No betting system changes the house edge on roulette. Martingale, d'Alembert and Fibonacci only change how much you stake and how your results are spread out — usually trading many small wins for occasional large losses. Over time, every one of them loses about the same share of the money staked as flat betting does.
That's a strong claim, so we tested it. This guide explains each system, then shows a simulation of 10,000 sessions for each, run with a script and settings you can reproduce.
Why a system can't beat a fixed edge
Each spin of a fair roulette wheel is unaffected by every spin before it. A betting system is just a rule for choosing your next stake based on past results. Because the past results don't change the next spin's odds, every individual bet still carries the full house edge — 2.70% on a single-zero wheel, as shown in our odds and house edge guide.
If every bet you place loses 2.70% on average, then any combination of those bets also loses 2.70% of the total staked on average. No ordering of stakes can add up negative numbers into a positive one.
The three systems
Martingale
Bet 1 unit on an even-money bet. After a loss, double the stake. After a win, go back to 1 unit. The idea: the first win recovers all previous losses plus 1 unit.
The catch is how fast the stakes grow. Here is the losing-streak table for an even-money bet on a single-zero wheel (win chance 18/37):
| Losses in a row | Chance of that streak starting now | Next stake needed | Total already lost |
|---|---|---|---|
| 5 | 3.57% | 32 | 31 |
| 6 | 1.83% | 64 | 63 |
| 7 | 0.94% | 128 | 127 |
| 8 | 0.48% | 256 | 255 |
| 10 | 0.13% | 1,024 | 1,023 |
A 7-loss streak sounds rare at under 1%, but it's a per-sequence chance. Over hundreds of spins, a streak like that becomes likely. When it hits, you either can't afford the next stake or a table limit stops you, and the whole run of small wins is wiped out in one go.
d'Alembert
Add 1 unit to your stake after a loss; subtract 1 unit after a win (never going below the base stake). It grows much more slowly than Martingale, which makes it feel safer. But stakes still drift upward during losing patches, so you end up staking more in total — which means paying more of the edge.
Fibonacci
Stakes follow the sequence 1, 1, 2, 3, 5, 8, 13… Move one step forward after a loss and two steps back after a win. It's gentler than Martingale but still escalates during losing runs.
The simulation
To keep it honest, every system used identical settings. The setup is fictional and is a model, not a record of real play:
- Single-zero wheel, even-money bet (win chance 18/37, pays 1:1).
- Budget 100 units, base stake 1 unit, up to 100 spins per session.
- If a stake was bigger than the remaining balance, the player bet everything left.
- A session ended at 100 spins or when the balance hit zero ("bust").
- 10,000 sessions per system, same random seed for each system.
| System | Average final balance | Sessions finishing ahead | Sessions bust | Median final balance | Average total staked | Loss as % of staked |
|---|---|---|---|---|---|---|
| Flat 1 unit | 97.38 | 35.5% | 0.0% | 98 | 100 | 2.62% |
| Martingale | 92.58 | 62.2% | 32.4% | 139 | 293 | 2.53% |
| d'Alembert | 88.48 | 55.4% | 23.8% | 111 | 481 | 2.40% |
| Fibonacci | 94.55 | 75.0% | 16.6% | 115 | 230 | 2.37% |
What the table shows
The loss rate barely moves. Every system lost between about 2.4% and 2.6% of the total amount staked. That's the house edge (2.70%) showing through, with a little noise and some shortfall where busted sessions stopped betting early. The system doesn't decide the rate; the wheel does.
Systems make you stake more. Flat betting staked 100 units per session. Martingale staked nearly three times as much, d'Alembert almost five times. Because the edge applies to everything staked, the systems produced bigger average losses: 7.4 units for Martingale and 11.5 for d'Alembert, against 2.6 for flat betting.
Systems make most sessions look good. Fibonacci finished ahead in three sessions out of four; Martingale in nearly two out of three. Those wins are small, typically a few dozen units. The losing sessions are large: a bust means losing the full 100. That's the trade every progression makes, and it's why systems feel like they work. You remember the frequent small wins; the rare total loss looks like bad luck instead of the system doing exactly what the maths says it will.
Medians mislead. The Martingale median of 139 looks impressive next to flat betting's 98. But the median ignores how big the losses are. The average is the figure that tells you the cost.
Worked example: one fictional Martingale run
A fictional player, Theo, starts with 100 units and plays Martingale with 1-unit base bets.
- He wins 30 cycles in a row of "lose a few, then win". Each cycle nets +1. Balance: 130.
- He then hits 7 losses in a row: 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 lost. Balance: 3.
- The next stake should be 128. He can only bet 3.
Thirty careful wins, erased by one streak with a roughly 1-in-100 chance of starting on any given cycle. That's not unusual; it's the expected shape of the system.
Checklist: before trying any system
- Accept that no system changes the edge; it only changes the ride.
- Work out your worst case: what's the largest stake the system could ask for within your budget?
- Check the table limit; it caps how far you can escalate.
- Track total staked, not just your balance. Expected cost = total staked × house edge.
- Set a loss limit and a time limit in advance, and stop when you reach either.
- Treat any money you bring as the price of entertainment.
If you play colour wheels on crypto sites, the same logic applies with a higher edge; see our guide to roulette variants. Roulette is gambling. If you're using a system to try to win back losses, that's a warning sign; our responsible gambling page lists free support.
Questions readers ask
Does the Martingale system work in roulette?
It produces frequent small wins and rare large losses. In our simulation 62% of sessions finished ahead, but 32% lost the whole budget, and the average result was still a loss. The house edge is unchanged.
Which roulette betting system has the lowest house edge?
None of them. The edge is set by the wheel. On a single-zero wheel every system loses about 2.7% of the total amount staked over time; systems only change how much you stake and how results are spread.
Why do betting systems feel like they work?
Most sessions end with a small win, which is memorable. The losses are rarer but much larger, so the average is negative even when most sessions look good.
Can a table limit protect a Martingale player?
A table limit makes the system fail sooner, not later. Once the next doubled stake is above the limit you can no longer recover the losses in one win.