Same strategy, different risk per trade
| Risk per trade | Units to ruin | Risk of ruin (formula) |
|---|
The classic risk of ruin formula
The textbook version comes from the gambler's ruin problem and assumes every win and every loss is the same size, 1:1. If you win with probability p, lose with probability q = 1 − p, and you are U losing trades away from ruin, then:
Take a 1:1 strategy that wins 52% of the time, with a 10% ruin line. At 1% risk, U is 10 and RoR is (0.48 ÷ 0.52)^10, about 45%. A thin edge with little room is nearly a coin flip on survival. Double the room to a 20% line and it falls to about 20%. Every extra unit of room multiplies the risk of ruin by q ÷ p again.
The version this calculator uses
Most traders do not trade 1:1. A strategy with 2R winners and 1R losers needs a formula that handles uneven payoffs. The calculator finds the number λ (the adjustment coefficient from risk theory) that balances one trade's outcomes:
For 1:1 trades this gives exactly the classic answer. For any other payoff it gives the probability of ever reaching the ruin line, with no time limit. With fixed sizing the wins, losses and U are measured in R. With compounding they are measured in log returns, because each bet is a percentage of the balance you have at the time. If expectancy is zero or negative, there is no λ above zero and risk of ruin is 100%: given enough trades, you will get there.
With fixed sizing, when the ruin line is a whole number of average losses away, this formula is exact. When the last loss can overshoot the line (a fractional number of losses, or compounding), it becomes a slightly cautious upper estimate. The simulation beside it plays out real sequences for a set number of trades, so it answers a slightly different and more practical question: what are the odds you hit the line within the next 500 trades?
A worked prop firm example
You are on a $100,000 evaluation with a 10% static max loss, so ruin is a $10,000 drawdown from the start. Your journal shows a 45% win rate, average winner +2R, average loser −1R: expectancy is +0.35R, a genuinely good strategy.
| Risk per trade | Units to ruin | Risk of ruin |
|---|---|---|
| 0.5% ($500) | 20 | about 0.1% |
| 1% ($1,000) | 10 | about 3.4% |
| 2% ($2,000) | 5 | about 18.5% |
Same trader, same setups, same skill. Going from 1% to 2% makes failure roughly five times more likely. Now suppose your live win rate turns out to be 40%, not 45%, which is a common gap between backtest and live. At 1% risk the risk of ruin climbs to about 14%. That is why the calculator shows a table across risk levels: it lets you pick a size that survives being wrong about your own edge.
What moves risk of ruin the most
- Risk per trade. It sets U, and U sits in the exponent. Small cuts in size make large cuts in ruin.
- Room to the ruin line. Same effect as risk per trade. A daily loss limit is a second, closer line, so check that too with the prop firm drawdown calculator.
- Edge. A higher expectancy raises λ. But edge is an estimate, and a small sample can overstate it.
- Sizing style. Compounding shrinks bets after losses. It usually lowers ruin when the edge is solid, though for very thin edges it can do the opposite.
Getting honest inputs
Use at least 50 to 100 trades of the strategy you will actually trade, with results net of costs. The win rate and R-multiple pages explain how to measure them properly, and the risk of ruin glossary entry has a second example. If you want to see the paths and drawdowns behind the probability, run the same numbers through the Monte Carlo trading simulator.
Measure your edge, then size it
The journal calculates your win rate, Avg Win R, Avg Loss R, max consecutive losses and a ½-Kelly ceiling from your own trades, which are exactly the inputs this calculator needs.
Start free, no cardFAQ
Frequently asked questions
What is risk of ruin in trading?
Risk of ruin is the probability that a strategy loses enough to reach a level you cannot or will not continue from, such as a blown account or a prop firm max loss. It depends on win rate, payoff, risk per trade and how far the ruin line is.
What is the risk of ruin formula?
For trades where wins and losses are the same size, risk of ruin = (q / p) to the power U, where p is the win rate, q is the loss rate and U is the number of losing trades between you and ruin. For uneven payoffs, this calculator solves p × e^(−λ × win) + q × e^(λ × loss) = 1 for λ and uses e^(−λ × U).
What is an acceptable risk of ruin?
That is a personal call, but many traders aim to keep it well under 1% for an account they cannot afford to lose. Because risk per trade sits in the exponent, the usual way to get there is to cut size rather than to find a better strategy.
Why do the formula and the simulation differ?
The formula gives the chance of ever reaching the ruin line with no time limit, and is a slightly cautious estimate when the last loss can overshoot the line. The simulation counts only runs that hit the line within the number of trades you set, so it can come out a little lower. It also carries sampling noise of a few tenths of a point, which shrinks as you add runs.