Risk of Ruin Calculator
Risk of ruin is the probability that a losing streak takes your account down to a loss you cannot accept, such as −50%. Enter your win rate, average win in R and risk per trade to get a reproducible Monte Carlo estimate over your number of trades, the classic formula, and a table by risk per trade.
Strategy and account settings Example values Replace them with numbers from your own trade log or backtest.
- 5th–95th percentile range
- Median path
- 20 sample paths
- Ruin threshold
Risk of ruin by risk per trade
Same win rate, average win, threshold, trades, simulations and seed. Only the risk per trade changes.
| Risk per trade | Monte Carlo risk of ruin (N trades) | Closed-form (unlimited trades) | Median ending equity | Chance of drawdown ≥ X |
|---|
Equity is shown with the starting balance set to 100, so 61.2 means a 38.8% loss. Everything runs in your browser. Nothing is saved or sent.
How the risk of ruin calculator works
The calculator models each trade as a coin flip with your win rate. A loss costs 1R, the amount you risk. A win pays your average win in R. It then plays the same sequence of trades thousands of times with different random outcomes.
- Size each trade. With fixed-fractional sizing, 1R is the risk % of your current equity, so trades shrink after losses and grow after wins. With fixed $ risk, 1R is always the risk % of the starting balance.
- Draw the outcome. A seeded random number generator (mulberry32) decides win or loss. The same seed and inputs always give the same paths, so you can share or recheck a result.
- Track the path. Equity, its running peak and the deepest peak-to-trough drawdown are updated after every trade.
- Stop at ruin. If equity falls to or below the ruin threshold, the path is counted as ruined and stops trading, as a trader who hit the limit would.
- Count. Risk of ruin = ruined paths ÷ all paths. The ± figure is the 95% sampling interval, 1.96 × √(p × (1 − p) ÷ simulations).
Expectancy tells you the average result per trade. It does not tell you the path. Two strategies with the same expectancy can have very different risk of ruin if one risks 1% per trade and the other 10%. For more on this, read understanding expectancy and why win rate alone doesn’t matter.
The classic risk of ruin formula
Risk of ruin comes from the gambler’s ruin problem in probability. A player wins or loses one unit per bet with probabilities p and q = 1 − p and stops at zero. Columbia University course notes on the gambler’s ruin problem show that, with no upper target, a player who starts with i units and has p > 0.5 avoids ruin forever with probability 1 − (q/p)^i. So the probability of ruin is (q/p)^i. Writing edge = p − q gives the form traders usually quote:
It is exact only under strict assumptions. Treat it as an approximation for real trading:
- Wins and losses are the same size (average win = 1R).
- The bet size is a fixed dollar amount; it does not shrink after losses.
- Trades are independent and the win rate never changes.
- You trade forever until ruined. Over a limited number of trades the real figure is lower.
Worked example: classic formula
Win rate 55%, average win 1R, fixed $ risk of 2% of the starting balance, ruin at −50%.
- edge = 0.55 − 0.45 = 0.10.
- U = 50% ÷ 2% = 25 losing units.
- (1 − 0.10) ÷ (1 + 0.10) = 0.45 ÷ 0.55 = 0.8182.
- 0.8182^25 = 0.0066, or 0.66%.
At 5% risk per trade U falls to 10, and the same edge gives 0.8182^10 = 13.4%. With a 52% win rate and 2% risk it is 0.9231^25 = 13.5%. Small changes in edge or bet size move the result a lot.
When wins are bigger than losses, or sizing compounds
For any other average win or for fixed-fractional sizing, the calculator uses a general closed-form estimate from ruin theory. It finds the positive number θ that solves
For even payoffs and fixed $ risk this reduces to the classic formula. In the other cases it is an upper bound for unlimited trades under the model’s assumptions: the true unlimited-trade risk is at or below it. If the expected log growth per trade (p × a − q × b) is zero or negative, the estimate is 100%: given enough trades, the account is expected to hit any threshold.
This matters for fixed-fractional sizing. A strategy can have positive expectancy in R and still lose money over time if the risk per trade is too high, because a 10% loss followed by a 10% gain leaves you at 99%, not 100%.
Worked example: the default inputs
Win rate 40%, average win 1.8R, 2% of current equity per trade, ruin at −50%, 500 trades, 10,000 simulations, seed 12345.
- Expectancy = 0.40 × 1.8 − 0.60 × 1 = +0.12R per trade. Break-even win rate = 1 ÷ 2.8 = 35.7%.
- A loss multiplies equity by 0.98 and a win by 1.036. Expected log growth per trade = 0.40 × ln(1.036) + 0.60 × ln(0.98) = +0.0020 (about +0.20% per trade), slightly positive.
- Ruin at −50% needs about ln(0.5) ÷ ln(0.98) = 34.3 net losses without offsetting wins.
- Monte Carlo result: 1.47% of paths (147 of 10,000) hit −50% within 500 trades, with a 95% interval of ± 0.24 points. An exact calculation over all win/loss sequences gives 1.56%, inside that interval. The closed-form estimate for unlimited trades is 2.06%.
- Median ending equity is 275.3 (start = 100) and the 5th percentile is 95.8. Even so, 86.8% of paths had a peak-to-trough drawdown of 25% or more.
The thin edge is the point of this example. With a 35.7% break-even win rate, a true win rate of 40% leaves little room. If the real win rate were 37% instead, the expectancy would fall to +0.036R and the risk of ruin would rise. Try it in the calculator.
What drives risk of ruin
| Input | If it goes up | Why |
|---|---|---|
| Risk per trade | Risk of ruin rises fast | Fewer losses are needed to reach the threshold. |
| Win rate | Risk of ruin falls | Losing streaks become rarer and shorter. |
| Average win (R) | Risk of ruin falls | Each win repairs more of the damage from losses. |
| Ruin threshold (deeper) | Risk of ruin falls | More room, but the loss you accept is bigger. |
| Number of trades | Risk of ruin rises toward the unlimited-trade value | More trades give a bad streak more chances to appear. |
Losing streaks are longer than most people expect. With a 40% win rate, the chance that any given 10 trades are all losses is 0.6^10 ≈ 0.6%. Over 500 trades, there are hundreds of such windows. Plan your risk per trade for the streak, not for the average. The position size calculator turns a risk % into a position size, and the risk/reward calculator checks the R multiple of a single setup.
Limits: why real risk is usually higher
- Fat tails and gaps. The model assumes every loss is exactly 1R. In real markets prices can gap through a stop-loss, so some losses are 2R or more. Rare large moves happen more often than a simple coin-flip model allows.
- The edge changes. Win rate and average win drift as market conditions change. A backtest edge can shrink or disappear in live trading.
- Trades are not independent. Losses tend to cluster when a strategy stops fitting the market, which makes long streaks more likely than the model shows.
- Input uncertainty. A win rate measured over 50 trades is a rough estimate. Run the calculator with a lower win rate and a smaller average win to see a cautious case. A backtesting spreadsheet helps build a larger sample.
- Costs and leverage. Fees, spreads and funding reduce the average win and increase the average loss. Leverage can cause losses larger than the money deposited.
Regulators stress the same point. The SEC’s investor guide Day Trading: Your Dollars at Risk says “day traders should only risk money they can afford to lose.” Investor.gov’s What is Risk? page says “All investments involve some degree of risk.” A low number from this calculator is a model output, not a promise.
Common mistakes
- Using the classic formula with an average win far from 1R. It ignores payoff size, so it overstates risk for big winners and understates it for small ones.
- Entering a win rate from a short or optimised backtest without allowing for a worse live result.
- Ignoring compounding. With fixed-fractional sizing a high risk % can drag the median ending equity down even when expectancy in R is positive.
- Treating a 1% risk of ruin as “safe”. It means about 1 in 100 traders with exactly these statistics would hit the threshold, in the model alone.
- Reading one Monte Carlo run as exact. Check the ± interval, or raise the number of simulations.
FAQ
What is risk of ruin in trading?
Risk of ruin is the probability that a series of losing trades cuts an account down to a level at which the trader can no longer continue or has decided to stop. Ruin does not have to mean a zero balance. Many traders define it as a fixed loss from the starting balance, such as 50%, because recovering from a 50% loss needs a 100% gain.
How do you calculate risk of ruin?
For the simplest case, where every trade wins or loses the same fixed amount, the gambler’s ruin result gives risk of ruin = ((1 − edge) ÷ (1 + edge))^U, where edge = win rate − loss rate and U is the number of fixed-size losses your threshold allows. With a 55% win rate, edge = 0.10, and a 50% threshold with 2% risk per trade gives U = 25, so risk of ruin = (0.45 ÷ 0.55)^25 ≈ 0.66%. For uneven payoffs or compounding position sizes, a Monte Carlo simulation is the practical method.
What is an acceptable risk of ruin?
There is no official standard. It is a personal limit that depends on how much of the account you can afford to lose. Keep in mind that the calculated figure assumes your win rate and payoff stay exactly as entered and that trades are independent, so a real-world risk is usually higher than a model shows. Compare several risk-per-trade levels in the table rather than relying on one number.
Does a high win rate mean a low risk of ruin?
Not on its own. Risk of ruin depends on the win rate together with the size of wins relative to losses and the amount risked per trade. A 60% win rate with wins half the size of losses has a negative expectancy of −0.10R per trade, so over enough trades the account trends down whatever the win rate.
Why does the Monte Carlo result differ from the formula?
The formula answers a slightly different question: the chance of ever hitting the threshold if you trade forever, with fixed bet sizes. The simulation counts only the trades you enter, and it can model compounding position sizes and wins larger than losses. A simulation also has sampling error, which this calculator shows as a 95% interval.
How much should I risk per trade to keep risk of ruin low?
The table under the calculator shows the risk of ruin for 0.5%, 1%, 2%, 5% and 10% risk per trade with your other inputs unchanged. Smaller risk per trade means more losing trades are needed to reach the threshold, so the risk of ruin falls. The right level is a personal decision, and no level makes trading safe if the strategy has no real edge.
Related tools and guides
- Position size calculator
Turn a risk % into units or shares. - Risk/reward calculator
R multiple of a single trade setup. - Backtesting spreadsheet
Measure win rate and average win from your rules. - Understanding expectancy
Average result per trade, explained. - Why win rate alone doesn’t matter
Win rate vs payoff size.
Educational tool only, not financial or investment advice. The results come from a simplified model with the inputs you enter. They do not predict real trading results and do not include gaps, fees, leverage, changing market conditions or correlated losses. Sources: Columbia University notes, Gambler’s Ruin Problem, SEC, Day Trading: Your Dollars at Risk, Investor.gov, What is Risk?. Retrieved 27 Oct 2026.