Bet one base unit on an even-money proposition (red or black). After a loss, double the next bet. After a win, reset to one base unit. If the doubled bet exceeds the table maximum, bet the table maximum. The session ends when 200 spins are played or the bankroll cannot cover the next required bet, whichever comes first.
European roulette, single zero. Win probability 18/37 = 0.486486, house edge 1/37 = 2.7027% of turnover. Starting bankroll 1,000 EUR. Base unit 10 EUR, i.e. 1% of bankroll. Table maximum 500 EUR on even-money bets. 200,000 independent sessions per configuration. Spins are independent; no wheel bias, dealer signature or tracking is assumed. Random seed 20260908, so every figure on this page is reproducible.
Every run below uses the same wheel, the same bankroll and the same table limit. The only variable is how long the player stays at the table.
| Session length | Ruin rate | Hit table limit | ROI on turnover | ROI on bankroll |
|---|---|---|---|---|
| 50 spins | 28.13% | 34.55% | −2.620% | −3.59% |
| 100 spins | 43.77% | 59.34% | −2.722% | −6.86% |
| 200 spins | 60.71% | 84.36% | −2.755% | −11.69% |
| 500 spins | 77.72% | 99.10% | −2.737% | −20.88% |
| 1,000 spins | 86.39% | 99.99% | −2.681% | −29.68% |
Read the fourth column first. ROI on turnover sits at roughly −2.7% no matter how long the session runs, which is the house edge of a single-zero wheel to three decimal places. Doubling after a loss does not move it. It cannot: expected value is the sum of each bet multiplied by its own edge, and every bet in the sequence carries the same 2.70% against the player. Changing the size of the bets changes the size of the numbers, not the sign.
The fifth column is where the damage shows. Flat betting the same bankroll over 200 spins loses about 5% of it. Martingale loses 11.69%, because it forces more than twice the turnover through an unchanged edge.
Martingale rests on one promise: the next win recovers every prior loss plus one unit. That promise holds arithmetically and fails practically, because the bet it requires grows past both the table limit and the bankroll long before the losing streak becomes rare.
| Consecutive losses | Chance of at least one such run in 200 spins | Next bet required | Total bankroll needed |
|---|---|---|---|
| 5 | 97.77% | €320 | €630 |
| 6 | 84.40% | €640 | €1,270 |
| 7 | 60.37% | €1,280 | €2,550 |
| 8 | 37.19% | €2,560 | €5,110 |
| 9 | 20.97% | €5,120 | €10,230 |
| 10 | 11.26% | €10,240 | €20,470 |
With a €10 base unit, the sixth consecutive loss already calls for a €640 bet, which the €500 table maximum will not accept. The seventh calls for €1,280 against a €1,000 bankroll that no longer exists. And a run of seven losses is not an outlier: it happens in 60.37% of 200-spin sessions.
That is the whole failure in one line. The streak that breaks the system is the common case, not the tail.
One figure in our raw output needs care. Measured inside the simulation, runs of nine or more consecutive losses appear in 0.00% of sessions, which looks as though those streaks do not happen. They do, in about 21% of 200-spin stretches. They are absent from the observed data because the player is already broke before the ninth spin of the run resolves. The streak is not avoided, it is merely never survived.
Over 200 spins the distribution of results is not a bell curve around a small loss. It has two humps.
| Percentile | Session result |
|---|---|
| 1st | −€1,000 |
| 5th | −€960 |
| 25th | −€730 |
| 50th | −€550 |
| 75th | +€800 |
| 95th | +€1,040 |
| 99th | +€1,110 |
38.9% of sessions finish in profit, and those winners cluster between +€800 and +€1,100, because each completed cycle banks one unit and roughly a hundred cycles complete in 200 spins. The 61.1% that lose cluster near the full €1,000, because the way a Martingale session ends badly is by ending completely.
This is why the system feels effective. Most short sessions produce a steady drip of small wins, and the ruin arrives as a single event rather than a gradual decline. The average of −€117 per session is not something a player experiences; it is the average of winning €900 and losing everything.
The figures above scale with the base unit. Halving it to €5 buys one more step in the doubling sequence, which pushes the ruin rate over 200 spins down but does not remove it, and ROI on turnover stays at the house edge. Raising the table limit has the same shape of effect. No combination of base unit, bankroll and table limit produces a positive expectation, because none of them touch the 2.70% built into each individual spin.
The only variable that changes expected value is the edge itself. On a double-zero wheel it doubles to 5.26%, and every number in this analysis gets worse.
The result is specific to the parameters above. A smaller base unit relative to bankroll buys additional steps in the doubling sequence and lowers the ruin rate over a fixed number of spins; it does not remove ruin and does not change ROI on turnover. The model assumes a hard table maximum and no ability to reset the sequence across sessions, which is how online even-money limits usually behave but not how every physical table does. It also assumes the player follows the progression exactly; discretionary deviation changes the distribution in ways this backtest does not measure. Finally, the simulation stops at 200 spins by default, and session length has a large effect on the ruin rate, as the first table shows.
Martingale does not beat the house edge and cannot. Across every session length tested, ROI on turnover held at roughly -2.7%, matching the single-zero house edge to three decimal places. What the progression does change is the shape of the risk: it more than doubles turnover, raises the loss on bankroll from about 5% to 11.7% over 200 spins, and ends 60.7% of those sessions with the bankroll gone. The system is not a way to win; it is a way to convert a slow, predictable loss into a near coin flip between a modest win and losing everything. It is not a scam and it is not broken arithmetic. It simply redistributes the same negative expectation into a less survivable form.