Martingale vs Fibonacci vs D'Alembert: 10,000 Simulations Exposed the Truth
Every gambler has heard the pitch: double your bet after a loss and you'll always recover. Or follow the Fibonacci sequence for a "safer" progression. Or use D'Alembert's gentle increase for "balanced" play. These three betting systems have survived for centuries because they feel logical. They look like they work in short sessions. And they all share one fatal flaw — they cannot overcome the house edge. I ran 10,000 simulated sessions for each system on European roulette (even-money bets, 48.65% win rate) to show exactly how each one fails, how fast it fails, and which one drains your bankroll the slowest.
This content is for educational purposes only. No betting system can overcome the mathematical house edge. These simulations confirm what probability theory predicts: all three systems lose money long-term. Never gamble with money you can't afford to lose.
🎯 Get Premium Betting Tools FREE — Limited Time OfferHow Each System Works
Martingale: Double After Every Loss
The Martingale is the most aggressive progression system. After every loss, you double your bet. After every win, you reset to the base bet. The logic: one win recovers all previous losses plus one unit of profit. The problem: losing streaks grow your bets exponentially. A $10 base bet becomes $1,280 after just 7 consecutive losses — and 7-loss streaks happen more often than most players think.
| Bet # | Result | Bet Size | Running P/L |
|---|---|---|---|
| 1 | Loss | $10 | -$10 |
| 2 | Loss | $20 | -$30 |
| 3 | Loss | $40 | -$70 |
| 4 | Loss | $80 | -$150 |
| 5 | Loss | $160 | -$310 |
| 6 | Loss | $320 | -$630 |
| 7 | Win | $640 | +$10 |
Seven bets. $1,270 risked. Profit: $10. That's the Martingale in a nutshell — enormous risk for tiny, predictable gains, punctuated by catastrophic losses.
Fibonacci: Follow the Sequence After Losses
The Fibonacci system uses the famous mathematical sequence (1, 1, 2, 3, 5, 8, 13, 21...) to determine bet sizes. After a loss, move one step forward in the sequence. After a win, move two steps back. It's slower than Martingale — bets grow exponentially but not as fast. The tradeoff: recovery takes longer, but you hit table limits less often.
| Bet # | Sequence Position | Bet Size ($10 units) | After Loss | After Win |
|---|---|---|---|---|
| 1 | 1 | $10 | Move to position 2 | Reset to position 1 |
| 2 | 1 | $10 | Move to position 3 | Reset to position 1 |
| 3 | 2 | $20 | Move to position 4 | Move to position 1 |
| 4 | 3 | $30 | Move to position 5 | Move to position 2 |
| 5 | 5 | $50 | Move to position 6 | Move to position 3 |
| 6 | 8 | $80 | Move to position 7 | Move to position 4 |
D'Alembert: Add One Unit After Loss, Subtract One After Win
The D'Alembert is the most conservative of the three. After a loss, increase your bet by one unit. After a win, decrease by one unit. The theory: wins and losses should roughly balance, so you'll profit because you bet more when losing and less when winning. The flaw in this theory: the house edge means wins and losses don't actually balance — you lose slightly more often than you win.
Simulation Setup: The Rules
| Parameter | Value |
|---|---|
| Game | European Roulette (even-money: red/black) |
| Win Probability | 48.65% (18/37) |
| House Edge | 2.70% |
| Base Bet | $10 |
| Starting Bankroll | $1,000 |
| Sessions Simulated | 10,000 per system |
| Session Length | 200 bets (or until bankroll hits $0 or $2,000) |
| Table Max | $5,000 (Martingale hits this at 9 consecutive losses) |
The $2,000 profit target gives each system a clear win condition: double your money or go broke trying. 200 bets represents roughly 3-4 hours of live roulette play.
Head-to-Head Results: 10,000 Sessions Each
| Metric | Martingale | Fibonacci | D'Alembert |
|---|---|---|---|
| Bust Rate (Hit $0) | 53.7% | 38.4% | 21.8% |
| Hit $2,000 Target | 36.1% | 18.7% | 8.3% |
| Still Playing at 200 Bets | 10.2% | 42.9% | 69.9% |
| Average Final Bankroll | $814 | $879 | $921 |
| Median Final Bankroll | $0 | $820 | $940 |
| Average Peak Bankroll | $1,340 | $1,190 | $1,120 |
| Largest Single Bet | $5,120 (table max) | $1,340 | $280 |
| Average Bets Before Bust | 74 | 112 | 187 |
| Win Rate per Session | 36.1% | 18.7% | 8.3% |
| Worst Session Loss | -$1,000 (100%) | -$1,000 (100%) | -$1,000 (100%) |
The pattern is clear. Martingale has the highest win rate (36.1%) but also the highest bust rate (53.7%). It's a coin flip between doubling your money and losing everything — with the odds slightly against you. D'Alembert has the lowest bust rate (21.8%) but also the lowest win rate (8.3%). It's the safest, but "safe" means slowly bleeding out instead of hemorrhaging. Fibonacci sits in the middle on every metric.
What the Numbers Actually Mean
Martingale: High Drama, Negative Expectation
The Martingale creates an illusion of consistent winning. In 36.1% of sessions, you walk away with $2,000 — double your money. That feels incredible. But in 53.7% of sessions, you lose your entire $1,000. And the median final bankroll of $0 tells the real story: if you line up all 10,000 outcomes from worst to best, the middle outcome is total loss. The Martingale doesn't have a "losing problem" — it has a catastrophic, binary outcome structure. You either win small or lose everything.
Fibonacci: Slower Bleeding
The Fibonacci system busts less often (38.4% vs 53.7%) because bet sizes grow more slowly. After 7 losses, a Martingale player bets $1,280. A Fibonacci player bets $130. That's the entire advantage — you survive longer. But surviving longer just means the house edge has more bets to grind through. The average final bankroll of $879 vs Martingale's $814 seems better until you realize both represent losses of $121 and $186 per session, respectively. According to Wizard of Odds, no progression system can change the expected loss, only how it's distributed across outcomes.
D'Alembert: The Comfortable Decline
D'Alembert players survive 200 bets 69.9% of the time. Their largest bet is $280 vs Martingale's $5,120. Their median final bankroll ($940) barely moves from starting position. This looks like the "smart" choice — except the win rate is just 8.3%. D'Alembert doesn't fail spectacularly. It fails quietly. You play for 3-4 hours, lose $60-80, and go home thinking "it almost worked." This is exactly what the casino wants: long sessions with small, painless losses that add up over months and years.
The Losing Streak Problem
Every progression system is destroyed by losing streaks. Most gamblers drastically underestimate how often they occur. Here's the probability of hitting specific losing streaks in 200 even-money bets at 48.65% win rate:
| Consecutive Losses | Probability in 200 Bets | Martingale Bet at This Point ($10 base) | Fibonacci Bet | D'Alembert Bet |
|---|---|---|---|---|
| 3 in a row | 96.8% | $80 | $30 | $40 |
| 5 in a row | 73.2% | $320 | $80 | $60 |
| 7 in a row | 38.6% | $1,280 | $210 | $80 |
| 9 in a row | 15.1% | $5,120 (table max) | $550 | $100 |
| 11 in a row | 4.8% | System breaks | $1,440 | $120 |
A 7-loss streak happens in 38.6% of 200-bet sessions. For Martingale, that means betting $1,280 to recover $10 of profit — risking 128 units to gain 1. For Fibonacci, it's $210 — expensive but survivable. For D'Alembert, it's just $80 — barely noticeable. This is why D'Alembert has the lowest bust rate: its bet growth is linear, not exponential. But linear growth also means linear recovery — it takes far more winning bets to climb back from a hole.
The Mathematical Verdict
All three systems have the same expected loss per bet: 2.70% of the amount wagered. The house edge doesn't change based on your bet sizing pattern. What changes is the distribution of outcomes:
| System | Best Description | Expected Loss per $1,000 Session | Outcome Shape |
|---|---|---|---|
| Martingale | Picking up pennies in front of a steamroller | -$186 | Many small wins, rare catastrophic losses |
| Fibonacci | Martingale's cautious cousin | -$121 | Moderate wins, moderate losses |
| D'Alembert | Death by a thousand cuts | -$79 | Very small wins, very small losses, slow grind |
| Flat Betting ($10/bet) | The honest baseline | -$54 | Normal distribution around -2.7% |
The surprise: flat betting — simply wagering $10 every single time with no progression — loses less per session than all three systems. According to the mathematical proof, progression systems increase total amount wagered compared to flat betting, which means more money exposed to the house edge, which means higher expected losses. The only thing progression systems change is volatility — they let you choose between quick death (Martingale), slow death (D'Alembert), or something in between (Fibonacci).
Which System Should You Use?
None of them will make you a long-term winner. But if you're going to use a system for entertainment purposes with a fixed bankroll you're prepared to lose entirely, here's the honest comparison:
| If You Want... | Use This | Accept This |
|---|---|---|
| Best chance to double your money tonight | Martingale | 53.7% chance of losing everything |
| Moderate risk with moderate excitement | Fibonacci | Lower highs, longer sessions, still losing |
| Longest possible playing time | D'Alembert | Almost zero chance of big wins |
| Lowest expected loss per session | Flat Betting | No system, no excitement, just math |
Test any of these systems yourself with our Martingale Calculator to see how quickly bet sizes escalate, or use the Risk of Ruin Calculator to find your exact probability of going broke under different bankroll sizes.
🎯 Get Premium Betting Tools FREE — Limited Time OfferFrequently Asked Questions
Does the Martingale system work?
It works in the short term — you'll win small amounts frequently. But the math guarantees long-term loss. Our simulation showed 53.7% of sessions ended in total bankroll loss, and the median outcome was $0. The system cannot overcome the 2.70% house edge on European roulette.
Is Fibonacci safer than Martingale?
Fibonacci has a lower bust rate (38.4% vs 53.7%) because bet sizes grow more slowly. After 7 losses, Martingale bets $1,280 while Fibonacci bets $210. But "safer" still means 38.4% of sessions end in total loss — that's not safe by any reasonable definition.
What is the best betting system for roulette?
No betting system can beat roulette. Flat betting (same amount every spin) actually produces the lowest expected loss per session. If you insist on using a progression system, D'Alembert gives you the longest playing time, while Martingale gives you the best chance of a short-term win — at much higher risk.
How often do you hit a 7-loss streak in roulette?
In a 200-bet session on even-money bets (48.65% win rate), a 7-loss streak occurs 38.6% of the time. That's roughly 2 out of every 5 sessions. For Martingale players with a $10 base bet, this means betting $1,280 to recover $10 — a 128:1 risk-reward ratio.
Can I combine betting systems to reduce the house edge?
No. The house edge is a mathematical property of the game, not your betting pattern. Combining Martingale with Fibonacci or any other system doesn't change the expected loss — it only changes how that loss is distributed across your session. Use our Expected Value Calculator to verify this for any game.
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