The Martingale is the oldest roulette system: bet one unit on an even-money outcome such as red; after every loss double the bet; after a win go back to one unit. Every win recovers all previous losses plus one unit. The catch is the streak you cannot afford. On a European wheel an even-money bet loses with probability 19/37, about 51.4%, so six losses in a row happen with probability (19/37) to the power 6, about 1.8%, and in 200 rounds the chance of meeting at least one six-loss streak is about 98%. Seven losses in a row cost 127 units.
Martingale calculator
Enter your base bet, your bankroll and the table maximum. The calculator finds how many consecutive losses you can absorb, the probability of a bust in one round and over a session, and the expected result. Formulas are below the cards.
With base bet $B$, loss probability $q$ and $k$ affordable doublings: the $k$-th bet is $2^{k-1}B$, the total lost after $k$ straight losses is $B(2^k - 1)$, the probability of that streak is $q^k$, the chance of at least one bust in $N$ rounds is $1 - (1 - q^k)^N$, and the expected result per round is $B\left(1 - (2q)^k\right)$, negative whenever $q > 1/2$. $k$ is limited by both the bankroll and the table maximum.
Simulate 1,000 Martingale sessions
Same settings as above. Each session plays the chosen number of rounds or stops at a bust. Watch how many sessions end with a small profit and how many end with the large loss, and compare the average with the expected value.
Why the Martingale cannot win in the long run
Expected value is linear: $\mathbb{E}\left[\sum b_i X_i\right] = \mathbb{E}[X]\sum b_i$. Whatever rule sets the bet sizes, the expected loss is the house edge times the total amount staked. Doubling after losses makes the total staked grow fast, so the expected loss grows with it. The system turns a steady drip of small losses into a stream of small wins punctuated by one large loss, with the same average.
The formal result: a martingale strategy fails even with unlimited time as long as there is any limit on bets or earnings, which follows from the optional stopping theorem. Casinos supply the limit twice, as a table maximum and as your bankroll.
Real players behave as the system assumes. In 18 hours of casino security video from Reno (139 players, 24,131 bets), after six or more identical even-money outcomes 85% of bets were placed against the streak, the Martingale reflex, while the wheel showed no bias at all.
Sources
- Wikipedia. "Martingale (betting system)": definition, the loss formulas $q^n$ and $B(2^n-1)$, the expected profit $B(1-(2q)^n)$ and the optional-stopping argument. en.wikipedia.org/wiki/Martingale_(betting_system) (accessed 24 October 2026).
- Mitzenmacher, M. and Upfal, E. (2005). Probability and Computing. Cambridge University Press, p. 298 (optional stopping theorem applied to betting).
- Croson, R. and Sundali, J. (2005). "The Gambler's Fallacy and the Hot Hand: Empirical Data from Casinos." The Journal of Risk and Uncertainty, 30(3), 195–209. doi:10.1007/s11166-005-1153-2
- Wizard of Odds. "Roulette for Beginners: Rules, Odds and House Edge." wizardofodds.com (house edge 2.70% / 5.26%).
Frequently asked questions
Does the Martingale system work in roulette?
No. It wins small amounts often and loses a large amount rarely, and the average is the house edge times everything you staked. On a European wheel the chance of six straight even-money losses is about 1.8% per round, and over 200 rounds the chance of hitting at least one such streak is about 98%. A six-loss streak costs 63 base units; seven costs 127.
How much bankroll does the Martingale need?
To survive k consecutive losses you need 2^k minus 1 base units: 63 units for six losses, 255 for eight, 1,023 for ten. The table maximum usually stops you first: with a €5 base bet and a €1,000 limit you can double only seven times.
What are the odds of losing 8 times in a row on red?
About 0.48% per attempt on a European wheel, since red loses with probability 19/37 each spin (zero counts as a loss). Over a long evening that is not rare: the expected number of 8-loss streaks grows with every round you play.
Is the reverse Martingale, or any other progression, better?
No progression changes the expected value, because expected value is linear in the bet size. Anti-Martingale, d'Alembert, Fibonacci and Labouchère all redistribute the same expected loss across different patterns of wins and losses.
Why do casinos allow the Martingale?
Because it increases the total amount staked, and the casino's expected profit is the edge times the amount staked. The table maximum exists to cap the casino's variance, not to stop the system from winning; the system cannot win on average with or without the cap.