No. Doubling your bet after every loss turns many small wins into one large, rare loss. The house edge is untouched: whatever the system, you lose on average 2.70% of everything you stake at European roulette.
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What the martingale is
It is the most famous betting system. You bet €1 on red. If you win, you start again at €1. If you lose, you double: €2, then €4, then €8. When red finally comes up, you win back everything you lost, plus €1.
On paper it looks impossible to lose, because red has to come up eventually. And in practice it works almost every time. That is the problem.
Why it seems to work
With €100 and bets starting at €1, you can double six times in a row (1 + 2 + 4 + 8 + 16 + 32 = €63). To lose the series, six non-reds have to come up in a row. That happens in 1 in every 54 series. The other 53 end €1 up.
So it feels great: you win, win, win. Plenty of nights end in profit. And anyone who tries it a few times becomes convinced they have found something.
Where it breaks
When the bad run comes, and it always comes, you lose €63 in one go. That is what you had made in 63 good series. But on average you had only won 53 before it arrived. The sums do not add up.
The martingale does not change how much you lose on average. It changes how you lose it: instead of a slow drip, many small wins and one large, rare loss. Every bet still costs 2.70% of what you put on the table, and the system only makes you put more on it.
Try it below with your own money, bet and table limit. The table is exact, not a simulation.
The martingale, bet by bet
Change the money, the starting bet or the table limit. The last row is where the system breaks.
Wheel
How the bet on red grows every time black comes up
Bet
Stake
Staked so far
Chance of getting here
1
€1
€1
100.0%
2
€2
€3
51.4%
3
€4
€7
26.4%
4
€8
€15
13.5%
5
€16
€31
7.0%
6
€32
€63
3.6%
7
You can’t: you would need €127 and you don’t have it.
You win the series
98.17% · +€1
You lose the series
1.83% · −€63
Average result per series
-€0.174
Reaching +€50 before losing a series
48.8%
You win almost every time, but only your starting bet. When you lose, you lose €63 in one go: the winnings of 63 wins together. The system does not change how much you lose on average, only how: many small joys and one big fall.Series you win, on average, before losing one: 53.5. E[series] = p_win·b − p_lose·L = 0.9817·1 − 0.0183·63 = -0.1735 = −(1 − 2p)·E[staked] = −0.0270 · 6.420.
One night with the martingale
Every spin on red, doubling after every loss. When you can’t double, you start again with what is left.
Not enough left for the minimum bet on spin 62.
What if I have more money?
It helps less than it seems. Every time you double your money you only get one more bet before you break, and the lost series costs twice as much. With €1,000 you survive nine losses in a row; the run that breaks you comes once every 400 series, but then you lose €511. And in a real casino the table limit usually cuts in first: with a €5 minimum and a €500 maximum, you cannot go past seven bets in a row, however much money you have.
To see what happens when thousands of people play the martingale at once, the Ruin Lab simulates it.
TechnicalWhy no system can work
If each one-unit bet has expectation −e (e = 1/37 on a European wheel), a strategy that stakes st on spin t, chosen with the information available up to then, has total expected gain −e · E[Σ st]. The expectation of the sum is the sum of the expectations, and every term is negative. The order and size of the bets only change E[Σ st], the total staked, which the martingale actually increases.
Formally, the balance is a supermartingale, and Doob’s optional stopping theorem says no bounded stopping rule achieves E[final balance] > starting balance. The betting system and the mathematical concept share their name for a reason.
The table above checks it: E[series] = −(1 − 2p) · E[staked in the series], with p = 18/37. The code is in src/lib/martingale.ts, with tests.
Because it costs them nothing. Every euro staked leaves the house 2.70 cents on average, with or without a system. And the table limit cuts the progression short exactly when the player would need it most.
Does the martingale work in sports betting?
No. The logic is the same, and the fee built into the odds (around 6–8% on the 1X2 market) is higher than the roulette edge. Doubling after every miss multiplies what you pay in fees.
What about the reverse martingale, or Paroli?
Doubling after a win instead of after a loss changes the shape of the results, not their average. With the Paroli you lose a little many times and win a lot now and then. The average loss is still 2.70% of what you stake.
How much money does the martingale need to work?
An infinite amount, and a table with no limit. Surviving 10 losses in a row takes 1,023 times the starting bet, and that run comes on average once every 784 series. With finite money there is always a run that wipes it out.
Do other systems work, like D’Alembert, Fibonacci or Labouchère?
No. They all change how much you bet based on what happened before, but the wheel has no memory and every bet loses the same on average. No order of bets turns a sum of expected losses into a gain.