The Fibonacci System is based on the Fibonacci Sequence developed by the Italian mathematician Leonardo Pisan, born in Pisa in 1170.
The Fibonacci System is based on the Fibonacci Sequence, developed by the Italian mathematician Leonardo Pisan, born in Pisa in 1170.
The sequence goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on. As you have probably figured out, the next number in the series is simply the sum of the previous two numbers. When playing The Fibonacci System, you start betting one unit on an evenmoney bet. If the first bet is won, then there is no sequence, and you start from scratch again by betting 1 unit. If the first bet is lost, then you write down 1 on a piece of paper. The next number in the sequence represents the size of the next bet. For example, the next bet will be 1 unit. If you lose again, then the next bet will be 2 units. When you win, you will cross out the last two numbers in the sequence. The sequence is finished when all the numbers are crossed out. You can see an example in the table. This example shows that you have lost 5 spins and won only 3. This gives you an accumulated win, which is the good thing about this system. 

The Fibonacci system is less aggressive (see table below). It will take a longer row of losses to wipe you out than when using the Martingale System. However, again it will not earn you a profit in the long run. Eventually, a row long enough to wipe you out will appear.
Losses In A Row:  Fibonacci bet size:  Fibonacci accumulated loss:  Martingale bet size is:  Martingale accumulated loss: 

1  1 unit  1 unit  1 unit  1 unit 
2  1 unit  2 units  2 units  3 units 
3  2 units  4 units  4 units  7 units 
4  3 units  7 units  8 units  15 units 
5  5 units  12 units  16 units  31 units 
6  8 units  20 units  32 units  63 units 
6  8 units  20 units  32 units  63 units 
7  13 units  33 units  64 units  127 units 
8  21 units  54 units  128 units  255 units 
9  34 units  88 units  256 units  511 units 
10  55 units  143 units  512 units  1023 units 
11  89 units  232 units  1024 units  2047 units 
The Fibonacci System is less aggressive, which is why it takes more than a single win to make up for a row of losses.