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

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.

Follow-up, September 2026: nobody experiences the average

A reader with a formal probability background read the study and pushed back on two points — that the outcome distribution must be bimodal rather than merely skewed, and that two players covering opposite sides of one wheel would change the casino’s position. Both are testable, so we tested them: 400,000 further sessions, same rules, seed 20260830.

The distribution is bimodal, and the mean falls in the gap. Final balances from a $200 bankroll:

Final balance	Share of sessions
$0–25 (wiped out)	8.06%
$50–75	16.36%
$75–100	10.73%
$100–225 (the valley — contains the $181 mean)	~2%
$225–250	22.36%
$250–300	39.57%

Two populated modes with an empty stretch between them, and the average result sits in the empty stretch. The mean describes an outcome that almost no session produces. A player who runs this system a hundred times will have won modestly perhaps sixty times and been wiped out perhaps thirty-six — and never once finished at the average. That is a sharper version of the point above: it is not that players remember wins and forget losses, it is that the average is not an available outcome.

Two players on opposite sides of one wheel: same rate, different correlation. We ran 200,000 sessions with a Fibonacci player on red and another on black spinning the same wheel, against 200,000 sessions of the same two players on separate wheels:

	Paired (one wheel)	Independent (two wheels)
House take, % of turnover	2.74%	2.71%
House standard deviation per session	$129	$136
Sessions where both players busted	11.65%	13.00%

The rate does not move — both sit at the 2.70% house edge, as they must. What pairing changes is structure. Because one player’s win is usually the other’s loss, the house mostly collects the difference between two diverging ladder bets, and its per-session variance falls. Simultaneous ruin becomes less likely, since one ladder is resetting while the other climbs. The single exception is the zero: on 2.70% of spins the house books both bets at once, which is precisely where its edge lives.

The casino does earn more from two players than one — from twice the turnover, not from a better rate. That distinction is the whole subject of this study, restated at the table level.

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.

September 2026 follow-up. Seed random.seed(20260830), 300-round sessions, same game, bankroll, base unit and table maximum. Two setups of 200,000 sessions each: paired (two Fibonacci players resolving against one spin, one on red and one on black, with the zero losing both) and independent (the same two players on separate spin streams). Final-balance histogram bucketed as shown above. Everything else matches the original run.

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.