In probability theory, a martingale is a sequence of random variables where the expected future value equals the present value — a different concept from the betting system.
Odds, Probability & Bankroll
Martingale strategy
The martingale strategy is a betting system where the stake is doubled after each loss, so the first win recovers all prior losses and returns a profit equal to the original stake.
Key points
- The system assumes an unlimited bankroll and no table limits — in practice, a losing streak quickly makes the next bet unaffordable 12.
- A single win ends the sequence and returns a net gain equal to the original stake, but the risk of ruin grows exponentially with each loss 13.
- The martingale does not change the house edge; it only redistributes the timing of losses 2.
- In probability theory, a martingale satisfies E[M_{n+1} | M_n, ..., M_0] = M_n — a mathematical property unrelated to betting 34.
Martingale strategy example
Start with a £10 bet on red. If it loses, bet £20 on red. Lose again? Bet £40. Lose a third time? Bet £80. When red finally hits, the £80 win covers the £10+£20+£40 = £70 lost so far and leaves a £10 profit — the original stake 12.
The catch: four consecutive losses cost £150, and the next bet would be £160. A table limit of £100 or a bankroll of £150 stops the system before recovery is possible.
Martingale loss streak
| Losses in a row | Total lost so far | Next bet required |
|---|---|---|
| 1 | £10 | £20 |
| 2 | £30 | £40 |
| 3 | £70 | £80 |
| 4 | £150 | £160 |
| 5 | £310 | £320 |
| 6 | £630 | £640 |
Why the martingale fails
The system works in theory only with infinite funds and no bet limits. In real casinos, a losing streak of 6–10 bets is common and will either hit the table maximum or exhaust the player's bankroll 2.
Because each loss doubles the required next stake, the risk of ruin grows exponentially while the potential profit stays fixed at the original bet. Over many sessions, the house edge ensures the player loses the expected percentage of total money wagered 1.
Common questions
What is martingale strategy in trading?
In trading, a martingale strategy means increasing the position size after a losing trade, aiming to recover losses on the next winning trade. It carries the same exponential risk as in gambling and is generally considered dangerous for retail traders.
Does martingale strategy work?
The martingale works in the short term if a win arrives before the bankroll runs out, but it fails over the long term. A long losing streak will either hit table limits or wipe out the bankroll, and the house edge ensures an expected loss on all money wagered 2.
Is martingale strategy legal?
Yes, the martingale strategy is legal. Casinos do not ban it because it does not give the player an advantage; they simply enforce table limits that stop the system from working past a few losses 1.
Where this term is used
Not the same as
- Martingale system blackjack — the same doubling-after-loss system applied specifically to blackjack, rather than the general betting-system term
Related terms
Sources
- Martingale (betting system) en.wikipedia.org Defines the martingale betting system and its doubling mechanism.
- Martingale Betting System wizardofodds.com Provides the bankroll ratios and explains why the system fails in practice.
- dsg pollock: brief notes—martingales le.ac.uk Supports the definition and the mathematical martingale property.
- MARTINGALES arxiv.org Supports the probability-theory definition of a martingale.
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.