Odds, Probability & Bankroll
Martingale strategy roulette
A betting system for roulette in which the player doubles the wager after every loss on an even-money bet, so that the first win recovers all previous losses and returns a profit equal to the original stake.
Key points
- The player doubles the bet after every loss on an even-money wager until a win or bankroll/table limit is reached.13
- A single win recovers all prior losses and yields a net profit equal to the original stake.12
- The system cannot overcome the house edge; in American roulette the expected loss is 5.26% of total money bet.5
- A long losing streak quickly escalates stakes, risking bankroll exhaustion or hitting the table maximum.
How the martingale works in roulette
- Choose an even-money bet, such as red or black, and place a base stake (x).
- If the bet loses, double the next stake (2x, then 4x, and so on).34
- On the first win, collect the payout. The total of all losses plus the winning stake equals one base unit of profit.
- Reset the stake to x after a win, or stop if you cannot double (bankroll or table limit).
Where this term is used
Not the same as
- Martingale strategy — the general betting system applied to any even-money game, not limited to roulette
- Martingale system blackjack — the same doubling-after-loss system applied to blackjack, where hand outcomes and splits alter the progression
Related terms
Odds & probability
Martingale strategy
The general negative-progression betting system used across even-money games.
Odds & probability
Roulette payouts
The odds and payouts for each type of roulette bet.
Odds & probability
Martingale system blackjack
Applying the martingale doubling system to blackjack hands.
Odds & probability
Casino roulette payouts
Payout tables for European and American roulette.
Odds & probability
Kelly criterion
A bankroll-management formula that maximises growth rate, contrasting with the martingale.
Odds & probability
Kelly betting
A proportional betting method derived from the Kelly criterion.
Sources
- Martingale (betting system) en.wikipedia.org Defines the martingale betting system and its application to roulette even-money bets.
- Roulette en.wikipedia.org Describes the recovery of losses and profit on the first win in roulette.
- arXiv:1807.04635v1 [math.LO] 10 Jul 2018 arxiv.org Describes the stake-doubling sequence and the recovery of losses on a win.
- Biased roulette wheel: A Quantitative Trading Strategy Approach ar5iv.labs.arxiv.org Provides the mathematical sequence of stakes after each loss.
- Betting Systems - Martingale - Wizard of Odds wizardofodds.com States the expected loss for the martingale under American roulette rules.
Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.