## Fibonacci (Whittacker)

#### Strategy principles

The Fibonacci or Whittacker bet system is, like the Classic Martingale or the Great martingale, a betting system with a negative progression, that means based on the increase of stakes following the losses.

The Fibonacci sequence is a very old, made famous in the book Liber Abaci (the book of calculation) published at the beginning of the 13th century by the Italian Leonardo Fibonacci.

The sequence starts with 0 and 1, then each number is the result of adding the two numbers that precede it:

0 . 1 . 1 . 2 . 3 . 5 . 8 . 13 . 21 . 31 . 55 . 89 …

Although very simple to understand and calculate, this sequence is one of the most popular in the world of mathematics. The Fibonacci sequence also appears frequently in nature! It has always intrigued and fascinated mathematicians, more details in this article on Wikipedia.

The popularity of this sequence inspired gamblers to see a relation with the evolution of bets in gambling. In the Fibonacci betting system, the gambler bets the sum of his previous two wagers as long as he loses. Exactly as in the Fibonacci sequence.

#### Rules of the Fibonacci method

Although it can be applied to any type of betting; sports, horse racing or even in trading, the Fibonacci betting system is popular in casinos and more particularly in roulette with simple bets (red / black, odd / even pair …).

Before you begin, prepare the Fibonacci sequence starting from the base bet unit, for a bet unit of \$10, the sequence will be:

\$10 – \$10 – \$20 – \$30 – \$50 – \$80 – \$130 – \$210 – \$340 …

Two rules and two exceptions :

1. A step forward after a loss, intuitively, the amount of a bet following a loss is the sum of the last two bets of the Fibonacci sequence.
2. Two steps back following a win, with two exceptions:
1. Return to the first base bet unit, if you are in the second row of the sequence (it is not possible to bet 0).
2. Return to the beginning of the sequence if a positive profit is made in the current cycle.

#### Example

In this example simulated on GSimulator, played Odds are 2 (US +100), probability 50% and the bet unit is \$10 :

#SequenceCost (\$)ResultWin (\$)Cycle (\$)Bankroll (\$)
110 10 + 1010 Reset10
210 10 0– 100
310-10 10 0– 20– 10
410-10-20 20 0– 40– 30
510-10-20-30 30 + 30– 100
610-10 10 + 10010
710 10 0– 100
• In this example, following the first winning bet, we replay the first bet, which corresponds to 1 * \$10 in the Fibonacci sequence.
• First loss after the second round, we bet the next number of the sequence 1 * \$10.
• For the next losses, we increase the bet following our Fibonacci sequence, each bet is the sum of the last two bets.
• After the fifth round, we move two steps backwards on the current sequence, we then bet \$10.
• Following the sixth winning bet, it is not possible to jump two steps back, we return to the base bet unit.

#### Benefits and risks

The principle of the Fibonacci method is to cancel by a win the last two losses. Unlike the traditional Martingale which always tries to cancel all the last consecutive losses, The Fibonacci system only covers the last two. And so, its progression is less brutal.

But the second exception of the second rule of this system (return to the beginning of the sequence if a profit was made in the current cycle) makes the application of the method in real conditions very complicated because it requires to keep track of the progression of the game.

The Fibonacci betting system can be lucrative in the short term but like all other strategies with negative progression, the gambler is never safe from a black serie which will cause high amounts of bets exceeding his capacities or the maximum betting limits imposed by casinos or online betting websites.

#### GSimulator

GSimulator simulates the progression and the results of a Fibonacci betting system, taking into account all the parameters of the game (starting bet, odds other than 2, number of repetitions or the bankroll limit). It also provides the tools to analyze results and compare cost differences with other strategies.

Start a free simulation of the Fibonacci (Whittacker) strategy in the GSimulator or consult the documentation for more informations.

#### Other betting systems

Other strategies and betting systems exist and try to limit the losses, or to increase the profit, by making changes to the rules of stakes following the losses (negative progression) or following the wins (positive progression) :