Fibonacci vs Labouchere: 200,000 simulated roulette sessions
Fibonacci and Labouchere compared with real numbers: 100,000 simulated sessions each on a single zero wheel. Win rates, bust rates, worst sessions, and why neither beats the house edge.
The two systems in one breath
Fibonacci: The Fibonacci walks up the sequence 1, 1, 2, 3, 5, 8, 13 and so on after each loss, and steps back two places after each win. Stakes are that sequence multiplied by your base unit.
Labouchere: You write down a short line of numbers, for example 1, 2, 3, 4. Each bet is the first number plus the last. If it wins, you cross both off. If it loses, you add the amount you just lost to the end of the line.
The numbers side by side
| Fibonacci | Labouchere | |
|---|---|---|
| Sessions that finished ahead | 73.8% | 31.3% |
| Sessions that ran out of money | 23.0% | 67.8% |
| Average result per session | -29.3 points | -84.2 points |
| Typical (median) result | +75 points | -360 points |
| Worst session seen | -440 points | -500 points |
| Average total staked | 1,071.6 points | 3,159.5 points |
| Loss predicted by the edge | 29 points | 85.4 points |
The honest verdict
Neither system beats the house edge, and the table shows it twice. Each system's average loss sits next to the loss the edge predicts from its own staking (29 points for Fibonacci, 85.4 points for Labouchere): the wheel took its 1 in 37 of everything each system staked, and nothing more or less.
What actually differs is the shape of the risk. Fibonacci finished ahead more often (73.8% against 31.3%). Labouchere emptied its bankroll more often (67.8% against 23.0%). Fibonacci lost less on average (-29.3 points against -84.2 points), mostly because it staked less in total. Choosing between them is choosing which kind of bad day you prefer, not which one wins.
Common questions
Which is better, Fibonacci or Labouchere?
Neither, by expectation: both averaged a loss in line with the house edge applied to what they staked (-29.3 points against -84.2 points per session). They differ in risk shape. Fibonacci finished ahead more often (73.8% against 31.3%), while Labouchere ran out of money more often (67.8% against 23.0%). Pick, if at all, by which bad day you would rather have.
Can I combine two systems to beat the wheel?
No. Any mix of two systems is still a sequence of bets on a wheel that keeps 1 point in 37 staked, so the combination changes the shape of your results, never their long run average. That is exactly what our side by side numbers show for each system alone.
Run both yourself
The Lab in the app runs either system with your own budget, base bet, and rounds, on virtual points. Watch each one's bad day happen instead of taking our word for it.