Martingale Calculator
Calculate the risk of ruin and bankroll requirements for the Martingale betting strategy. Enter values for instant results with step-by-step formulas.
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\nTotal loss on 7 consecutive losses: $10 x (2^7 - 1) = $1,270 (exceeds bankroll at step 7)\nProbability of 7 consecutive losses: (1 - 0.486)^7 = 0.514^7 = 0.94%\nWins needed for $100 profit: 100/10 = 10 wins\nProbability 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\nTotal at risk after 10 losses: $5 x (2^10 - 1) = $5,115\nProbability of 10 consecutive losses: 0.514^10 = 0.134%\nExpected rounds before bust: 1/0.00134 = ~746 rounds
Result: Can survive 10 consecutive losses | Bust probability per streak: 0.134% | Expected ~746 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 accurate are the results from Martingale Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.