A good trading system can be ruined by bad money management. I see a lot of bad money management systems, one of which is Fibonacci Staking. You won't see Fibonacci mentioned in financial literature with relation to money management. If you mention it then expect to be laughed at.
Another system that you may have heard of is the Martingale system, an 18th century invention to "help" a bad gambler get his money back. After losing a bet, the Martingale gambler doubles his next bet to get a return that covers the winnings of the current bet and the loss of the previous bet. The problem with the Martingale system is that if the gambler is on a losing streak then doubling up soon encompasses the whole of his bankroll. If the bad gambler loses again then he is penniless. Casinos have a maximum table stake so a Martingale gambler won't even get the chance to place a large enough bet to cover their losses so you can ignore all those YouTube videos promising you how to get rich quick playing roulette.
A Fibonacci staking plan is not much different to a Martingale. The stake is not doubled but increased by the Fibonacci series, where any number in the Fibonacci sequence is the sum of the two previous numbers.
The Fibonacci series - 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ... and so on
Again a losing streak will soon ramp up the size of your bets and eventually require a bet greater than your bankroll (or table maximum if you are in a casino). You will last a little longer than a Martingale gambler as you are not quite doubling up but not for much longer. If your system is a losing system then all that Fibonacci or Martingale betting will do is help you to lose your money more quickly.
The problem with Martingales (and derivatives such as Fibonacci) is that the stake bears no relationship to the probability of the event being gambled upon. There is no relationship between any two separate sporting events that yields a Fibonacci series or any other series. As we know from Kelly Criterion and its underlying information theory, a gambler should always bet in proportion to their certainty. A gambler with 100% certainty should bet their house, regardless of what their staking plan says. Of course, a one horse race is never run.
Anything gamble less than a 100% certainty must be judged against the odds being offered. This is where you look for your edge (See Kelly Criterion). If there is no edge then you keep your money in your wallet. Offered evens on the toss of a coin, the intelligent gambler does not bet unless the coin is biased towards his chosen head or tail.
Another fact, derived from Kelly Criterion, is that you should decrease your stake after a loss and not increase it. You should only increase your stake after a win. In other words, chase your winnings because you have more money to risk and never chase your losses. All this should demonstrate to the intelligent gambler that a staking plan that is not based on edge is doomed to fail.
Because you lost your last bet, why should the certainty of your next £55 bet be related to the previous £34 just because 55 follows 34 in the Fibonacci series? Fibonacci staking smacks of superstition and that a losing gambler has read a New Age book on the magic of the Fibonacci series and thinks it can cast a magic spell over a probabilistic event. Poppycock!