The Fibonacci System

Fibonacci Roulette System Strategy

This system uses a negative progression bet pattern based on a sequence of numbers created by the Italian mathematician, Fibonacci. On a loss, you must increase the bet and decrease it on a win. The Fibonacci relies on even-money bets and can be used in other games of chance other than Roulette including Sic Bo, Baccarat, Blackjack, and Craps.

Leonardo of Pisa aka Fibonacci

To answer a query about the number and rate of rabbit reproduction in one year, 13th century mathematician, Fibonacci, posed a sequence of 12 numbers. Each unit represented a pair of rabbits for each month of the year: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

With the exception of the first two numbers, each unit is the sum of the two units left of it. The Fibonacci system uses this sequence to turn a profit in games of chance.

How to Use the Fibonacci System

The Fibonacci number sequence is central to the effectiveness of this system. That's why, we recommend using a notepad and pen to keep track of bets, wins, and losses. Below are 10 numbers of the sequence for reference. Each number represents 1 bet unit.

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55

To apply this system to roulette, follow these basic steps:

  • For the first round, place 1 unit on an even-chance bet of your choice.
  • 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
  • On a loss, move along the sequence of numbers 1 space the right to select the next bet.
  • 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
  • On a win, move 2 spaces to the left. If you are not able to, because you haven't moved along the sequence far enough yet, then go back to the beginning of the sequence.
  • 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
  • Repeat steps 2 and 3 until you achieve a profit.

"When selecting a base bet, keep in mind that negative progression systems can become costly in just a few rounds. Start with a low value unit to avoid reaching either the table limit or your personal limit."

Best Bets for the Fibonacci

This system recommends the use of even-money bets including black/red, even/odd or low 18/high 18. Due to house edge, each offers a 47% chance to win each round. The payout for these outside bets is 1/1. So, if you bet $5 the payout will only amount to $5. These are considered the lowest risk bets available in Roulette.

A Tableside View of the Fibonacci at Work

You login to your favorite online casino with a notepad and pen. Across the top of the paper, you have the number sequence 1, 1, 2, 3, 5, 8 which reflects your total loss limit of $100 when using bet units worth $5 each.

  • Ready to begin, you place a chip on high 18.
    1, 1, 2, 3, 5, 8
  • The ball selects 6 black resulting in a loss of -C$5. Following along the number sequence, you place 1 chip on high 18 again.
    1, 1, 2, 3, 5, 8
  • This time the ball lands on 5 red. Now, your net loss is -C$10. You have a look at your numbers and place 2 chips on the same outside bet.
    1, 1,2, 3, 5, 8
  • Your luck fails again as 10 black is selected. This puts your net cash loss at -C$20. It seems that you have a small losing streak on your hands, but you steel yourself and place 3 units on high 18.
    1, 1, 2, 3, 5, 8
  • This time, you relax a bit as 35 black is selected. It pays out C$15, bringing your total net loss to C$5. Now, you must move left two spaces in the series to select the next bet. So, you place 1 chip on high 18.
    1, 1, 2, 3, 5, 8
  • Another win as the ball lands on 22 black awarding a payout of C$5 for a total net profit of C$0. You bet 1 chip again and cross your fingers as the wheel spins.
    1, 1, 2, 3, 5, 8
  • It's a win! The payout puts you C$5 ahead, so you reset back to the beginning for the next session.

This example shows how the system can award a profit for a loss to win ratio of 3:3. This ratio improves as you move to the right of the series, allowing you to recover from a 4 round losing streak with 3 wins or 6 with 4 wins. Of course, the further along you go, the more expensive it becomes.

The Logic of the Fibonacci System

Increasing the bet by one number in the series allows the partial recovery of losses in the event that the next spin wins. With each loss, the bet grows larger and larger. In the beginning, the bet progression seems slow, but in just a dozen rounds, the numbers grow too large for any roulette table limit to allow.

Decreasing the bet by two numbers in the series is intended to lower the cost of the next bet while recovering some losses if the next spin wins. This helps a bit, particularly as the bet only increases by one place in the series on a loss but moves two places back on a win.

So long as an extensive losing streak doesn't occur, this system's mathematical theory should pull through for small profits. Of course, anything can happen in real-life scenarios, so don't count your chips till you've won!

Pros Cons
Under the right circumstances, this can award a profit with less wins than losses. Profit potential is low due to the use of even-chance bets.
At first, the bet progression is slower than 'double up' systems giving you a few rounds before bets snowball. A bit inconvenient as you need a pen and paper to use during gameplay.
Can be applied to any game of chance that allows even-money bets. Negative progression systems carry the risk of reaching the table bet limit too quickly to be effective.

The Reverse Fibonacci Variation

This system relies on positive progression instead of negative. In other words, it requires that you raise your bet on a win instead of a loss.

The steps would look something like this:

  • For the first round, place 1 unit on an even-chance bet of your choice.
  • On a loss, move along the sequence of numbers 2 spaces left, or not at all if you haven't lost yet.
  • On a win, move 1 space to the right to select the next bet.
  • Repeat steps 2 and 3 until you achieve your profit goal.

Positive progression systems rely on getting more wins than losses to profit. However, they also allow you to take advantage of increased profit potential from winning streaks.

Does This System Really Work?

The Fibonacci system can produce a profit under the right set of circumstances. You've already seen a best case scenario for this system with 3 losses followed by 3 wins proving that it can potentially award a profit with about the same number of losses as wins. Mathematically, the system should come back from a losing streak eventually, but isn't always able to due to table limits or personal budget.

Let's see how this plays out with a longer initial losing streak of 7.

Round Bet in Units Win/ Lose Net Units
1 1 Lose -1
2 1 Lose -2
3 2 Lose -4
4 3 Lose -7
5 5 Lose -12
6 8 Lose -20
7 13 Lose -33
8 21 Win -12
9 8 Win -4
10 3 Lose -7
11 5 Lose -12
12 8 Win -4
13 3 Lose -7
14 5 Win -2
15 2 Win 0
16 1 Win 1

This extended session demonstrates a scenario that awards a profit of 1x the base bet despite a ratio of 10 losses to 6 wins. Notice how this session began with a losing streak of 7, pushing the bet as high as 21 units. That can be an expensive wager depending on what you've chosen as a base bet. Ultimately, it could be argued that the profit is much lower than the risk warranted.

When selecting a bet unit, it is always best to count the cost before beginning a session. If you reach the table limit before the system has a chance to work, then you will be in for some serious losses. Have a look at the bet progression when each unit is worth $10.

Round Bet in Units Bet in Cash Net Cash Loss
1 1 C$10 -C$10
2 1 C$10 -C$20
3 2 C$20 -C$40
4 3 C$30 -C$70
5 5 C$50 -C$120
6 8 C$80 -C$200
7 13 C$130 -C$330
8 21 C$210 -C$540
9 34 C$340 -C$880
10 55 C$550 -C$1430
11 89 C$890 -C$2320
>12 144 C$1440 -C$3760

In just 12 rounds, you could break both your bankroll and the table limit. While a losing streak of 12 is unlikely, it does happen. If you choose a bet unit in the amount of $5, you can cut those numbers in half.

Another thing to take into consideration, is that negative progression systems don't do as well with initial winning streaks as initial losing streaks. Have a look at how the Fibonacci system does when the session begins with a winning streak of 4 followed by a losing streak of 3.

Round Bet in Units Win/Lose Net Units
1 1 Win 1
2 1 Win 2
3 2 Win 3
4 3 Win 4
5 5 Win 3
6 2 Win 2
7 1 Win 0

It just manages to break even. Not a bad scenario. Now, let's compare it to a session that starts off losing 4 rounds, then winning 3.

Round Bet in Units Win/Lose Net Units
1 1 Lose -1
2 1 Lose -2
3 2 Lose -4
4 3 Lose -7
5 5 Win -2
6 2 Win 0
7 1 Win 1

Unlike the earlier example, this session profits despite having more losses than wins. This is because negative progression systems don't take advantage of winning streaks and focus more on regaining losses after losing streaks.

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Responsible Gambling

  • When using a negative progression bet system, always count the cost before selecting a base unit. Both bets and losses increase dramatically in a short amount of time.
  • Don't chase your losses. Set a budget and stick with it despite the Fibonacci instructing you to stop only when you gain a profit.
  • There are no guaranteed winnings with this or any roulette system. Each session varies despite even-chance odds.

Is This the Method for You?

If your pockets are deep, and you don't mind having to track your net units on paper, then you may find that this system makes a good fit. When used correctly, it can eventually award a bit of profit if it doesn't hit too long a losing streak.