The Fibonacci, named after the Fibonacci sequence, is based on a natural sequence of numbers, found more than 900 years ago:
1-1-2-3-5-8-13-21 and so on. Each following number being the sum of the previous two.
The numbers represent betting units, e.g. £10, £10, £20, £30, £50, £80 and so on.
A fairly simple strategy at that: With each winning bet one would go back two numbers and with each losing bet, one would start off with the next increment.
An example of the system would be the following:
One has, for example, lost one’s first four bets to a total loss of 7 units. The next bet would be 5 chips. If it is a winning bet, it wins back the two former losses (3 and 2). The total loss now would be 2 units. Stepping back two numbers, one would now bet 2 units. If that bet wins, one wins back the 1 and 1, thus cancelling all losses.