The Fibonacci sequence dates back all the way to 13th century and it has since found its ways in many aspects of our life. The Fibonacci sequence found its way into mathematics, physics, computers, architecture and even music and art. Therefore, as dizzying as it may seem, the Fibonacci sequence has found its way into the gambling world as well.

The Fibonacci sequence is a series of numbers that progress by adding the sum of the previous 2 numbers of the sequence as the next number. The sequence starts with 1, 1 and moves on. For example: 1, 1, 2, 3, 5, 8, 13, 21.
1+1 is 2, 1+2 is 3 and so on.

If we apply this sequence to roulette, we end up with a betting pattern that increases over time and by following its rules, can lead us to a higher profit over a long playing session. Similarly to other systems such as the martingale system, which has you double your bet every time you lose, you increase the bet when you lose but the raise spreads over more rounds, buying you more time before you hit the table limit.

An example of using the Fibonacci sequence with the roulette would have you bet on 1 unit (usually the minimum bet). If you lose, you go on to the next number of the sequence which is 1. If you win, you cross out the previous 2 numbers of the sequence and continue to the next number based on the 2 numbers the come before the two you've just crossed out.
The sequence end you get back to 1.

For example, let try the following scenario:
1st Bet 1 unit – lose
2nd Bet 1 unit – lose
3rd Bet 2 units – lose
4th Bet 3 units – lose
5th Bet 5 units – win. 2 and 3 are crossed out.
6th Bet 2 units – win. Sequence ends.

At this point We've ended the sequence with the addition of 1 betting unit to our bankroll.

Like many other betting systems, the Fibonacci betting system has its flaws. It's still superior to the martingale system but shares its weakness for the table limits.
Using betting systems may not always make you a big winner, but it can definitely enrich your time at the table.