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D'Alembert vs Fibonacci Systems in Live Roulette
Roulette betting systems have attracted the mathematically inclined for centuries. The D'Alembert system and the Fibonacci system are two of the most popular.
Words by Buddy Grant2 min read
Roulette betting systems have attracted the mathematically inclined for centuries. The D'Alembert system and the Fibonacci system are two of the most popular. Both rest on a fundamental error in thinking.
The D'Alembert system says: increase your bet after a loss, decrease after a win. The idea is that losses and wins balance out, so you exploit the "regression to the mean." In practice, roulette spins are independent. A loss does not make a win more likely. The system does not work.
The Fibonacci system uses the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13) as bet sizes. You bet the next number in the sequence after each loss. After a win, you start over. The idea is similar: the sequence somehow captures probability. It does not.
Why These Systems Fail
Both systems share a core mistake: they assume that roulette outcomes are not random. They assume there is a pattern. Roulette wheels are designed to prevent patterns. Each spin is independent. The probability of red on the next spin is 48.65% regardless of the previous result.
The D'Alembert system would work if roulette outcomes were correlated (a loss made a win more likely). But they are not. Each bet faces the same 48.65% probability and 51.35% probability against.
The Fibonacci system would work if there were some mathematical property of the sequence that matched probability. There is not. The sequence is arbitrary relative to roulette.
Both systems are appealing because they create the illusion of control. A bettor who follows the system feels like they are doing something strategic. In reality, they are just placing a series of bets at the same negative expected value.
Both systems share a core mistake: they assume that roulette outcomes are not random.
The Mathematics
Roulette on a single-zero wheel has a 2.7% house edge. This means that over time, the player loses 2.7% of all money wagered. No betting system changes this. Bet size does not matter. Sequence does not matter.
A player using D'Alembert loses 2.7% of their total action. A player using Fibonacci loses 2.7% of their total action. A player betting randomly loses 2.7% of their total action.
The only thing that matters is how much you wager in total. The system you use to determine bet sizes is irrelevant.
What systems do accomplish is changing variance. D'Alembert tends to increase bet sizes, which increases variance. Fibonacci tends to have high variance as well. A system that decreases bets as you lose would reduce variance.
But variance management is not the same as winning. Both systems will lose over time. The better system is the one that loses slower, which is the one with lower variance, which is the one where you bet smaller amounts.
Neither D'Alembert nor Fibonacci achieves lower variance. Both increase variance. Both are worse than flat betting the same amount every spin.
If you are going to play roulette, accept the 2.7% house edge. Bet the same amount every time. Do not use a system. Systems do not work. They merely provide comfort to someone who has not accepted the mathematics.