The Fibonacci betting system is another negative progression betting system. It is simple and easy to follow. In its most basic form, you follow the Fibonacci sequence on a losing streak, and reset to betting 1 on a win.

The Fibonacci sequence is Xn+1 = (Xn + Xn-1) where Xn:-1 =0 and Xn:0 =1.
Thus first few items of the sequence is: 1,1,2,3,5,8,13,21,34,55,89...

So an example of a betting using the basic Fibonacci system:
Bet Amount	Bet Result	Total Profit
1	Loss	-1
1	Loss	-2
2	Loss	-4
3	Loss	-7
5	Win	-2
1	Win	-1
1	Win	0
1	Loss	-1
1	Loss	-2
2	Loss	-4
3	Loss	-7
5	Loss	-12
8	Loss	-20
13	Loss	-33
21	Loss	-54
34	Win	-20
1	Loss	-21


As can be seen in the example above, the Fibonacci betting system is not sustainable using a payout of 2, because it does not progress fast enough on a loss. Using a higher payout can be an alternative.

Alternative methods to use the Fibonacci sequence is in a similar way to d'Alembert, to step 1 step right in the sequence on a loss, and step 1 step left in the sequence on a win.
Bet Amount	Bet Result	Total Profit
1	Loss	-1
1	Loss	-2
2	Loss	-4
3	Loss	-7
5	Win	-2
3	Win	1
2	Win	3
1	Loss	2
2	Loss	0
3	Loss	-3
5	Loss	-8
8	Loss	-11
13	Loss	-24
21	Loss	-45
34	Loss	-79
55	Win	-24
34	Loss	-58


This is a slightly more profitable method than the basic Fibonacci, but suffers from the same fundamental flaw as the d'Alembert strategy; requiring an equal amount of wins and losses.

The system can further be customized by adjust the number of steps to take into the sequence on a win or a loss. You can, for example, step 2 steps right on a loss and 1 step left on a win.

The Fibonacci system can be reversed into a positive progression system as well, by increasing your bet on a win and decreasing your bet on a loss instead.