Fibonacci sequence and gambling (roulette case)

Joanlui74

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As you may know, the Fibonacci sequence is a numerical progression in which each number is the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, etc.). This mathematical regularity has also been adopted as a betting strategy in games of chance, particularly roulette. The idea is to use the sequence to manage bets and gradually attempt to recover losses, achieving a small positive margin when winning.

Application to Roulette Columns
Unlike bets on red/black or odd/even, which have probabilities close to 50%, the Fibonacci method can also be applied to columns, which offer a 2 to 1 odds ratio. European roulette has 37 pockets, including 36 numbers and the zero. Each column contains 12 numbers: the probability of winning is therefore 12/37 ≈ 32.43%. If you lose, you advance one step in the sequence, increasing your stake; if you win, you move back two positions. For example, after a losing streak with bets of 1, 1, 2, 3, and 5, a win on the column would return 10 units (5 x 2), largely covering previous losses and producing a small profit.

Advantages and Disadvantages
The Fibonacci system has the advantage of a less aggressive growth pattern than other systems like the Martingale, which doubles each time. The gradual increase reduces immediate pressure on the budget. In the long run, however, the math remains unfavorable. Over 100 roulette spins, you can expect an average of about 32 wins and 68 losses.

Simulations and concrete results
To better understand the method's effectiveness, I asked the AI to simulate thousands of 100-game sessions on European roulette, applying the Fibonacci sequence to column bets. The average result was a loss of approximately 143 units per session, with occasional small wins and potentially huge losses in the event of long losing streaks.
This means that, despite the progression, losing streaks are frequent and can quickly lead to very high bets. Starting bets with 1 coin, after 10 consecutive losses, the sequence already requires 89 coins, a significant financial commitment.
 
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