📊 Risk of Ruin Calculator
Enter your gambling parameters to calculate the probability of losing your entire bankroll. The calculator uses the classic gambler's ruin formula adapted for various betting scenarios.
Risk Level Visualization
🔄 Bet Size Impact Analysis
See how changing your bet size affects your risk of ruin:
| Bet Size | % of Bankroll | Bankroll Units | Risk of Ruin | Rating |
|---|
Key Insight: Notice how risk of ruin increases exponentially as bet size grows. Even small increases in bet size can dramatically increase your probability of going broke.
🎯 Example Scenarios
Click a scenario to load it into the calculator:
Conservative Bettor
$1,000 bankroll, $10 bets (1%)
Moderate Risk
$1,000 bankroll, $50 bets (5%)
Aggressive Bettor
$1,000 bankroll, $100 bets (10%)
Sports Bettor (+EV)
$5,000 bankroll, $100 bets at -110
Roulette Player
$500 bankroll, $25 on red/black
Underfunded Gambler
$200 bankroll, $20 bets (10%)
Understanding Risk of Ruin: The Mathematics of Going Broke
Risk of Ruin (RoR) is one of the most important concepts in gambling mathematics. It represents the probability that you will lose your entire bankroll before achieving your goals—essentially, the chance of going completely broke. This concept was first formally analyzed in the context of gambling by mathematicians studying the "gambler's ruin problem," a classic probability puzzle that dates back to the 17th century and correspondence between Blaise Pascal and Pierre de Fermat.
Understanding your risk of ruin is essential for proper bankroll management. Even if you're playing a game with favorable odds (positive expected value), poor bet sizing can lead to ruin. Conversely, even with a house edge against you, proper bankroll management can extend your playing time significantly.
The Gambler's Ruin Formula
The classic risk of ruin formula for a simple random walk (where you win or lose one unit at a time) is:
RoR = Risk of Ruin (probability of losing entire bankroll)
p = Probability of winning a single bet
q = Probability of losing (1 - p)
n = Number of betting units in bankroll
For more complex scenarios with unequal payouts, the formula adapts to account for the edge calculation. This calculator uses the generalized formula based on the work documented in academic gambling mathematics research, including foundational work from the UNLV Gaming Research & Review.
Why Bet Size Matters More Than You Think
The relationship between bet size and risk of ruin is exponential, not linear. This means:
- Doubling your bet size more than doubles your risk of ruin — the effect compounds rapidly
- Small changes have big effects — going from 1% to 2% of bankroll per bet can dramatically increase ruin probability
- The number of units matters most — having 100 betting units is far safer than having 10, regardless of total dollar amount
- Even with an edge, you can go broke — betting too large a percentage makes ruin likely even with positive expected value
This is why professional gamblers and the National Council on Problem Gambling emphasize bankroll management as the most critical skill for anyone who gambles.
Recommended Risk of Ruin Thresholds
| Risk Level | RoR Range | Recommendation |
|---|---|---|
| Very Safe | 0% - 1% | Excellent bankroll protection. Recommended for recreational gamblers. |
| Safe | 1% - 5% | Good protection. Standard for professional bettors with proven edge. |
| Moderate | 5% - 20% | Significant risk. Only acceptable if bankroll is replenishable and edge is verified. |
| High Risk | 20% - 50% | Dangerous. High probability of losing everything. Reduce bet size immediately. |
| Extreme Risk | 50%+ | Near-certain ruin. Completely inadequate bankroll for chosen bet size. |
Risk of Ruin vs. House Edge
It's important to understand that risk of ruin and house edge are related but different concepts. The house edge determines your expected loss per bet, while risk of ruin determines your probability of going completely broke. You can have a high house edge but low risk of ruin (by betting small), or a small house edge but high risk of ruin (by betting too large).
Critical Understanding: With a negative expected value (house edge against you), risk of ruin approaches 100% in the long run no matter how small you bet—it's just a matter of time. The formulas only tell you the probability of ruin before reaching a certain goal. If you play indefinitely against a house edge, ruin is mathematically certain.
This is why games with negative expected value are fundamentally different from advantage play. For a detailed exploration of this concept, see our guide on variance and expected value in gambling.
How to Use This Calculator Effectively
- Be honest about your win probability. Don't overestimate your edge—use realistic numbers from the Wizard of Odds game analysis or similar authoritative sources.
- Include all fees and costs. Factor in vig, rake, and other costs that reduce your effective win rate.
- Use the bet size comparison table. Find the bet size that gives you acceptable risk while still allowing meaningful play.
- Target 1-5% risk of ruin. Unless you have a verified edge and replenishable bankroll, keep your RoR below 5%.
- Recalculate as your bankroll changes. Risk of ruin changes as your bankroll grows or shrinks—adjust bet sizes accordingly.
For more on optimal bet sizing when you have an edge, see our Kelly Criterion Calculator. The Kelly formula and risk of ruin are closely related—Kelly betting minimizes risk of ruin while maximizing growth.
Practical Applications
Understanding risk of ruin has applications beyond gambling. The same mathematics applies to:
- Investment portfolio sizing — determining how much to allocate to individual positions
- Business risk management — understanding the probability of business failure
- Insurance and actuarial science — calculating reserve requirements
- Sports betting bankroll management — sizing bets appropriately for your edge and bankroll
For those interested in the broader applications, the mathematical principles are explored in depth in works like "Fortune's Formula" by William Poundstone, which traces the history of these ideas from gambling to Wall Street.
Frequently Asked Questions
What is Risk of Ruin in gambling?
Risk of Ruin (RoR) is the probability of losing your entire bankroll before reaching a profit goal or stopping point. It's a fundamental concept in gambling mathematics that helps bettors understand how likely they are to go broke given their betting parameters—including win rate, bet size, and total bankroll.
How is Risk of Ruin calculated?
Risk of Ruin is calculated using the formula: RoR = (q/p)^n for simple cases, where p is win probability, q is loss probability (1-p), and n is the number of betting units in your bankroll. For unequal payouts, more complex formulas incorporate the edge and payout ratio. The key variables are your win rate, bet size relative to bankroll, and the odds offered.
Why is Risk of Ruin important for gamblers?
Risk of Ruin helps gamblers make informed decisions about bet sizing and bankroll management. Even with a positive edge, betting too large a percentage of your bankroll can lead to ruin due to variance. Understanding RoR allows you to balance potential growth against the risk of going broke, which is essential for long-term survival in any betting endeavor.
What is a safe Risk of Ruin percentage?
Most professional bettors aim for a Risk of Ruin below 5%, with many preferring 1-2% or lower. A 5% RoR means there's a 1 in 20 chance of going broke. The acceptable level depends on your risk tolerance, whether your bankroll is replenishable, and whether you have a verified edge. Lower is always safer for long-term survival.
How does bet size affect Risk of Ruin?
Bet size has an exponential effect on Risk of Ruin. Doubling your bet size more than doubles your risk of ruin—the relationship is not linear. This is why bankroll management experts recommend betting only 1-2% of your bankroll per bet. It dramatically reduces ruin probability while still allowing for meaningful growth when you have an edge.
Can you have 0% Risk of Ruin?
True 0% risk of ruin is only possible if you don't gamble at all, or if you have an infinite bankroll. In practice, with a house edge against you, risk of ruin approaches 100% over infinite time—you will eventually go broke if you play long enough. Even with a positive edge, there's always some risk due to variance. The goal is to minimize RoR to acceptable levels, not eliminate it entirely.
How does Risk of Ruin relate to the Kelly Criterion?
The Kelly Criterion and Risk of Ruin are closely related. Kelly betting (when you have an edge) is designed to maximize long-term growth while keeping risk of ruin at zero in theory. In practice, full Kelly can still have high variance, so many professionals use fractional Kelly (25-50%) to reduce volatility. Kelly only applies when you have positive expected value—if the house has the edge, Kelly recommends not betting at all.
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