The Fibonacci system is a series of bets based on the Fibonacci sequence. It is composed of a series where each number equals the sum of previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.
The player bets one chip on colour (even/odd, 1-18 / 19-36). If he wins, he bets one chip again. If he loses, he writes down a new number of the sequence (1) and bets one chip again. If he loses again, he adds another number of the sequence (1, 1) betting their sum. Every time he wins, he checks off the last two numbers and bets the sum of the last two numbers in the sequence left on the paper. Obviously, writing on the paper in the casino would look unprofessional, and so it is necessary to remember the numbers or to play online.
The player is guaranteed a profit when there are no numbers of the sequence left on the paper. Interestingly, this happens even if he experiences more losses than wins. This strategy is slightly less risky than Martingale, but also a little less profitable. In contrast with Martingale, one win is not enough to reverse a series of loses.
In the charts, we see a gradual growth of all deposits until a series of losses brought them zero (as in Martingale). The player with the red chart was the exception, managing to hold on for 10,000 iterations with overall profit, despite a few significant losses. He was quite lucky, being all-in twice during play, and coming out successfully both times.
As we have shown, each of the described strategies will guarantee loss if played for long enough. Sadly, this is how statistics works. This means there is really no way to cheat at roulette.