Risk of Ruin: How to Calculate the Probability of Going Broke

The Mathematics of Ruin

Risk of ruin depends on four variables: win rate (W), reward-to-risk ratio (RRR), position size as a percentage of account (f), and the number of trades (N). The basic ROR formula for a 50% drawdown threshold is approximately: ROR = ((1 - Edge) / (1 + Edge))^(N), where Edge is your expectancy per trade as a fraction of your account. More practically, ROR is calculated using Monte Carlo simulation — run 10,000 simulated sequences of N trades with your parameters and count how many sequences hit the ruin threshold. At 2% risk per trade with a 50% win rate and 2:1 RR, less than 1 in 1,000 sequences hits ruin over 100 trades. At 10% risk per trade, nearly half of all sequences hit ruin. The relationship between position size and ROR is exponential, not linear. Use Monte Carlo to simulate risk of ruin →

The ROR Formula (Simplified)

For a trader with win rate p, loss rate q (1-p), and average win/loss ratio R, the approximate probability of losing X% of your account before doubling it is: ROR = ((q / p) ^ (f)) ^ (X / f). Where f is the fraction of your account risked per trade (as a decimal). This is a simplified version that assumes fixed bet sizes. In reality, risk of ruin is best estimated through simulation because trade outcomes have varying sizes. The simplified formula understates ROR for strategies with high variance in trade sizes. Always use simulation for serious capital allocation decisions.

Optimal Position Size: Balancing Growth and Ruin

The optimal position size maximizes your geometric growth rate while keeping risk of ruin acceptably low (below 1%). This optimal point is found by plotting position size against both expected growth and ROR. At very small position sizes (0.1%), ROR is near zero but growth is too slow. At very large position sizes (10%+), growth may be higher in theory but ROR is unacceptably high. The sweet spot for most traders with typical win rates (40-60%) and RRRs (1.5:1 to 3:1) is 1-2% risk per trade. This range balances meaningful growth with near-zero ROR. The Kelly Criterion suggests higher sizes (4-10% depending on parameters), but Kelly assumes your estimates are perfectly accurate and you will trade infinitely — neither is true. Fractional Kelly at 25-50% of full Kelly typically lands in the 1-3% range, consistent with empirical best practices. Calculate your expectancy to find optimal size →

How Position Size Affects ROR

The relationship is stark. A trader with a 55% win rate and 2:1 RR: at 1% risk per trade, ROR over 500 trades is effectively 0%. At 2% risk, ROR is 0.5%. At 3% risk, ROR is 3%. At 5% risk, ROR is 18%. At 10% risk, ROR is 55%. The jump from 2% to 5% triples the risk percentage but multiplies ROR by 36 times. This nonlinear relationship is why professional traders are obsessive about position sizing. They know that a small increase in risk produces a massive increase in ruin probability. The difference between a surviving trader and a blown-out trader is often just 2-3% in position size — with the exact same strategy. Build a complete risk management framework →

What is risk of ruin in trading?

Risk of ruin (ROR) is the probability that your account will decline to a level where you cannot continue trading, typically defined as a 50% or 100% loss of starting capital. It is calculated from your win rate, reward-to-risk ratio, position size per trade, and the number of trades you plan to execute. A 1% ROR means that if you ran your strategy 1,000 times, you would go broke in 10 of those runs. Professional traders aim for ROR below 1% over their expected trading career. ROR is distinct from drawdown — you can have a 30% drawdown and survive; ROR measures the probability that you do not survive.

How do I calculate my personal risk of ruin?

The most practical method is Monte Carlo simulation. Record your actual trade outcomes (in R-multiples) from your trading journal or backtest. Then run 10,000 simulated sequences of your strategy, each with the same number of trades as your actual history. In each simulation, randomly sample from your actual trade distribution. Count how many simulations hit your ruin threshold (e.g., 50% account loss). That percentage is your ROR. If your ROR is above 1%, reduce your position size. Tools like Tradervue, Edgewonk, and specialized ROR calculators can automate this process. Repeat the calculation periodically as your trade data grows — your ROR estimate becomes more reliable with more data.

What is an acceptable risk of ruin?

An acceptable risk of ruin depends on your risk tolerance and career stage. Professional traders targeting a full-time income from trading should maintain ROR below 0.5%. Part-time traders with other income sources can tolerate higher ROR (1-2%) because trading losses do not threaten their livelihood. Beginners learning with small accounts should accept ROR below 5% — the goal is learning, not income, so a small risk of losing the learning account is acceptable. Regardless of your situation, ROR above 5% means you are overbetting. Reduce your position size immediately. Survival is the first priority in trading. No strategy can compound returns if the account is gone.

Does risk of ruin change as my account grows?

Yes, risk of ruin changes with account size if you use fixed percentage position sizing. As your account grows, your dollar risk grows proportionally, but your ROR as a percentage of the starting account decreases because you have more capital to absorb losses. The ROR formula accounts for this — larger accounts have lower ROR for the same strategy because the distance to the ruin threshold (in dollars) is greater. However, many traders fall into the trap of increasing their risk percentage as their account grows, which offsets the protective effect of a larger account. Keep your risk percentage constant, and your ROR will decline naturally as your account compounds. This is one of the hidden benefits of fixed fractional position sizing. Review win rate and RRR combinations that minimize ROR →

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