📉 Risk of ruin
Risk of busting before hitting your target, and why Martingale collides with the table limit.
📉 Risk of Ruin Calculator
Calculates the mathematical risk of going bankrupt before reaching your profit goal.
Onde i = 20 (unidades iniciais), N = 30 (unidades alvo), e q/p = 1.0555
⚠️ Atenção: Martingale and other negative progressions are NOT winning strategies. They merely trade frequent small losses for rare but catastrophic ones, requiring exponentially growing bankrolls until they hit table limits. The house edge remains mathematically invariant.
What it is
Probability of ruin is the chance that a gambler exhausts their bankroll before reaching a target profit, given a fixed betting strategy and a negative expectation game. It is a mathematical inevitability over many trials, not a risk to be managed away.
How it works
The calculator uses the classic gambler's ruin formula. For even-money bets with a house edge, the probability of winning a single bet is p = (1 - houseEdge) / 2. With a starting bankroll of 20 units ($100 at $5 per bet) and a target of 30 units ($150), the chance of ruin is P = 1 − ((q/p)^i − 1) / ((q/p)^N − 1). Here q = 1 - p, i = starting units, N = target units in units. For European roulette (2.7% house edge), p = 0.4865, q = 0.5135, q/p = 1.0556. Then (q/p)^20 = 2.99, (q/p)^30 = 5.17, so P = 1 − (2.99 − 1)/(5.17 − 1) = 1 − 1.99/4.17 = 0.523, or 52.3%.
The Martingale progression doubles after each loss. With a base bet of $5 and a table limit of $500, a losing streak of 7 bets costs 5+10+20+40+80+160+320 = $635, and the 8th bet would exceed the limit. The "Max Bankroll Req." field shows the sum needed to survive the streak. The "Limit Break" field notes when the progression hits the table ceiling, which truncates the recovery exactly when it is most needed, turning a theoretical certainty into a practical loss.
How to use it
- Enter your "Starting Bankroll" in dollars, for example $100, and your "Base Bet" in dollars, say $5.
- Set the "House Edge (%)" to match the game, such as 2.7 for European roulette or 5.26 for American double-zero.
- Input a "Profit Goal" in dollars, for instance $50, which represents the bankroll level at which you would stop.
- Enter the "Table Limit" in dollars, e.g., $500, which is the maximum allowed single bet for the game you are considering.
- Select a "Betting Progression" from the options: Flat, Martingale, or Fibonacci, and then press Calculate.
How to read the result
- "Probability of Ruin" is the likelihood that you will go broke before reaching your profit goal, assuming you play until one of those endpoints. It is a long-run expectation; short-term results can vary wildly.
- "Bets until Ruin (Expected)" is the average number of bets, not the worst case. In a Martingale, a single long losing streak can cut that number dramatically.
- "Max Bankroll Req. (Losing Streak)" shows the largest bankroll needed to survive a worst-case losing sequence under the chosen progression. For Martingale, this is the cumulative loss of the streak.
- "Limit Break (Martingale)" indicates the first step in the progressive series that would exceed the table limit, meaning the Martingale cannot be completed past that point.
When not to trust the result
- The formula assumes even-money bets and constant stakes (or a fixed progression). In real casino games, bets are not perfectly even—even red/black has the zero—and the progression rules may differ.
- Martingale does not change the house edge. It transforms many small losses into a single large loss, but the expected value per dollar wagered remains negative. The calculator shows the probabilities, not a change in odds.
- The table limit truncates the Martingale recovery precisely when the gambler needs it most. If the required bet exceeds the limit, the progression fails and the full loss is realized, increasing ruin probability above the idealized formula.
- The results assume you always have the full bankroll available and never change your strategy. In practice, psychological or financial constraints often lead to deviations that alter the true probabilities.
- For flat betting, the formula assumes you bet the same amount every time. Real-world bankroll management often involves changing bet sizes, which this model does not capture.
Frequently asked questions
- Does a lower house edge guarantee I won't go broke?
- No. It reduces the probability of ruin but does not eliminate it. Even with a perfect coin flip (0% edge), the probability of ruin is 1 - (i/N) for flat betting, which is still positive unless you have infinite bankroll or a zero profit goal.
- Why is the Martingale considered risky if it seems to win often?
- Martingale produces frequent small wins and rare large losses. Over many sequences, the expected loss is the same as flat betting. The calculator shows that a long losing streak can wipe out a bankroll that appeared safe, because the required bet grows exponentially.
- Can I use this calculator to find a winning strategy?
- No. The purpose is to demonstrate that every negative-expectation betting system has a probability of ruin approaching 1 as the number of bets rises. No progression turns a losing game into a winning one; it only shifts the timing of losses.
- What does "Limit Break" mean for my actual play?
- It marks the bet in the Martingale sequence that would be illegal or impossible due to table limits. If you reach that point, you cannot double again, and the strategy breaks down, almost surely resulting in hitting the ruin threshold.