Fibonacci

The Fibonacci system uses the mathematical Fibonacci sequence as its basis. The Fibonacci sequence was devised by Italian mathematician Leonardo Pisan in the 12th century based on his observations of nature. The Fibonacci sequence can be observed in nature such as the curve of certain shells, the arc of a wave or even the procreation of rabbits.

The Fibonacci sequence is as follows:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

It is derived by adding the proceeding two numbers together. 1+1=2, 1+2=3, 2+3=5, 3+5=8…

In the game of blackjack the Fibonacci sequence can be utilised in a similar way as that described in the labouchere system. The player beings by betting the base of one unit. If they win the series is over and they begin again. If they lose the first hand then they continue with the sequence. In this case the second had would also bet one unit. The third would be two units and so on.

When a hand eventually wins, the previous two numbers get erased. Since a win will not necessarily cover all losses in that sequence it is necessary to continue until all numbers up to that point are also crossed out. Example:

1, 1, 2, 3, 5, 8

With the series above five losses would call for a bet of 8 units. In a $1 base unit game this equals $8. If the hand wins the profit is $8. However the player has incurred a loss of 1+1+2+3+5=12 units. We can subtract the 8 units we won from this loss by crossing out the last two numbers in the sequence (1, 1, 2, 3, 5). Now for this round we are still down by 12-8=4 units. We therefore need to carry on until the 1+1+2 units (4 units) are crossed out. At this point we will have covered all losses for that round. To do this we then carry on, so the next bet is 3 units. Presuming this wins we are only one unit down. This series is illustrated by the table below:

As you can see, the series ends when the player is up by one unit. Another series will then begin from scratch. Play continues until the player reaches a pre-determined win-limit.

The Fibonacci system is often compared with the better known martingale system since both require the player to increase bets after a loss. A Fibonacci progression system, however, is considerably less aggressive than the martingale system, which has the same objective of making a 1 unit profit per series. The table below shows the differences between the betting sizes and cumulative losses for each system based on ten consecutive losses.

The Fibonacci system is certainly not a guaranteed way to profit from blackjack. In fact in the long run you certainly risk losing your entire bankroll when using any betting system. In spite of this, when compared to martingale (which is used by a considerable number of gamblers) the Fibonacci system would take a much longer series of losing hands before wiping out your bankroll or reaching table limits.