Important first
Roulette is a game of chance with a built-in house edge. No system, including the one below, changes the odds in the player’s favor over time. Most players lose money in the long run, and nobody should gamble money they cannot afford to lose. All dollar figures in this article are hypothetical, chosen to illustrate the mechanics.
How the system works
The martingale is the most widely known staking pattern in roulette. It is used on even-money bets such as red or black. The rule is:
- Choose a base bet.
- After a loss, double the previous bet.
- After a win, return to the base bet.
The idea is that a single win after a run of losses recovers all of the losses plus a profit of one base bet. Since a win on an even-money bet is close to a coin flip, it can seem that eventually a win must come. The reasoning is partly right, which is what makes the system persuasive, and the problem is in the word “eventually.”
A worked example
Take a $5 base bet on red on a single-zero wheel. A run of losses looks like this:
| Bet number | Stake | Total staked so far |
|---|---|---|
| 1 | $5 | $5 |
| 2 | $10 | $15 |
| 3 | $20 | $35 |
| 4 | $40 | $75 |
| 5 | $80 | $155 |
| 6 | $160 | $315 |
| 7 | $320 | $635 |
| 8 | $640 | $1,275 |
If the seventh bet wins, the player receives $320 of profit on that bet but has lost $315 on the earlier six, for a net gain of $5, which is the base bet. The same net result occurs if the win comes at any bet in the sequence. Small gains, but each requires a stake that doubles.
Table limits
Tables have maximum bets, so the doubling cannot continue indefinitely. Suppose the table maximum on even-money bets were $500 (a hypothetical number). The eighth bet in the sequence above would need to be $640, which exceeds the cap. After seven losses the player can no longer double, and the $635 already lost cannot be recovered by the system. Real limits vary by table, and the minimum bet matters too: the higher the base bet, the sooner the limit is reached. Table limits like this are why the system cannot run indefinitely.
Bankroll limits
Even without a cap, a player has a finite budget. With a hypothetical bankroll of $300 and a $5 base bet, the system can fund five consecutive losses: 5 + 10 + 20 + 40 + 80 = $155. The sixth bet would be $160, but only $145 remains, so the system stops. In effect, the player has been betting a growing share of the budget for the chance to win $5. Bankroll sizing matters because a small budget supports very few doublings.
How likely is a long losing run?
On a single-zero wheel, an even-money bet loses with probability 19/37, about 51.35% (the 18 opposite pockets plus the zero).
- Five losses in a row: (19/37)^5 ≈ 0.0357, about 3.6%.
- Seven losses in a row: (19/37)^7 ≈ 0.0094, about 0.94%, or roughly 1 in 106.
On a double-zero wheel the loss probability is 20/38, about 52.6%, so seven in a row is about 1.1%, roughly 1 in 89.
These chances look small. But the system is repeated, so over many cycles a long losing run is more likely than not to turn up eventually. That is the nature of the law of large numbers: rare events are rare per attempt, and they are not rare across many attempts.
The expected result
Take the $500-cap example with seven allowed bets. In each cycle, the player either wins $5 or loses $635.
- Chance of a win somewhere in the first seven bets: 1 − 0.0094 ≈ 0.9906, for a $5 gain.
- Chance of losing all seven: about 0.0094, for a $635 loss.
Expected result per cycle is roughly 0.9906 × 5 − 0.0094 × 635 ≈ 4.95 − 5.98 ≈ −$1.03.
So about 99 cycles in 100 end in a $5 win, and the average is still a loss of about a dollar per cycle. The expected loss equals the house edge, 1/37 per dollar, multiplied by the average amount staked in a cycle, which is roughly $38. That check shows the system does not change the edge: it changes how losses are distributed (many small wins, occasional large loss), not their average. The logic is the same as for other bet progressions.
Why it feels like it works
A small sample of cycles will probably show only wins. Seeing a hundred consecutive $5 gains is not unusual, since the chance of getting through any cycle is about 99%. The rare large loss simply has not shown up yet. This is a case of small samples hiding a heavy tail. Memory and enthusiasm do the rest, and stories of “systems that worked” tend to omit the session that ended at the table limit.
Risk of ruin is the right way to think about it: with a finite bankroll and a doubling rule, the chance of a bad run is concentrated into a rare, very costly event. Standard deviation per cycle is also large compared with the $5 profit.
Other points
- The system gives no protection from the zero, which is why a single-zero wheel at 2.70% and a double-zero wheel at 5.26% are different in cost.
- Applying doubling after losses can also encourage chasing losses, which tends to make things worse.
- Raising stakes in response to losses is the opposite of what responsible gambling suggests: setting a fixed budget in advance and stopping when it is gone.
If gambling is causing difficulty, a local support service can help.