Risk of Ruin in Trading: The Maths of Blowing an Account
Risk of ruin is the chance your account hits a set loss before you reach your goal. See how risk per trade, win rate and reward-to-risk drive it.
Every trading method has losing runs, and every account has a level below which you would stop. Risk of ruin puts a number on the chance that the first reaches the second, and that number depends far more on how much you risk per trade than on how good your entries are.
Quick answer: Risk of ruin is the probability that your account falls to a set loss, such as half its starting value or a prop firm’s limit, before it reaches your goal. It rises with the share of the account you risk per trade and falls as your edge, set by win rate and reward-to-risk, grows.
What is risk of ruin in trading?
The idea comes from probability theory, where the “gambler’s ruin” problem asks how likely a player with a fixed bankroll is to lose it all before reaching a target. In trading, total loss is rarely the line that matters: you would stop long before the account reached zero, or the broker would close the positions for you. So ruin is usually defined as a loss they choose in advance and treat as the end of the method:
- A personal line, such as 50% of the starting balance, the point where the money needed to recover becomes unrealistic (a 50% loss needs a 100% gain to recover).
- A psychological line, such as 20% or 25%, the drawdown at which you know you would abandon the plan.
- A rule set by someone else, such as a prop firm’s maximum loss of 10% or a broker’s margin close-out.
Risk of ruin is then the chance of touching that line, usually within a stated number of trades or before reaching a goal, such as doubling the account. Both parts of the definition matter. A risk of ruin with no horizon and no goal mixes up “this method loses eventually” with “this method loses soon”, and the two lead to very different decisions.
Brokers draw their own version of the line. Under the product intervention measures that the European Securities and Markets Authority (ESMA) agreed in March 2018, providers in the EU must close a retail client’s CFD positions when the account’s margin falls to 50% of the minimum required. The same press release reported that 74–89% of retail CFD accounts typically lose money. National regulators, and the FCA in the UK, later made those rules permanent, so a leveraged account can be closed out well before its balance reaches zero.
What drives risk of ruin: win rate, reward-to-risk and risk per trade
Three inputs set the probability. Two of them describe the method, and one describes you.
Win rate is the share of trades that make money. Reward-to-risk is the size of the average win compared with the average loss, measured in R, where 1R is the amount you risk on a trade (see risk-reward ratio). Together they give the expectancy, the average result per trade:
Expectancy (R) = win rate × average win (R) − loss rate × average loss (R)A 45% win rate with wins of 1.5R and losses of 1R gives 0.45 × 1.5 − 0.55 × 1 = +0.125R a trade. A 40% win rate at the same 1.5:1 gives 0.60 − 0.60 = 0R, exactly the break-even win rate for that ratio, which is 1 ÷ (1 + 1.5) = 40%. Our guides to trading expectancy and the risk-reward ratio cover how to measure both from your own records.
Break-even win rate = 1 ÷ (1 + R), where R is the reward-to-risk ratio. Costs push the real figure a little higher.
Notice that the visualiser above shows the same 1.5:1 case (25 pips of risk, 37.5 pips of reward) and the same 40% break-even.
The third input is risk per trade, the share of the account you lose when a stop is hit. Expectancy decides which way the account drifts over many trades; risk per trade decides how far a run of bad luck can push it before the drift has time to show. That is why risk per trade dominates the result. A method with a real edge can still touch a ruin line if each loss takes a large slice, and a method with no edge survives longer, though not for ever, if each loss is small.
The count of straight losses needed to reach a line shows the effect. With risk set as a fixed share of the current balance, each loss takes the same percentage of a smaller amount, so the losses needed are ln(1 − line) ÷ ln(1 − risk), rounded up.
Seven losses in a row is likely at some point for a method that wins 45% of the time: the streak table further down gives an 85% chance of eight in a row within 500 trades. Sixty-nine in a row is not a realistic event. The ladder below shows the first ten losses at any risk level you choose.
For comparison: at 1% you keep 90%, at 5% you keep 60%, at 10% you keep 35%.
The account after each of ten losing trades in a row at the chosen risk. At 5% ten losses leave about 60% of the account; at 10% about 35%. Move the slider down to 1% and the same streak leaves about 90%.
The risk of ruin formula for even-money bets
The classic risk of ruin formula covers the simplest case: every bet wins or loses the same fixed stake, so the payoff is even money (1:1). Call the chance of a win p and of a loss q = 1 − p, and say the account holds N stakes before it is gone. If there is no profit target and you keep betting for ever:
Risk of ruin = (q ÷ p) ^ N when p is above 50%
Risk of ruin = 100% when p is 50% or belowThe second line is the uncomfortable one. With no edge, or a negative one, ruin is certain if you play long enough, however small the stake. With an edge, the risk falls very fast as N grows, because the ratio q ÷ p is below 1 and is raised to the power N. If you also stop at a profit target M stakes above the start, the formula becomes:
Risk of ruin = (r ^ N − r ^ (N + M)) ÷ (1 − r ^ (N + M)), where r = q ÷ pAt exactly 50% that reduces to M ÷ (N + M): with the target as far above you as the floor is below, it is a coin toss.
| Win rate (1:1 payoff) | Expectancy | 10 stakes (10% risk) | 20 stakes (5% risk) | 50 stakes (2% risk) |
|---|---|---|---|---|
| 50% | 0R | 100% | 100% | 100% |
| 52% | +0.04R | 44.9% | 20.2% | 1.8% |
| 55% | +0.10R | 13.4% | 1.8% | 0.004% |
The stake here is a fixed amount, a share of the starting balance, and ruin means losing all of it. A 55% win rate at even money, after costs, is a large edge in forex terms. Even then, staking a tenth of the account gives roughly a one-in-seven chance of losing everything.
The formula is exact for the game it describes, and trading departs from that game in at least five ways:
- Payoffs are rarely even money. A 1.5:1 or 2:1 method needs a different calculation.
- Risk is usually a share of the current balance, so stakes shrink after losses and grow after wins. In theory the account never reaches zero.
- Ruin is a set loss within a horizon, not a total loss after infinitely many bets.
- Costs, slippage and weekend gaps make some losses bigger than 1R.
- Real results cluster: a method that suits trending markets can lose many trades in a row when the market goes sideways.
There are closed-form approximations for uneven payoffs, but they get complicated quickly, and they still assume independent trades. A Monte Carlo simulation is simpler and more flexible: you generate thousands of possible trade sequences with the right win rate and payoff, apply your sizing rule, and count how many sequences touch the line. As a check, we ran our simulation on the even-money case first. For a 52% win rate with 10 stakes and a target of 10 more, the formula gives 31.0% and 20,000 simulated accounts gave 30.7%.
Risk of ruin table at 1%, 2%, 5% and 10% risk per trade
These are the assumptions behind the tables in this section, so you can repeat them:
- Three methods, all with wins of +1.5R and losses of −1R: no edge (40% win rate, 0R), thin edge (45%, +0.125R) and clearer edge (50%, +0.25R). The win rates and payoffs are after costs.
- Fixed-fractional sizing: each trade risks 1%, 2%, 5% or 10% of the current balance.
- 500 trades per account, roughly two years at five trades a week, with each trade independent of the last.
- Ruin means the balance touches the line at any point, even if it recovers later.
- 20,000 simulated accounts for each cell, generated in Python with NumPy and a fixed seed (2026), so the same code gives the same numbers. Re-running with other seeds moved the results by about half a percentage point.
Chance of touching −50% within 500 trades
| Risk per trade | No edge (40%, 0R) | Thin edge (45%, +0.125R) | Clearer edge (50%, +0.25R) |
|---|---|---|---|
| 1% | 1.3% | 0 of 20,000 | 0 of 20,000 |
| 2% | 27.4% | 0.5% | 0 of 20,000 |
| 5% | 79.2% | 18.3% | 1.8% |
| 10% | 97.0% | 56.7% | 18.0% |
Chance of touching −20% within 500 trades
| Risk per trade | No edge (40%, 0R) | Thin edge (45%, +0.125R) | Clearer edge (50%, +0.25R) |
|---|---|---|---|
| 1% | 44.9% | 2.8% | 0.1% |
| 2% | 74.3% | 18.5% | 2.9% |
| 5% | 94.1% | 55.9% | 25.0% |
| 10% | 99.1% | 80.7% | 51.5% |
Three patterns stand out. First, the jump from 2% to 5% is where the thin-edge method goes from almost safe to a one-in-five chance of halving the account. Second, the clearer edge does not protect a trader who risks 10%: nearly one account in five still touches −50%. Third, the 1.3% for the no-edge method at 1% risk is a product of the horizon. Over 1,000 trades the same simulation gives 9.8%, over 2,000 trades 28%, and over 5,000 trades 57%, so the small size delays the line without moving the method away from it.
Prop firm challenges give a different shape of ruin. We ran the same three methods against a static floor 10% below the start and a target 10% above it, with risk measured from the starting balance, as challenges usually measure it, and no daily limit.
| Risk per trade | No edge: floor first | Thin edge: floor first | Clearer edge: floor first |
|---|---|---|---|
| 0.5% | 43.1% (13.4% still open at 500 trades) | 3.4% | 0.1% |
| 1% | 50.3% | 15.8% | 3.4% |
| 2% | 51.0% | 30.5% | 15.9% |
| 5% | 53.7% | 44.4% | 36.0% |
With no edge the result is close to a coin toss at any size, as the even-money formula predicts when the floor and target are the same distance away. With an edge, cutting the size is what cuts the chance of failing. Our guide to the prop firm challenge adds the daily loss limit and fees to the same maths.
The simulator below runs 100 trades at a time on the thin-edge settings. Run it several times and watch the worst drawdown change from run to run.
Each run uses the same settings with different luck. Run it several times: the shape changes, the drawdowns don't go away.
Losing streak probabilities
A losing streak is the event that turns a small risk per trade into a deep drawdown, so it is worth knowing how long a streak your win rate makes likely. The table gives the exact chance of at least one run of losses of a given length, assuming each trade is independent. We calculated it directly rather than by simulation.
| Win rate | 6 in a row within 100 trades | 8 in a row within 100 trades | 8 in a row within 500 trades | 10 in a row within 500 trades | 12 in a row within 500 trades |
|---|---|---|---|---|---|
| 40% | 87.3% | 49.0% | 97.1% | 70.5% | 35.1% |
| 45% | 72.9% | 30.7% | 85.4% | 43.3% | 15.6% |
| 50% | 54.6% | 17.0% | 62.5% | 21.5% | 5.8% |
| 60% | 21.2% | 3.6% | 17.7% | 3.0% | 0.5% |
At a 45% win rate, a run of ten losses somewhere in 500 trades is close to an even bet (43.3%). At 5% risk, ten losses take 40% off the account; at 1%, they take about 9.6%.
Two cautions go with the table. Real trades are not perfectly independent: a breakout method can lose many times in a row during a quiet range, so treat these figures as a floor, not a ceiling. And streaks feel longer than they are, because they arrive without warning. Our guide to the losing streak in trading covers how to tell an ordinary run from a broken method, and the Academy lesson on dealing with losing streaks covers the habits that keep you on the plan.
The recovery maths of drawdowns
A drawdown is the fall from the account’s highest point to its current value. Ruin lines are usually set as a drawdown from the start or from the peak, and the reason to set them early is that recovery is not symmetrical. After a loss of L, the gain needed to get back is L ÷ (1 − L).
| Loss | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25.0% |
| 30% | 42.9% |
| 50% | 100% |
| 75% | 300% |
| 90% | 900% |
The gain needed to recover from each loss. Up to about 20% the two are close; beyond 50% the required gain climbs steeply, which is why most ruin lines sit at or before −50%.
Fixed-fractional sizing makes recovery slower still, because after a fall the same percentage risk is a smaller amount of money. Take the thin-edge method at 2% risk. Its typical (median) growth works out at about 0.22% a trade, so getting back from −50% to the start takes about 320 trades at that pace: at four trades a week, around 18 months. At 1% risk the same method grows about 0.12% a trade at the median and needs about 190 trades to recover from −20%. Those are averages from the simulation’s settings, not a forecast for any real account, and a method with no edge has no recovery pace at all.
In practice, then, an account is ruined long before it is empty: it reaches a depth from which the method cannot climb back in a time you would accept. Our guide to drawdown in trading sets out rules for what to do at −5%, −10% and −20%, and the Academy lesson on the maths of drawdowns has a quiz on the recovery table.
How to use risk of ruin in a trading plan
To put risk of ruin into your plan, work in this order: fix the line, measure the method, then choose the size.
- Set the ruin line. Pick the loss at which you would stop trading the method and review it from scratch. For a personal account we suggest somewhere between −20% and −30%; for a challenge it is the firm’s floor.
- Measure the edge after costs. Use at least 100 trades from a backtest, a demo or a live record, net of spread and commission. Fewer trades leave the win rate too uncertain to rely on, as our guide to how to backtest a strategy explains.
- Pick the risk per trade. Find the level in the tables, or in your own simulation, where the chance of touching your line over the next 500 trades is small. We suggest under 5%. If your measured edge sits between two rows, use the weaker one.
- Write step-down rules. Cutting risk after a drawdown lowers the chance of reaching the line, because the last part of the fall happens at a smaller size. One simple form is to halve the risk at −10% and restore it after recovering to −5%.
- Re-check as the record grows. Every 100 trades, recompute the win rate and R and see whether the size still fits.
Then turn the percentage into a lot size for each trade. The calculator does this from your balance, risk and stop distance; our guide to position sizing in forex covers yen and cross pairs.
The Academy lesson on risk per trade shows the same choice for three traders on one setup, and the lesson on writing a one-page trading plan gives you a place to record the line and the step-down rule. Our guide to the 1% rule explains when 0.5% is the better default.
Common risk of ruin mistakes
Using the win rate you hope for
A risk of ruin figure is only as good as its inputs. A backtest without costs, or 30 trades from a good month, can make a no-edge method look like a thin edge, and the two rows in the tables are far apart. Use a measured, after-cost record and the weaker of two plausible estimates.
Thinking a small risk per trade makes ruin impossible
At 1% risk the no-edge method touches −50% in 1.3% of accounts over 500 trades and 57% over 5,000. Small sizing slows the decline. Only a positive edge changes its direction.
Raising the size to win back a drawdown
Doubling the risk after losses moves you down the tables at the worst moment. The step-down rule exists to do the opposite. Doubling the stake after each loss, the martingale method, is the same mistake built into a system.
Ignoring correlated positions
Three trades on EUR/USD, GBP/USD and AUD/USD at 1% each can behave like one 3% trade when the dollar moves. Count the total open risk, not just the risk per ticket.
Treating the tables as a forecast
The simulation assumes independent trades, fixed payoffs and no gaps. Real markets break all three at times. Treat the numbers as a lower bound on the danger and keep a margin below your line.
Frequently asked questions
What is risk of ruin in trading?
Risk of ruin is the probability that your account falls to a loss you have defined as the end of the method, such as 50% of the starting balance or a prop firm's 10% floor, before it reaches a goal or within a set number of trades. It depends on your win rate, your reward-to-risk and, above all, how much of the account you risk on each trade.
How do you calculate risk of ruin?
For even-money bets with a fixed stake, the risk of losing N stakes is (q ÷ p) to the power N, where p is the win chance and q the loss chance, provided p is above 50%. Trading has uneven payoffs, percentage sizing, costs and a set horizon, so a Monte Carlo simulation of thousands of trade sequences is the practical method.
What is an acceptable risk of ruin?
There is no official figure. As our own suggestion, keep the chance of touching the drawdown that would make you stop under about 5% over the next 500 trades, and the chance of losing half the account close to zero. In our simulation, a 45% win rate at 1.5:1 met both at 1% risk per trade but not at 2%.
Does risking 1% per trade prevent blowing an account?
It makes a fast collapse very unlikely, because it takes 69 straight losses to halve the account. It does not protect a method with no edge: in our simulation a break-even method at 1% touched −50% in 1.3% of accounts over 500 trades, but in 57% over 5,000. Small risk buys time to find out whether the edge is real.
How many losing trades in a row are normal?
It depends on the win rate and the number of trades. Within 500 independent trades at a 45% win rate, there is an 85% chance of at least eight losses in a row and a 43% chance of ten. At 50% the figures are 62.5% and 21.5%. Size your trades so that a run of that length costs a share of the account you can accept.
Is risk of ruin the same as maximum drawdown?
No. Maximum drawdown is the largest fall that actually happened in a record or a simulation. Risk of ruin is a probability: how likely the account is to fall past a line you chose. A method can have a modest past maximum drawdown and still carry a high risk of ruin if its size per trade is large.
Free course
Learn this step by step
“Risk & Money Management” is a free BrokerCut Academy course: 7 short lessons (about 59 minutes), quizzes, interactive tools and a certificate when you finish.
Enrol free
