Fibonacci numbers are a sequence of positive intergers (whole numbers) named after Leonardo of Pisa (1170-1250), also known as Fibonacci. The Fibonacci betting system for roulette builds on a sequence starting with these figures 1-1-2-3-5-8 (add the last two to get the next).

In fact, the first number of the sequence is 0, but for obvious reasons (if you bet zero and win you still would have zero) you would not need this number for betting. Each subsequent number is equal to the sum of the previous two numbers of the sequence itself - each successive number is calculated from the sum of the previous two.

In mathematical terms it is defined by the following recurrence relation (each term of the sequence is defined as a function of the preceding terms): the n-th Fibonacci number = (n-1)th + (n-2)th.

Example:

1 -> 1 -> 2 (1+1) -> 3 (1+2) -> 5 (2+3) -> 8 (3+5) -> 13 (5+8) -> 21 (8+13) etc.

This famous sequence goes all the way back to 200 BC and has a peculiar habit of showing up in various areas of life. These sequential members and the ratio between them respectively occur throughout both nature and arts, for example architecture (Greek temples etc.), music and biology (the numbers of ancestors of a male bee or the branching of certain plants).

Two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is equal to the ratio between the larger quantity and the smaller one. The golden ratio is approximately 1.6180339887. Incidentally, every third number of the sequence is even.

The ratio of a number from the Fibonacci sequence and its immediate predecessor progressively approximates, ever so closely, the golden ratio. The ratio of two consecutive Fibonacci numbers gets closer to the golden ratio as they increase (see table below).

Fibonacci Numbers and their ratio ( 1/1, 3/2, 8/5, 21/13, 55/34 ... )
Number	1	1	2	3	5	8	13	21	34	55	89	144	233	377	610	987
Ratio	1		1.5		1.6		1.6153		1.6176		1.6179		1.6180		1.6180

After the eighth sequence of calculations, if you keep dividing the former number by the latter one, you can clearly see this constant relationship between the numbers. It always yields 1.6180.

Compared to the Martingale strategy the Fibonacci system is somewhat "cheaper", as the size of your bets doesn't grow as fast and you don't need as large a bankroll. It also is a bit "slower", since you'll normally have to play more rounds before a sequence ends.

How to play with the Fibonacci system?

When you lose

When using the Fibonacci roulette system, each time you lose you raise your wager on the next round. But unlike the Martingale system, where you double your next bet, you follow the Fibonacci sequence. Example: Start by betting 1 unit. If you lose, bet 1 unit. If you lose a second time, bet 3 units, then 5, then 8, and so on.

When you win

When you win a round, you don't end the sequence at once like when using the Martingale strategy, but cross out the winning number and the one before that. Then use the highest number remaining for your next bet. Example: You bet 13 units and win, you cross out 13 and 8.

Your next bet is 5 units. If you win again, cross out 5 and 3.

Bet 2 units and so on. The sequence ends once you're back to betting 1 unit.

Conclusion

The Fibonacci system may not be the best choice for games with high minimum wagers (where your basic unit is $10 or more). As the numbers in your betting sequence increase with every losing bet the best tactic is to start with the smallest amount possible. The smaller the minimum betting amount is (1 or 5 units) the better you can cope with losses of the short term. In that respect the Fibonacci system is better suited than the Martingale strategy, though.

Whatever the pros and cons might be, playing the Fibonacci roulette system is bound to give you a good time at any table and will enhance your overall roulette experience.

The Fibonacci system is preferably used for clearing a casino bonus. However, bets using this system build slower than with the Martingale strategy. When playing with a system it's important to have a big enough bankroll. Therefore always chose a casino with a large match bonus.

Try it yourself without risking your bankroll

If you want to test the Fibonacci Betting System you can do it without risking your bankroll by playing in free online roulette casinos.

If you'd like to put the Fibonacci system to the test you may try this strategy for free on the 50/50 bets (Odd/Even, Red/Black, 1-18, 19-36) in roulette. To facilitate this, we are pleased to provide the following link: try Fibonacci Roulette System free.

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