Martingale Risk Calculator (chance of busting)

Understanding the martingale risk calculator — concept and principle

The martingale system doubles the stake after every loss so that the first win recovers all previous losses plus one base bet. It looks safe because most sequences end in a small win, but a long losing streak wipes out most of the bankroll. This calculator shows how many losses in a row your bankroll can absorb, how likely such a streak is, and the chance of at least one failed sequence over a planned number of sequences.

How it is calculated

Inputs: bankroll B, starting bet s, win probability per bet p, and number of sequences R. A sequence ends at the first win or when the next doubled bet can no longer be covered.

• Losses you can survive: k = ⌊log₂(B ÷ s + 1)⌋, because k losing bets cost s(2^k − 1) in total.
• Chance a sequence fails: (1 − p)^k.
• Chance of at least one failed sequence within R: 1 − (1 − (1 − p)^k)^R.
• Gain if every sequence wins: s × R. Loss when a sequence fails: s(2^k − 1); bankroll left = B − s(2^k − 1).

The principle

Each completed sequence wins one base bet, while a failed one loses a doubling series that grows exponentially. A small failure chance per sequence becomes likely over many repetitions. The expected value per bet in a game with a house edge stays negative no matter how stakes are sized: a betting system changes the shape of the outcomes (many small wins, rare large losses), not their average.

Worked example

Default inputs: bankroll $1,000, starting bet $10, win probability 48.65% (European roulette red, 18/37), 100 sequences.

1. B ÷ s + 1 = 101; log₂(101) = 6.66, so you survive 6 losses in a row.
2. Six losses cost 10 × (2⁶ − 1) = $630; a seventh bet of $640 cannot be covered.
3. Chance of 6 losses in a row: 0.5135⁶ = 1.833%.
4. Chance of at least one failed sequence in 100: 1 − (1 − 0.01833)¹⁰⁰ = 84.28%.
5. One failure leaves 1,000 − 630 = $370.
6. If all 100 sequences succeed you gain 10 × 100 = $1,000.

How to read the result

Above 50%, losing $630 at least once is more likely than not. Compare the gain if everything goes right with the loss when one sequence fails: here you risk $630 per failure to earn $10 per success, so you need more than 63 successes per failure just to break even, while the odds give only about 54.

Common mistakes

• Believing a loss makes a win "due" (independent spins have no memory).
• Ignoring table maximums, which stop the doubling early.
• Treating a 1–2% failure chance per sequence as negligible over hundreds of sequences.

Frequently asked questions

Does martingale beat the house edge?

No. The expected value of every bet stays negative, so the system cannot turn a losing game into a winning one.

Why does martingale feel like it works?

Most sessions end with small wins, and the rare large loss may not happen during a short trial.

Is martingale used in trading?

Adding to a losing position in doubling steps carries the same risk of a large, account-ending loss.

Sources: Feller, W., An Introduction to Probability Theory and Its Applications, Vol. 1 (gambler's ruin) · Epstein, R. A., The Theory of Gambling and Statistical Logic