Fabonacci Sequence

1-2-3-5-8-13-21-34. Go up one step with each loss, down 2 steps with each win. Note that every win pays for the two losses before it.

Example:

1. Bet $1 until you lose. Then bet $2.
2. If you win at $2, then return to step 1. If you lose, then bet $3.
3. If you win at $3, then return to step 1. If you lose, then bet $5.
4. If you win at $5, then return to step 2. If you lose, then bet $8.
5. If you win at $8, then return to step 3. If you lose, then bet $13.
6. If you win at $13, then return to step 4. If you lose, then bet $21.
7. If you win at $21, then return to step 5. If you lose, then bet $34.
8. If you win at $34, then return to step 6. If you lose, return to step 1.

Recommended variant for the high roller: instead of going down 2 steps with each win, go down 1 step with each win, until you win 2 in a row-then go down 2 steps. This variant may be as likely as any system to help you in the long run, and meanwhile you get some tremendous wins and excitement.

There are numerous other variants. However the usual Fibonacci is extremely unsatisfactory for the high roller-you lose often and never win big. Whereas for the player who prefers not to play 34 times his minimum bet if possible, it is debatable whether any Fibonacci is any better than Martingale, or just gives you 2 extra steps and then helps you fall off the cliff more often.

Therefore, no Fibonacci is recommended for the cautious player.