Does the Martingale system work?

No. In 100,000 simulated sessions on European roulette it lost 2.72% of everything wagered — the house edge is 2.70%, so the system changed nothing about the rate. What it did change is exposure: it busted a $200 bankroll in 56.93% of sessions and pushed average turnover from $250 to $632, so the average session lost $17.23 instead of $6.77.

Why do betting systems feel like they work?

Because most sessions do win. Our Fibonacci runs finished ahead 66.86% of the time with a median result of +$37 — but the average was −$15.62. Progressions convert many small wins into a few large losses. If you judge a system by how your typical night goes, it looks like it works; the arithmetic only shows up in the tail.

Is any betting system better than just betting the same amount every time?

Not in our data. Flat betting had the smallest average loss (−$6.77), a 0% bust rate, and the least money wagered. Every progression system lost more in absolute terms because every progression system increases turnover, and turnover multiplied by the house edge is your expected loss.

Would a bigger bankroll or a higher table limit make Martingale work?

It moves the bust rate, not the maths. The loss per dollar wagered stayed at the house edge across all four systems regardless of the progression shape. A larger bankroll buys more rounds before the doubling sequence outruns it — which means more total wagering, and therefore a larger expected loss, not a smaller one.

What actually reduces the house edge?

Choosing a lower-edge bet, and — in blackjack only — playing correct basic strategy. Our house edge statistics page ranks every major bet from 0.44% to 16.67%. Moving from American to European roulette halves the edge; no staking pattern does anything comparable.

Can I reproduce these numbers?

Yes. The methodology publishes the seed (20260803), the win probability (18/37), the bankroll, base unit, table maximum, session length and the exact progression rule for each system. Any Python environment will reproduce the same figures with the same seed.

data

We Simulated 400,000 Betting-System Sessions — Why Martingale Feels Like It Works and Still Loses

An original Monte Carlo study of Martingale, D'Alembert, Fibonacci and flat betting on European roulette. Every system lost 2.68–2.72% of everything wagered — the house edge, exactly. What changes is how much you wager and how often you bust. Full model and seed published.

By Casino Aurum Editorial Team · How We Rate

Published: 2026-08-03 · Updated: 2026-08-03 · 4min read

Key takeaways

Across 400,000 simulated sessions, all four systems lost between 2.68% and 2.72% of every dollar wagered — European roulette's house edge is 2.70%. No progression changed the rate, in either direction.
Systems lose more money because they make you bet more. D'Alembert wagered $1,632 per session against flat betting's $250 — 6.5 times as much — and lost 6.5 times as much: $43.72 vs $6.77.
Martingale busted the $200 bankroll in 56.93% of sessions before 250 rounds were up, even with a generous $500 table maximum.
Fibonacci is the clearest illustration of the illusion: it finished ahead in 66.86% of sessions with a median result of +$37 — while its average was −$15.62. Most sessions win a little; the minority that bust lose a lot.
Flat betting was the least bad on every measure that matters: 0% bust rate, the smallest average loss, and the least money put at risk.

Martingale, D’Alembert, Fibonacci. Every gambling forum has someone insisting one of them works, and they are not lying about their experience — most of their sessions really did end in profit. That is the interesting part, and it is measurable.

We simulated 400,000 sessions — 100,000 per system — on European roulette with a real table limit. Model and seed published below.

Every system lost exactly the house edge

System	Loss as % of money wagered	Average total wagered	Average net result	Busted
Flat betting	2.71%	$250	−$6.77	0.00%
Martingale	2.72%	$632	−$17.23	56.93%
D’Alembert	2.68%	$1,632	−$43.72	41.43%
Fibonacci	2.68%	$583	−$15.62	32.00%

European roulette’s house edge is 2.70%. Every system landed within 0.02 points of it.

That is the whole result. A staking pattern decides how much you wager and in what order — it has no mechanism to change what each wager is worth. Expected loss is turnover × house edge, and systems only move the first term.

Which is why the biggest loser is the system that bets the most. D’Alembert put $1,632 through the table per session against flat betting’s $250 — 6.5× the turnover, 6.5× the loss.

Why they feel like they work

This is the part worth understanding, because the feeling is real:

System	Finished ahead	Median result	Average result
Flat betting	31.21%	$194 (−$6)	−$6.77
Martingale	42.80%	$116 (−$84)	−$17.23
D’Alembert	46.70%	$176 (−$24)	−$43.72
Fibonacci	66.86%	$237 (+$37)	−$15.62

Look at Fibonacci. Two out of three sessions ended in profit, and the typical session finished $37 up — while the average session lost $15.62.

Both numbers are true at once. Progressions chase losses with bigger bets, so they usually claw back to a small win. The cost is concentrated in the sessions where the recovery never comes: 32% of Fibonacci runs busted the bankroll entirely. A few catastrophes outweigh many small wins.

If you judge a system by how your typical night goes, it looks like it works. That is not a failure of observation — it is exactly what the distribution does. The arithmetic only appears when you average over the tail, which no individual player ever experiences.

Martingale shows the same shape more violently: it wins more often than flat betting (42.80% vs 31.21%) and still loses 2.5× as much money, because 56.93% of sessions ended with the doubling sequence outrunning a $200 bankroll — and that is with a generous $500 table maximum. Table limits are not what break Martingale. Your bankroll breaks first.

The one honest conclusion

Flat betting won on every measure that matters: smallest average loss, zero bust rate, least money exposed. Not because flat betting is clever — because it puts the least turnover through a negative-expectation game.

If you want to lose less, the levers are real but boring: pick a lower-edge bet and wager less money. Our house edge statistics rank every major bet from 0.44% to 16.67% — moving from American to European roulette halves your cost, which is a bigger effect than any progression in this study achieved. And in blackjack, correct basic strategy is worth roughly five percentage points, the only case where in-game decisions genuinely move the number.

What this does not say

This is one game and one session length. European roulette even-money, 250 rounds, $200 bankroll, $1 base unit, $500 table max. Other parameters move the bust rates; they do not move the loss-per-dollar-wagered, which is the finding.
We do not model bet-sizing psychology. Real players deviate, chase harder, or stop early. Those change individual outcomes, not the expected value.
No system was rigged to fail. Each progression is implemented as commonly described, and flat betting — the control — was included precisely so the comparison is against something, not against nothing.
A 66.86% win rate is genuinely 66.86%. We are not disputing anyone’s winning sessions. We are showing what the other 33.14% cost.

Methodology (reproduce it yourself)

Environment: Python 3, standard library only (random).
Seed: random.seed(20260803) — fixed, so every figure is exactly reproducible.
Game: European roulette even-money bet, win probability 18/37 = 0.486486…, house edge 1/37 = 2.70%.
Session: bankroll $200, base unit $1, table maximum $500, 250 rounds. A session ends early (“busted”) when the player cannot cover the next required bet.
Progressions: Martingale — double after a loss, reset to base after a win, capped at the table max. D’Alembert — +1 unit after a loss, −1 after a win, floored at the base unit. Fibonacci — advance one step up the ladder on a loss, back two steps on a win. Flat — always the base unit.
Sample: 100,000 sessions per system, 400,000 total.
No cherry-picking: single runs at the stated seed, reported in full.

Gambling is paid entertainment with a built-in cost. Systems change the shape of the ride, never the price of the ticket. Play only what you can afford to lose, where it is legal for you.

FAQ

Does the Martingale system work?: No. In 100,000 simulated sessions on European roulette it lost 2.72% of everything wagered — the house edge is 2.70%, so the system changed nothing about the rate. What it did change is exposure: it busted a $200 bankroll in 56.93% of sessions and pushed average turnover from $250 to $632, so the average session lost $17.23 instead of $6.77.
Why do betting systems feel like they work?: Because most sessions do win. Our Fibonacci runs finished ahead 66.86% of the time with a median result of +$37 — but the average was −$15.62. Progressions convert many small wins into a few large losses. If you judge a system by how your typical night goes, it looks like it works; the arithmetic only shows up in the tail.
Is any betting system better than just betting the same amount every time?: Not in our data. Flat betting had the smallest average loss (−$6.77), a 0% bust rate, and the least money wagered. Every progression system lost more in absolute terms because every progression system increases turnover, and turnover multiplied by the house edge is your expected loss.
Would a bigger bankroll or a higher table limit make Martingale work?: It moves the bust rate, not the maths. The loss per dollar wagered stayed at the house edge across all four systems regardless of the progression shape. A larger bankroll buys more rounds before the doubling sequence outruns it — which means more total wagering, and therefore a larger expected loss, not a smaller one.
What actually reduces the house edge?: Choosing a lower-edge bet, and — in blackjack only — playing correct basic strategy. Our house edge statistics page ranks every major bet from 0.44% to 16.67%. Moving from American to European roulette halves the edge; no staking pattern does anything comparable.
Can I reproduce these numbers?: Yes. The methodology publishes the seed (20260803), the win probability (18/37), the bankroll, base unit, table maximum, session length and the exact progression rule for each system. Any Python environment will reproduce the same figures with the same seed.

Every system lost exactly the house edge

Why they feel like they work

The one honest conclusion

What this does not say

Methodology (reproduce it yourself)

FAQ

Sources

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