIBONACCI SYSTEM | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 |

MARTINGALE SYSTEM | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1,024 | 2,048 |

It is obvious that even an unusual 12 bet raise in the Fibonacci system will require a bet equivalent to 144 base bets, this should fall within the standard limits of the roulette tables found in most casinos. However, this cannot be said about the Martingale strategy, whose betting growth is the fastest among the rest of the roulette strategies.