There are two broad categories of progressive betting systems—positive and negative. The positive systems require wagers to increase in size when winning in order to maximize profit. By contrast, the negative systems require wagers to increase when losing in order to recover losses.
Based upon a famous mathematical sequence of numbers developed more than a millennium ago, the Fibonacci Betting System advocates a negative progression. It falls into the same category the Martingale, Labouchere and d’Alembert betting systems.
It is believed that series of integers at the heart of the system was originally discovered by mathematicians in India as far back as the 6th century. However, it was the Italian mathematician known as Leonardo Pisano Bigollo Fibonacci (1170~1250), who popularised the sequence and lent to it his name. Undeniably, Fibonacci deserves credit for introducing the number pattern to the Western world in the 13th century through the publication of his “Book of Calculation,” the Liber Abaci.
In simple terms, each number in a Fibonacci sequence is the sum of the two numbers that precede it. For example, if the series starts out with 0 and 1, it would continue to become 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, and so on. Expressed mathematically as an equation for any number n > 1, the sequence is
F(0)=0; F(1)=1; F(n) = F(n - 1) + F(n - 2)
As the numbers in the sequence grow, something quite interesting occurs. Dividing each larger number by its smaller neighbor yields a number that approaches the Golden Ratio, or about 1 : 1.618 or 0.618 : 1.
When applied to wagering, the Fibonacci Betting System works in a manner of cancelling numbers quite similar to that of the Labouchere Betting System. The player bets an amount equal to the most recent two losses, crossing them off from the series after a win and adding any newly lost amount to the end of the series.
The object is to cross off numbers twice as fast as they are added. Over time, all of the numbers in the series will be crossed off, resulting in a profit equal to whatever the initial bet was. Then, the progression begins again. Unlike Martingale, Fibonacci does not lead to risking large amounts at poor odds to recoup previous losses.
Because the Fibonacci sequence can start with any two numbers, the player can use them to set any profit objective desired. For example, to win five units, the player might start the sequence as 2 + 3 or 1 + 4. In either case, the initial wager would be five units. A win would end the series, while a loss would add the number 5 to the end, i.e. 2 + 3 + 5 or 1 + 4 + 5. The former requires betting 2 + 5 = 7 units on the next wager; the later requires 1 + 5 = 6 units to be bet.
Play and betting continues in this fashion, crossing off two numbers for each win or adding one for lost amounts at the end of the series. A profit of exactly five units will be claimed as soon as all of the numbers have been crossed off.
The Fibonacci Betting System is most widely used for “even money” wagers like Black or Red bets at the Roulette table, Pass or Don’t Pass bets at the Craps table and Banker or Player bets at the Baccarat table. With some modification, it can also be applied to Blackjack or sports betting where vigorish must be accounted for.
One clear advantage to using the Fibonacci Betting System is that outside observers may not even be able to tell that it is a form of progressive betting. The wagers become larger after losses, but they do not always revert to the original bet after a win. Bet size increases and decreases in small increments.