Fibonacci System

The Fibonacci betting system uses the famous Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... Each number is the sum of the two before it. After a loss, you move one step forward in the sequence. After a win, you move two steps back.

Example with $10 base: Bet $10 (lose), $10 (lose), $20 (lose), $30 (lose), $50 (win → go back 2), $20 (win → go back 2), $10. The sequence naturally controls bet growth.

The Fibonacci grows slower than the Martingale (which doubles every loss) but faster than D'Alembert (which adds one unit). After 10 losses, your Fibonacci bet is $890 versus $10,240 for Martingale or $110 for D'Alembert.

The system has an interesting property: you don't need to win as many bets as you lose to break even. In theory, winning just 1/3 of your bets can be enough to recover losses, depending on where in the sequence the wins occur.

But once again, this system cannot overcome the house edge. The mathematical expectation is the same as flat betting. What changes is the variance profile: moderate risk of large losses with moderate frequency of small wins.

Some players enjoy the mathematical elegance of the Fibonacci sequence. If you're going to use a betting system (accepting that none can beat the house), the Fibonacci is a reasonable middle ground between aggression and safety.