A description of the Fibonacci Betting System, with examples of basic play and how to win by applying the system as a wagering strategy.

## Fibonacci Betting System

Progressive betting systems fall into two broad categories: positive and negative. The former systems propose increasing the size of wagers when winning to maximize profits, while the latter advocate wagering more when losing in order to earn back losses.

The Fibonacci Betting System, which is based upon a famous mathematical sequence of numbers developed nearly a millennium ago, is an example of the negative variety. It belongs to the same category as the betting systems known as Martingale, Labouchere, and d’Alembert.

## Background

Italian mathematician Leonardo Fibonacci, who was born Leonardo Pisano Bigollo (1170~1250), has his name associated with this betting sequence, although there is evidence that the series of integers on which it is based was actually discovered by Indian mathematicians as long ago as the 6th century. Fibonacci’s major contribution was making it known to the Western world in the 13th century, when his Book of Calculation, the Liber Abaci, was published.

In the Fibonacci sequence, each number is the sum of the previous two numbers, beginning with 0 and 1. The series starts out 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, and so on. It can be defined mathematically as follows:

F(0)=0; F(1)=1; F(n) = F(n – 1) + F(n – 2) for n > 1

There is something quite interesting to note as the numbers in the sequence grow. Dividing the bigger number by its smaller neighbor results in a number that approaches the Golden Ratio, or approximately 1 : 1.618 or 0.618 : 1.

## Basic Play

Much like the Labouchere Betting System, Fibonacci uses a cancellation approach to determining how much to bet. The player wagers the amount of the last two losses, crossing them off from the series when a win occurs and adding any newly lost amount to the end of the series. The strategy is to cross off numbers twice as fast as they are added. Eventually, when all of the numbers in the series have been crossed off, the progression begins again. Unlike Martingale, it does not require risking huge amounts at unfavorable odds to recover previous losses.

Starting with the numbers 0 and 1, the player would first bet their sum, 0 + 1 = 1 unit. A loss would cause the wagered amount to be added to the sequence (0, 1, 1) and the sum of the last two losses would be bet, 1 + 1 = 2 units. Another loss would cause the process to be repeated (0, 1, 1, 2) with a wager of 3 units, etc. Any win causes the two numbers wagered to be crossed off.

Play and betting continues in this way, crossing off two numbers each time a win is recorded or adding each amount lost to the end of the series. Gradually, all of the numbers will be crossed off, resulting in a profit of one unit.

## Applying Fibonacci to Blackjack

One advantage to playing the Fibonacci Betting System is that it does not look like progressive betting to outside observers. The wagers do not always become larger. They increase and decrease in relatively small increments.

Like all progressions developed for even-money bets, Fibonacci requires a special strategy for non-even-money situations, such as splitting, doubling down, insurance, and higher odds paid for a natural 21. The typical approach is to set aside any extra money won for a successful split, double down, or 3-to-2 payout for a natural blackjack, treating it as “bonus” cash to cover the costs of additional losses on unsuccessful splits and double downs. Insurance can simply be ignored or else funded out of the bonus pool.

Beginning users of this system may at first find it difficult to remember the sequence without writing it down. A simple solution is to stack chips in piles representing the amount to be wagered: 1, 1, 2, 3, 5, 8, 13, 21, etc.