The Fibonacci Betting System

Fibonacci is really very interesting.

Not the betting system…it’s a load of horse shit.  The Fibonacci Sequence on the other hand is one of those things that has simple minded folk like myself scratching our heads in confusion and wonder.

The Fibonacci Sequence is the foundation of the Fibonacci Betting system so it’s worth looking at first before considering the system.

Fibonacci Sequence

Here it is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

Spot the pattern?

The sequence starts 1, 1 (or 0, 1) and then continues with subsequent numbers in the series equal to the sum of the previous two. Child’s play right?

The sequence was first introduced into Western European mathematics by its  namesake Leonardo Fibonacci in his 1202 book  Liber Abaci, but it does have earlier Indian origins.

So what’s so fantastic about sequence?

Consider this.

Begin with a square tile of size (length x width) of 1 unit, representing the 1st number in the sequence. Next to it, place a tile the size of the next number in the sequence creating a rectangle, then the next, then the next and so on. Then trace a circular arc connecting opposite corners of these tiles and you get a spiral pattern, the beginnings of which looks like this.

fibonacci spiral

Turns out this pattern is an approximation of what is known as the Golden Spiral. The bigger the Fibonacci Spiral gets (in terms of tile numbers, not your sheet of paper) the closer it approximates the Golden Spiral.

Now here’s the amazing part. This exact shape is observed over and over again in nature…

In small things…


In fun things…


In big things (satellite image of hurricane Sandy)…


In even bigger things


In online live dealer things…


OK, 0ne of these images you won’t find in any science journals. It’s a bit of a joke.

Which leads us to…

Fibonacci Betting System

Somewhere along the line, some adventurous gambler (not Leonardo Fibonacci) figured the Fibonacci Sequence would be a great foundation for betting on even money payout events. Unsure of the logic here. Maybe they were hoping that the use of a scientifically significant sequence with a little natural wonder attached to it might somehow imbue their system with some credibility? Your guess is as good as mine.

The system isn’t used exclusively on roulette. It also gets a run on other even money bets with a near 50/50 chance of success, and there are plenty out there including baccarat.

But for the purposes of this post, lets stick to its application to roulette even money bet options: red/black, odd/even, high/low.

Applying the system is simple. Here are the rules.

  1. Have the Fibonacci Sequence at the ready:
  2. Select a bet unit amount. Your bets will be equal to this amount multiplied by each applicable Fibonacci number. For simplicity here, our unit is $1.
  3. Initial bet (even money): the first Fibonacci number multiplied by your unit amount:
    1 x $1 = $1
  4. Subsequent bets are placed according to the following rules:
  • if preceding bet lost…next bet is next number in the sequence, so for $1 units:
    $1 then $1, then $2, then $3,then $5, then $8, then $13 and so on.
  • if preceding bet won, then:
    – if preceding was initial bet, then just start again: $1
    – otherwise, your next bet will be based on the Fibonacci number 2 places back in the sequence:
    eg, bet $8 and win. Next bet is $3

If you manage to return to the beginning of the sequence your net position will be positive.

Hypothetical outcomes to illustrate bet methodology

Sequence: 112358132134…

Units: $1

Bet number Fibonacci Bet Amount Win or Loss Net position
1st 1,1,2,3,5,8 $1 win +$1
2nd 1,1,2,3,5,8 $1 loss even
3rd 1,1,2,3,5,8 $1 loss -$1
4th 1,1,2,3,5,8 $2 loss -$3
5th 1,1,2,3,5,8 $3 loss -$6
6th 1,1,2,3,5,8 $5 loss -$11
7th 1,1,2,3,5,8 $8 win -$3
8th 1,1,2,3,5,8 $3 loss -$6
9th 1,1,2,3,5,8 $5 win -$1
10th 1,1,2,3,5,8 $2 win +$1
complete 1,1,2,3,5,8

The last win in this example gets us back to the start of the sequence, and a net (positive) position equal to the chosen unit. This is despite more losses (6) than wins (4), which on the face of it seems like a good thing.

But this is the whole point of a negative progression betting system where you are increasing bet amounts as you lose, and decreasing them as you win. The most aggressive negative progression system, Martingale, will have you in the positive from one win after 10 (or more) losing bets. This doesn’t mean it will work for you in the long term.

Similarly, playing Fibonacci you will complete the sequence more often than not and take your single unit gain. When you don’t, it will hurt a lot.

Play this system an infinite number of times on a roulette wheel with no bias and your net position will be consistent with the game’s house edge (negative unfortunately).  Why?

Because each spin in an independent event, and all possible bets for that even have a house edge.

That old chestnut!


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