Martingale Calculator
Calculate the risk of ruin and bankroll requirements for the Martingale betting strategy. Analyze consecutive loss probabilities and expected outcomes.
Martingale Calculator
Calculator
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Formula: Risk per streak = (1 - p)^n; Bankroll needed = B x (2^n - 1)
Worked example — Risk of bust per streak: 0.94% | Target probability: ~91% | But over 100 rounds, cumulative ruin risk is ~61%
Formula
Risk per streak = (1 - p)^n; Bankroll needed = B x (2^n - 1)
Where p = win probability, n = max consecutive losses supportable, B = base bet. The Martingale doubles bets after each loss, so required bankroll grows as 2^n - 1 times the base bet.
Worked Examples
Example 1: Roulette Red/Black Martingale
Problem:You have a $1,000 bankroll, bet $10 on red (48.6% win probability in American roulette), and want to profit $100. What is your risk?
Solution:Max consecutive losses before bust: floor(log2(1000/10)) + 1 = 7 Total loss on 7 consecutive losses: $10 x (2^7 - 1) = $1,270 (exceeds bankroll at step 7) Probability of 7 consecutive losses: (1 - 0.486)^7 = 0.514^7 = 0.94% Wins needed for $100 profit: 100/10 = 10 wins Probability of reaching target: (1 - 0.0094)^10 = 90.97%
Result:Risk of bust per streak: 0.94% | Target probability: ~91% | But over 100 rounds, cumulative ruin risk is ~61%
Example 2: High Bankroll Conservative Bet
Problem:With a $5,000 bankroll and $5 base bet at 48.6% win probability, how many losses can you survive?
Solution:Max consecutive losses: floor(log2(5000/5)) + 1 = 10 Total at risk after 10 losses: $5 x (2^10 - 1) = $5,115 Probability of 10 consecutive losses: 0.514^10 = 0.129% Expected rounds before bust: 1/0.00129 = ~777 rounds
Result:Can survive 10 consecutive losses | Bust probability per streak: 0.129% | Expected ~777 rounds before bust
Frequently Asked Questions
What is the Martingale betting strategy?
The Martingale strategy is one of the oldest and most well-known betting systems in gambling history. The core idea is simple: after every loss, you double your bet so that the first win recovers all previous losses plus a profit equal to the original base bet. For example, if you start with a $10 bet and lose, you bet $20 next. If you lose again, you bet $40. When you finally win, you recover everything and gain $10 net profit. While mathematically elegant in theory, the strategy has a fatal flaw in practice: table limits and finite bankrolls mean a long losing streak will completely wipe out your funds before you can recover.
Why does the Martingale strategy fail long-term?
The Martingale strategy fails long-term because the required bets grow exponentially while the profit per successful sequence remains constant at just one base bet unit. After 10 consecutive losses starting with $10, you would need to bet $10,240 just to win back $10 in profit. Furthermore, casino games have a built-in house edge, meaning the expected value of every bet is negative. No betting pattern can overcome a negative expected value game over time. The strategy creates an illusion of frequent small wins punctuated by catastrophic rare losses, and those rare losses eventually consume all prior gains and more.
How much bankroll do I need for the Martingale strategy?
The bankroll requirement for the Martingale strategy depends on how many consecutive losses you want to survive. To survive N consecutive losses with a base bet of B, you need B multiplied by (2 to the power of N minus 1). For a $10 base bet: surviving 5 losses requires $310, surviving 8 losses requires $2,550, surviving 10 losses requires $10,230, and surviving 15 losses requires $327,670. Even with a large bankroll, table maximum limits at casinos typically prevent the strategy from being executed beyond 8 to 10 doublings, making catastrophic loss inevitable over enough play sessions.
What is the risk of ruin in the Martingale system?
Risk of ruin represents the probability that a gambler will lose their entire bankroll before reaching their profit target. In the Martingale system, risk of ruin depends on the win probability, bankroll size relative to the base bet, and how many rounds you plan to play. For a fair coin flip (50% win probability) with a $1,000 bankroll and $10 base bet, you can survive about 7 consecutive losses. The probability of 7 consecutive losses is roughly 0.78%, which seems low, but over 100 rounds of play, the cumulative risk of ruin climbs substantially because you face that risk repeatedly each session.
Are there safer alternatives to the Martingale strategy?
Several alternatives carry lower risk than the Martingale system. The D'Alembert system increases bets by one unit after a loss and decreases by one unit after a win, creating a much gentler progression. The Fibonacci system follows the Fibonacci sequence for bet sizing, growing more slowly than doubling. The Kelly Criterion takes a mathematically optimal approach by sizing bets proportional to your edge, which is ideal for positive expected value situations. Flat betting, where you wager the same amount every round, is the simplest and often most sustainable approach. No system can overcome a negative expected value game, but gentler progressions reduce the speed and severity of potential losses.
How does a table maximum stop the Martingale from working?
The strategy needs an unbounded doubling sequence, but every table has a posted maximum. Starting at one unit, the nth bet in a losing run is 2^(n-1) units, so a table with a 500 unit cap and a 5 unit minimum allows only about six doublings before the next required bet is illegal. At that point the losing run cannot be continued and the accumulated loss of 2^n - 1 base units is locked in. The cap converts a rare catastrophic loss into a merely uncommon one, which is exactly why it exists.
How many consecutive losses should I expect over a long session?
For a bet with win probability p, a specific run of n losses has probability (1 - p)^n, and over N trials the expected number of starting positions for such a run is roughly N x (1 - p)^n. On an even-money European roulette bet where p = 18/37, ten straight losses have probability around 0.00126, so across a few thousand spins you should expect to meet that streak rather than treat it as impossible. Streak length grows only logarithmically with session length, which is why longer play reliably finds the streak that breaks the system.
Why does doubling after a loss not cancel the house edge?
Expectation is linear: the expected value of a sequence of bets is the sum of the expected values of the individual bets, regardless of how the stake sizes were chosen. Each spin carries a fixed negative expectation set by the house edge, so any staking pattern based only on past results produces a total expectation that is negative in proportion to total money wagered. Because the Martingale wagers far more money than flat betting to chase the same small profit, it typically increases expected losses rather than reducing them.
What is the difference between the Martingale and the anti-Martingale?
The Martingale doubles after every loss and resets after a win, producing many small wins and rare very large losses. The anti-Martingale, also called the Paroli, doubles after every win and resets after a loss, producing many small losses and rare large wins. The two mirror each other in shape but share the same expected value, since neither changes the per-bet edge. The practical difference is risk profile: the Martingale risks the whole bankroll on losing streaks, while the anti-Martingale only ever risks previously won money.
How does the Grand Martingale differ from the classic version?
The Grand Martingale doubles the previous stake and then adds one extra base unit, so a losing run yields a profit of more than one unit when it finally breaks. The cost is that the stake sequence grows faster than 2^n, so the bankroll required for a given streak length is materially larger and the table maximum is reached sooner. It improves the payoff of the common outcome while worsening the rare one, which sharpens the trade-off the classic version already makes rather than fixing it.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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