Roulette Betting Systems: Why Martingale Does Not Remove the House Edge

The Martingale system, doubling your bet after every loss so that the first win recovers everything plus one unit, does not remove the house edge: it only changes how your results are distributed. You win a small amount most of the time and, rarely, lose a large amount when a losing run reaches the table maximum or your bankroll. On a single-zero table the average cost stays exactly where it was, 2.70% of everything you stake. The calculation below uses a real limit: Loto-Québec’s live Roulette A table, which in October 2026 took bets from $1 to $5,000.

How does the Martingale system work?

You bet one unit on an even-money bet such as red. If you win, you take the profit and start again at one unit. If you lose, you double the next bet. Every win therefore recovers all the losses in the run and adds one unit of profit. The idea depends on one thing: being able to keep doubling until a win comes.

Where does the table limit stop it?

Each table has a maximum. At Roulette A, with a $1 start and a $5,000 maximum, the doubling sequence runs:

After 13 losses in a row, the next bet in the sequence, $8,192, is above the $5,000 limit. At that point the sequence has lost $8,191 and the system cannot continue as designed.

Lower starting bets do not solve this. Loto-Québec’s Roulette table runs from 50¢ to $10,000; starting at 50¢, the fifteenth bet in a row would be $8,192, and the sixteenth, $16,384, would be over the maximum, after a run that had already lost $16,383.50 to chase a 50-cent profit.

How likely is a run of 13 losses?

On a single-zero wheel, red loses on 19 of 37 numbers (18 black plus the zero). The chance of 13 losses in a row is (19/37) to the power of 13, about 0.017%, or roughly 1 run in 5,800. That is rare in any single sequence, which is exactly why the system feels as if it works: most evenings end with a small profit, and the losing evening, when it comes, takes back far more than the small wins added up. But a player who completes 100 sequences in an evening faces a 1.7% chance of hitting it at least once, and someone who plays the system for weeks will meet it eventually.

Why does the house edge stay the same?

Work out the average result of one full Martingale sequence at Roulette A:

• Probability the sequence fails (13 losses): p = (19/37)^13, about 0.0001727.
• Expected result: win $1 with probability 1 minus p, lose $8,191 with probability p. That is 0.99983 minus 1.41459, about minus $0.41 per sequence.
• Expected amount staked per sequence: each bet of 2^k dollars is placed only if the k bets before it all lost, so the expected stake is the sum of (19/37)^k × 2^k for k from 0 to 12, which comes to about $15.33.
• Cost as a share of stakes: $0.41 divided by $15.33 is about 2.7%.

The house edge per dollar staked is the same 2.70% as flat betting on red. Martingale moves the losses into rare, large events; it does not reduce them.

What if your bankroll runs out first?

For most players the bankroll, not the table limit, ends the sequence. With $500, you can cover 8 doubling bets from $1 (a total of $255); the ninth, $256, would take you over $500. The chance of 8 losses in a row is (19/37)^8, about 0.48%, roughly 1 sequence in 207. Over 100 sequences, the chance of losing $255 at least once is about 38%. The average cost per dollar staked is, again, about 2.7%.

Do other betting systems do better?

No staking pattern can change the expected return of the bets themselves. Every even-money bet on a single-zero wheel returns 97.30% on average, or 98.65% at a table with La Partage, whatever size it is and whatever came before it. Systems that increase bets after wins, follow patterns or space out bets change the shape of your results, not their average. Our explainer on La Partage and En Prison shows the only kind of change that lowers the cost: a different rule, not a different staking plan.

What should you take from this?

• The edge is set by the wheel and the rules: 2.70% on a single-zero table, 5.26% on a double-zero table, 1.35% on even-money bets with La Partage. Our comparison of European and American roulette shows the difference.
• A system that doubles after losses needs both a large bankroll and a high table limit, and it still loses the same share of what you stake.
• The useful part of any staking plan is a cap on what you can lose: decide your session limit before the first spin and set it in your account. Support and self-exclusion options are on our responsible gambling page.

What we could not confirm

• Table limits at roulette tables whose details appear only after login. BetRivers in Ontario, for example, showed minimum bets from $0.10 to $1 in its public lobby but not maximums.

Run the numbers on your own table

Note the table’s minimum and maximum, and your bankroll. Count how many times you can double from the minimum before you exceed either. Then compute (19/37) to the power of that number: that is your chance of a wipe-out in each sequence on a single-zero wheel. The bet layout itself is explained in our guide to roulette bets and payouts.