# Risk of Ruin - The Math Every Trader Should Know > Risk of ruin is the probability that your trading account will hit zero before your strategy has time to work. Here is what the math shows and how to use it. **Tags:** risk-of-ruin, mathematics, probability, money-management **URL:** https://traderjournal.app/money-management/risk-of-ruin-the-math-every-trader-should-know --- # Risk of Ruin - The Math Every Trader Should Know Risk of ruin is a statistical concept that answers a specific question: given your win rate, your average risk-reward ratio, and your risk per trade, what is the probability that your account will eventually lose all of its capital before you have a significant winning run? Most retail traders have never heard of this concept. Many of the ones who have heard of it ignore it. This is a mistake because it shows, with mathematical precision, why certain combinations of risk percentage and win rate are unsuitable for real trading. --- ## The Basic Concept Imagine a coin flip game. Heads you win $2, tails you lose $1. Your win rate is 50%, your R:R is 2:1. Even with a positive expectancy, if you bet everything on each flip, you will eventually flip tails enough times in a row to go broke - even though the game is favorable. Trading is structurally similar. Positive expectancy does not guarantee survival. The sequence of wins and losses matters. Consecutive losses can deplete an account before the long-run edge has time to emerge. Risk of ruin quantifies this probability. --- ## A Simplified Formula A commonly used approximation for risk of ruin: RoR = ((1 - Edge) / (1 + Edge)) ^ (Capital / Risk_Per_Trade) Where: - Edge = (Win_Rate x R:R) - (1 - Win_Rate) - Capital = total account in units of risk (if account = $10,000 and risk = $100, capital = 100 units) **Example:** Win rate: 50% R:R: 1:2 (average win = 2x average loss) Risk per trade: 2% of account = 1/50 of account Edge = (0.50 x 2) - (0.50 x 1) = 1.0 - 0.5 = 0.5 RoR = ((1 - 0.5) / (1 + 0.5)) ^ 50 = (0.5 / 1.5) ^ 50 = 0.333 ^ 50 = essentially 0% (extremely low risk of ruin) This combination (50% win rate, 1:2 R:R, 2% risk) has an extremely low risk of ruin. The positive edge is strong enough to overcome the variance. --- ## Where Risk of Ruin Becomes Dangerous Change the parameters slightly. Same win rate (50%), same R:R (1:2), but increase risk per trade to 10%: RoR = (0.333) ^ 10 = approximately 1.9% A 1.9% risk of ruin sounds small but it means that across 52 different traders using this setup, roughly one will go broke even with a positive expectancy strategy. Over a long enough trading career, running 10% risk per trade with a 50% win rate is not a question of if you blow the account - it is a question of when. --- ## Key Insights From Risk of Ruin Math **Reducing risk per trade dramatically reduces risk of ruin.** Going from 5% to 1% per trade does not just divide risk of ruin by 5 - it reduces it exponentially. This is why the 1-2% rule is so powerful. **A poor win rate requires a large R:R to compensate.** A 35% win rate with 1:1 R:R has negative expectancy and infinite risk of ruin (you will eventually go broke with certainty). The same win rate with 1:3 R:R has positive expectancy and manageable risk of ruin at normal risk percentages. **High R:R does not save poor win rates below the breakeven level.** If your win rate is below breakeven for your R:R, no risk percentage makes the game survivable long-term. Fix the strategy first. --- ## Practical Application You do not need to calculate your exact risk of ruin for daily trading. The practical takeaway is simpler: 1. Keep risk per trade at 1-2% 2. Maintain positive expectancy (win rate and R:R combination above breakeven) 3. Never deviate from your risk rule during drawdowns (the temptation to "make it back faster" with bigger sizes is exactly when risk of ruin becomes acute) Your journal data shows you your actual win rate and R:R. Use those numbers to periodically verify that your strategy has positive expectancy. A strategy with negative expectancy will eventually produce ruin regardless of your risk percentage. Download Trader Journal at android.traderjournal.app or ios.traderjournal.app.