# Fibonacci

## Fibonacci sequence

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc. He carried the calculation up to the thirteenth place (fourteenth in modern counting), that is 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.

### How it works

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers.
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: 1,1,2,3,5,8,13,21,34,55,89,144,233, 377 …

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 -16
13 Loss -29
21 Loss -50
34 Loss -84
55 Win -29
34 Loss  -63

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.