Financial betting strategies are not the best betting option, however some bettors believe they can be effective in the long run. We decided to test the Fibonacci sequence betting system in practice to see if this is actually the case.

** Who is Fibonacci? **

Leonardo of Pisa is the first major mathematician of medieval Europe. Best known by the nickname Fibonacci. Fibonacci was born in the Italian city of Pisa, presumably in the 1170s (in some sources it is 1180).

He expounded a significant part of his own knowledge in his “Book of Abacus”. This book consists of 15 chapters and contains almost all the arithmetic and algebraic information of that time, presented with exceptional completeness and depth. The first five chapters of the book are devoted to the arithmetic of integers based on decimal numbering.

In chapters VI and VII, Leonardo sets out actions on ordinary fractions. In VIII-X chapters, methods of solving problems of commercial arithmetic, based on proportions, are presented. Chapter XI deals with mixing problems. Chapter XII contains problems on the summation of series – arithmetic and geometric progressions, a series of squares and, for the first time in the history of mathematics, a recurrent series leading to a sequence of so-called Fibonacci numbers.

Chapter XIII sets out the rule of two false positions and a number of other problems that can be reduced to linear equations. In chapter XIV, Leonardo, using numerical examples, explains the methods of approximate extraction of square and cube roots. Finally, Chapter XV contains a number of problems on the application of the Pythagorean theorem and a large number of examples for quadratic equations. Leonardo was the first in Europe to use negative numbers, which he regarded as debt.

** Fibonacci numbers and the essence of the strategy **

Fibonacci numbers are elements of a numerical sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, … ,

where the first two numbers are either 1 and 1, or 0 and 1, and each subsequent number is equal to the sum of the two previous numbers.

The principle of the Fibonacci strategy for football betting is quite simple: bet on a draw, and if you lose, bet on another. Repeat this procedure until you win. There are only two additional important rules to follow:

- Only place a bet if the odds are higher than 2.618.
- If you lose, raise the next bet according to the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, etc.

This principle is based on a theory developed in 1989: it is most difficult for bookmakers to predict a draw, and therefore, this fact can be used. The bottom line is that you keep raising rates, so any winnings will offset previous losses. Someday there will be a win, and in the end you will remain in the black.

** Fibonacci strategy in practice **

In the English Premier League, an average of 24.5% of matches (in the last season) end in a draw. Similar statistics are found in other leading European football leagues. It is interesting to note that the odds for the draw on all 380 games were above the threshold of 2.618, which is proposed as one of the main conditions for betting.

It turns out that on average, a payout should be made every four games. Consequently, theoretically, the fourth number of the Fibonacci sequence turns out to be winning: 5 with the total amount of each bet of 100 rubles (the winning bet is added to the lost ones: 1, 1 and 3). Taking into account that the average odds of betting on a draw during the season was 4.203, this means that the average winnings would be 210 rubles with a net profit of 10 rubles, if you subtract the amount of the bet.

For more than 380 games, the theoretical amount will be 178670 rubles – and this is all with an initial bet of only 10 rubles.

** Shortcomings of the strategy **

In fact, there are many practical limitations that make this system not a way to make easy money. As a reminder, many games are played at the same time, so you cannot raise your bet to the next Fibonacci number unless the result is a draw, since the games end at the same time. Instead, players can apply Fibonacci sequence bets to specific teams. However, the sample of games will decrease significantly.

At the same time, this method means that long series of matches without a tie can significantly reduce the amount of money in players’ banks. You can recall the longest streak without a draw in the Premier League (Manchester United’s performance in the 2008-2009 season), when the Red Devils played twenty games without a draw, before finally losing the world 0-0 with Arsenal.

According to the Fibonacci sequence, the increase in rates occurs exponentially, so players would have to bet 109,460 rubles on the last game in order to comply with the principles of the system. Including this amount, anyone with the strategy would have to bet 286,560 pounds rubles, which is a huge amount for a system that provides a winnings of only 210 rubles. At the same time, the odds of betting on a draw for this game were 4.10, which would provide a win of 448,786 rubles or a profit of 162,226 rubles. Using the Fibonacci strategy, we raised the rates and got a good result.

** Strategy Explanation **

The Fibonacci sequence is one of the most famous number sequences in mathematics. It is expressed by a simple formula:

N ^{ 3 } = N ^{ 1 } + N ^{ 2 }

This means that after two seeds, each next number in the sequence is the sum of the previous two. The Fibonacci sequence begins like this: 1, 1, 2, 3, 5, 8, 13 and 21. The beginning of the sequence can be described as follows.

- N
^{ 1 }= 1, N^{ 2 }= 1, therefore N^{ 3 }= 2 - N
^{ 1 }= 1, N^{ 2 }= 2, therefore N^{ 3 }= 3 - N
^{ 1 }= 2, N^{ 2 }= 3, therefore N^{ 3 }= 5 - N
^{ 1 }= 3, N^{ 2 }= 5, therefore N^{ 3 }= 8

** Does the Fibonacci strategy work? **

The Fibonacci sequence betting strategy is best viewed as a kind of mathematical concept, since all progressive betting systems work ideally only with an unlimited bankroll and no other restrictions. Taking into account all the existing limits, the Fibonacci strategy, like all other betting strategies in real conditions, comes down to obscurity.

If we take the above example with the drawless streak of Manchester United, the player would have to risk the sum of 286,560 rubles for 21 times to make a profit of 162,220 rubles. Anyone who did not have 109,460 for a winning bet on 21 attempts would lose 200 thousand rubles.

Since all bettors have their limits due to a limited bankroll or under the influence of the bookmaker (and possibly their own emotions), the use of the Fibonacci sequence cannot last forever, so this strategy most likely will not serve as a profitable decision in a long distance.