The Martingale betting system: why doubling up fails, in numbers

How Martingale works

You pick bets at odds of about 2.00 and start with a base stake, say €10. After a loss you double the stake; after a win you go back to €10. Because each stake at 2.00 returns twice its amount, the first win in a series pays back every earlier loss plus €10.

That is the whole idea, and it is correct as far as it goes: as long as you can keep doubling, each completed series ends €10 up. The problem is the “as long as”.

The maths: eight losses in a row

After eight losses in a row you have lost €2,550, and the next stake is €2,560, which is 256 times your base stake (2⁸), to win back €10. In general, after n losses the next stake is 2ⁿ × base and the money lost is (2ⁿ − 1) × base. Each extra loss doubles both.

A bankroll of €2,550 therefore survives seven losses and loses everything on the eighth. To survive ten losses you would need €10,230 to chase a €10 win.

How often a losing run happens

Odds of 2.00 at a bookmaker don't mean a 50% chance; the margin is in the price. Assume a true probability of 48% (a loss chance of 52%). Then eight losses in a row from any given start happen with probability 0.52⁸ ≈ 0.53%, about once in 187 series. Rare per series, but you play many series. The chance of at least one run of eight or more losses somewhere in your bets:

Exact values from a Markov chain over independent bets, rounded. Even at a perfectly fair coin with no margin, a run of eight is more likely than not within 500 bets.

With €10 base stakes and a €2,550 bankroll, over 1,000 bets you would win about 480 series of €10, roughly €4,800, and you would very probably hit at least one run that wipes out €2,550. Often more than one: at a 52% loss chance you expect about 2.5 such runs in 1,000 bets. This is the classic progression trap: frequent small wins, rare large losses.

Maximum stakes stop the system

Even with unlimited money, Martingale runs into the bookmaker's rules:

• Maximum stakes. Every market has a maximum stake, and on many accounts it is far below €2,560, especially on smaller markets. Once you hit it, you can no longer double, and the series is lost.
• Odds below 2.00. Real prices on even contests are usually around 1.85 to 1.95. To recover losses L plus your target at odds o, the next stake must be (L + target) ÷ (o − 1). At 1.90 that means multiplying by about 2.1 each time, not 2, so stakes grow faster.
• Deposit limits. Deposit limits, whether set by you or by the bookmaker, can stop a series in the middle.

Why expected value doesn't change

Every bet in the series has the same expected value per euro: 0.48 × 2.00 − 1 = −4%. A staking plan only decides how much you put on each bet, so the expected result is always the total staked × −4%. Worked through for one series with eight bets at most:

expected stake per series = €10 × (1 + 1.04 + 1.04² + … + 1.04⁷) ≈ €92.14
expected result = −4% × €92.14 ≈ −€3.69
check: 0.99465 × (+€10) + 0.00535 × (−€2,550) ≈ €9.95 − €13.63 = −€3.69

Both routes give the same answer: about −€3.69 per series, around 2.07 bets on average. The many small wins and the rare large loss are just the shape of the same negative expectation. The idea that a win is “due” after many losses is the gambler's fallacy: each match is independent of your last bet. Our guide on winning long term explains where that −4% comes from.

Variants and “safe” versions

• Capped Martingale (stop after five doublings): smaller disasters, more frequent ones. EV unchanged.
• Reverse Martingale (double after wins): many small losses, rare large wins. EV unchanged.
• Fibonacci and d'Alembert: slower stake growth, same principle, same EV.

There is no safe version, because no staking plan can turn bets with negative expected value into positive ones. Stake sizing only matters once the bets themselves are good; for that, see bankroll management. If you notice you are doubling stakes to win back losses, that is chasing, a recognised warning sign; our responsible gambling page lists free help.

Frequently asked questions

Does the Martingale system work for sports betting?

No. It wins small amounts most of the time, but a run of losses forces stakes to grow until a maximum stake or your bankroll stops you, and that single loss outweighs the small wins. The expected value per euro stays the same as for any other bet at the same odds.

How often do 8 losses in a row happen?

At odds of 2.00 with a 52 percent chance of losing each bet, eight losses in a row from a given start happen about once in 187 series. Over 1,000 bets, the chance of at least one such run is about 93 percent, and about 86 percent even with a fair 50 percent chance.

Is there a safe version of Martingale?

No. Capping the number of doublings, doubling after wins instead, or using Fibonacci only changes how often and how large the losses are. No staking plan can turn bets with negative expected value into positive ones.

Sources

• Wikipedia: Martingale (betting system)
• Wikipedia: Gambler's ruin
• Wikipedia: Gambler's fallacy
• Wikipedia: Expected value
• Spielsuchthilfe (Austria): counselling for gambling problems

As of October 2026. Probabilities calculated by us for independent bets; all figures are worked examples.

Betting involves risk, including sure bets: prices move, bets get voided and accounts get limited. Only bet money you can do without. Our responsible gambling page lists free, confidential help.

Not betting, financial, legal or tax advice. 18+. As of October 2026.