A profitable strategy can still breach an account’s loss limit. Risk of ruin estimates the probability of that happening under a defined set of assumptions. Here’s how win rate, payoff size and position sizing affect the calculation, and why prop firm rules require more than a simple formula.
The useful question is not just “Does my strategy make money on average?” It is also “Can my account survive the losses that may come first?”
Key Takeaways
- Define ruin before calculating it: a fixed account floor, a daily loss limit and a trailing drawdown are different boundaries.
- The classical formula assumes independent trades, fixed monetary wins and losses, and an unlimited trading horizon.
- Lower risk per trade can sharply reduce breach probability, but there is no universal reduction factor.
- A larger average win lowers the breakeven win rate, provided the measured results include costs.
- A model estimate is not a guarantee. The payoff distribution, trade dependence and account rules affect the result.
What Is Risk of Ruin?
Risk of ruin is the probability of reaching a specified loss boundary within a chosen trading horizon. Some calculations cover the next 100 trades; others ask whether the account ever reaches that boundary if trading continues indefinitely.
Ruin does not have to mean losing the whole account. It might mean falling to a fixed equity floor, breaching a prop firm’s rules or reaching a personal stopping point.
For example, a hypothetical $100,000 account with a fixed floor at $90,000 has a $10,000 buffer at the outset. Risking a fixed $1,000 per trade puts ten loss-sized units between the starting balance and that floor. The probability of using up that buffer depends on the trade outcomes and how long trading continues.
This example uses a static floor, not a limit that moves with the account’s highest equity.
The Risk of Ruin Formula
A classical result gives the probability of eventually reaching a fixed floor when each trade wins or loses the same fixed amount. Karl Sigman’s Columbia University probability notes derive the equal-step model and its unlimited-horizon result.
Use the formula only under these assumptions:
- Each trade wins exactly +1R or loses exactly -1R, measured after costs.
- R is a fixed monetary amount, not a percentage recalculated from changing equity.
- Outcomes are independent, and the win probability stays constant.
- The loss boundary stays fixed. Profits remain in the account, with no withdrawals or deposits.
- Trading continues without a time limit or profit target.
- The starting distance to the boundary is a whole number of risk units in the examples below.
| Symbol | Meaning |
|---|---|
| p | Probability of a winning trade |
| q | Probability of a losing trade: 1 – p |
| R | Fixed monetary gain or loss per trade |
| N | Starting distance to the fixed loss boundary, divided by R |
Eventual risk of ruin = (q / p)^N, when p > 0.5
Eventual risk of ruin = 100%, when p <= 0.5Equal average wins and losses are not enough to make this exact. A strategy with variable outcomes can have those same averages and a different probability of ruin.
Likewise, the 100% result applies to continued trading indefinitely under the stated model. It does not mean every finite sample ends in failure.
Equal-Payoff Example: Why the Horizon Matters
Return to the hypothetical $100,000 account, its fixed $90,000 floor and a fixed $1,000 win or loss on each trade. Here, N = $10,000 / $1,000 = 10.
At a 55% win rate:
p = 0.55
q = 0.45
N = 10
Eventual risk of ruin = (0.45 / 0.55)^10
= approximately 13.44%The same model produces these results:
| Win rate | Eventual fixed-floor breach probability |
|---|---|
| 40% | 100% |
| 45% | 100% |
| 50% | 100% |
| 55% | 13.44% |
| 60% | 1.73% |
These are unlimited-horizon probabilities, not estimates for a month or a challenge attempt. At a 50% win rate, for example, the probability of reaching the same floor within 100 trades is approximately 31.97%, not 100%.
Smaller positions do not create an edge. However, they can reduce the probability of crossing a boundary within a finite trading period, including when the strategy has no positive expectancy.
Unequal Payoffs: Risk of Ruin Over 100 Trades
What changes when a winning trade earns more than a losing trade costs?
For this comparison, keep the fixed $1,000 loss and the $10,000 starting buffer. Change only the win probability and the size of each winning outcome. Every loss is exactly -1R, and every win pays the fixed amount shown in its column, after costs.
Unlike the previous table, this table measures breach within 100 trades. The floor stays fixed, profits remain in the account and there is no profit target. Trades are independent, with unchanged probabilities throughout.
| Win rate | Win +1R | Win +1.5R | Win +2R | Win +3R |
|---|---|---|---|---|
| 35% | 99.20% | 75.52% | 36.46% | 8.02% |
| 40% | 91.98% | 40.58% | 12.50% | 2.49% |
| 45% | 67.25% | 13.87% | 3.35% | 0.76% |
| 50% | 31.97% | 3.29% | 0.81% | 0.23% |
We calculated these illustrative probabilities by tracking the probability of each surviving account balance after every trade. Any path touching or crossing the floor is counted as ruined. This handles boundary crossings directly rather than treating a single root formula as exact for every payoff size.
The calculation is deterministic, not a random simulation. Results are rounded to two decimal places; their precision describes this simplified model, not confidence in a live strategy.
The Breakeven Win Rate
If the average loss is 1R and the average win is bR, expectancy reaches zero when:
Breakeven win rate = 1 / (1 + b)| Average win, with a 1R average loss | Breakeven win rate |
|---|---|
| 1R | 50.00% |
| 1.5R | 40.00% |
| 2R | 33.33% |
| 2.5R | 28.57% |
| 3R | 25.00% |
These thresholds assume the averages include trading costs. A 2R win against a 1R loss is a reward-to-risk ratio of 2:1, or a risk-to-reward ratio of 1:2.
The threshold tells you where trading expectancy crosses zero. It does not establish a safe position size. In the 100-trade table, a 35% win rate with +2R wins has positive expectancy but still carries a 36.46% fixed-floor breach probability.
Increasing a planned profit target does not automatically improve the strategy. A more distant target may reduce the win rate. Our risk-reward ratio guide explains the difference between planned targets and realised results.
How Position Size Changes Risk of Ruin
Position size is a decision you can make before entering a trade. To isolate its effect, return to the equal-payoff model with a 55% win rate and an unlimited horizon.
Keep the starting account at $100,000 and the fixed floor at $90,000. Each row uses a different fixed monetary stake for both wins and losses. The percentage is based on the initial account size, not current equity.
| Risk per trade, as % of initial capital | Fixed monetary risk | Risk units N | Eventual breach probability |
|---|---|---|---|
| 2.0% | $2,000 | 5 | 36.66% |
| 1.0% | $1,000 | 10 | 13.44% |
| 0.5% | $500 | 20 | 1.81% |
| 0.25% | $250 | 40 | 0.03% |
Halving the stake from $1,000 to $500 reduces the modelled probability from 13.44% to 1.81%. That is a roughly 7.4-fold reduction, not a universal tenfold rule.
Under this particular formula, halving the stake doubles N and squares the original probability. A 20% estimate would become 4%; an 80% estimate would become 64%. The size of the improvement depends on where you start.
These are sensitivity examples, not recommended trading sizes. Our guide to position sizing for prop firms connects risk per trade with account limits and remaining drawdown room.
What the Formula Cannot Tell You
The classical formula is a useful baseline. It is not a complete model of a funded-account challenge.
Daily resets and trailing limits. A daily loss limit resets according to account rules. A trailing floor moves as equity or balance changes. Neither behaves like the fixed floor used in these tables.
Profit targets and stopping points. A challenge can end when a trader reaches its target. The relevant question is then whether the loss boundary is reached before that target or before a chosen deadline.
Changing stakes and variable outcomes. Risking a fixed percentage of current equity changes the monetary stake after each trade. Partial exits, large losses and variable winners also change the distribution. Average win and loss alone do not describe it.
Costs, gaps and open positions. Actual losses can exceed planned stop risk. An equity-based rule can be breached during a trade even if the eventual closing result looks acceptable.
Dependence and uncertain inputs. Losing trades can cluster, and several open positions can share the same exposure. A historical win rate is an estimate, not a permanent property of the strategy.
For these situations, use a model that represents the actual rules and trade behaviour. Simulation can help, but randomly shuffling individual trades does not preserve loss clustering. Stress scenarios or resampling blocks of related trades can expose risks that independent-trade assumptions miss.
Why Positive Expectancy Does Not Guarantee a Pass
At a 35% win rate, the probability of at least one run of eight consecutive losses within 100 independent trades is approximately 68.96%. That is a losing-streak probability, not an account-breach probability.
Whether those losses end the account depends on the equity at the time, risk per trade and applicable boundaries. Breaches can also arise from mixed sequences of wins and losses, not just uninterrupted losing streaks.
The practical lesson is to test the path as well as the average. A strategy can have positive expectancy and still be poorly sized for the account rules.
Risk of Ruin, Drawdown and Expectancy
| Measure | Question it answers | Important limitation |
|---|---|---|
| Trading expectancy | What is the expected result per trade? | Does not describe the full path or probability of crossing a boundary |
| Historical maximum drawdown | What was the largest peak-to-trough decline in this sample? | A future decline can be larger; simulated future drawdowns can also be modelled |
| Risk of ruin | How likely is a specified loss boundary to be reached over a stated horizon? | Depends on the boundary, sizing policy, outcome model and input estimates |
None replaces the others. Expectancy helps assess an edge, drawdown describes declines along a path, and ruin modelling tests a particular stopping boundary.
A Practical Risk-Testing Workflow
- Define the breach rule. Record the equity or balance boundary, reset times, trailing behaviour and whether touching the limit counts as a breach.
- Measure outcomes after costs. Keep the full distribution of wins and losses, not just their averages. Separate materially different setups.
- Choose the horizon and stopping conditions. Decide whether you are testing the next 100 trades, a calendar period or reaching a target before a loss limit.
- Compare sizing policies. Distinguish fixed monetary risk from a percentage of current equity. Include overlapping exposure where relevant.
- Stress-test the estimates. Lower the win rate, reduce typical wins, increase costs and introduce clustered losses or gaps. Look for results that depend on overly favourable assumptions.
- Recheck as evidence changes. Monitor whether live outcomes still resemble the data used in the model. A calculation built on an outdated edge can give false confidence.
This extends the process in our guide to finding and validating a trading edge. Risk modelling is one part of validation, not a substitute for it.
Frequently Asked Questions
What is risk of ruin in trading?
Risk of ruin is the probability of reaching a defined loss boundary within a chosen trading horizon. It depends on the trade-outcome distribution, sizing policy and account rules. The boundary need not be a zero balance.
How do you calculate risk of ruin?
For independent trades with fixed equal-sized wins and losses, a fixed floor and an unlimited horizon, use (q/p)^N when the win probability p exceeds 50%. Here q = 1 – p and N is a whole-number starting distance to the floor in risk units. Other models may require a probability recurrence or simulation.
Is ruin certain at a 50% win rate?
In the unlimited-horizon, fixed-stake, equal-payoff model, yes. That does not mean failure is certain over a finite number of trades. It also does not apply automatically to strategies with unequal payoffs, changing stakes or a profit-target stopping rule.
What is a good risk of ruin?
There is no universal acceptable percentage. First specify the loss boundary, horizon and model assumptions. Then consider the consequences of breaching the account and how the estimate changes under less favourable inputs. A low result from an unsuitable model is not evidence of safety.
Can positive expectancy coexist with high risk of ruin?
Yes. A positive average result does not prevent losses from reaching an account boundary first. Position size, the sequence of outcomes and the account’s rules determine whether that edge has room to operate.
Can a risk of ruin calculator predict a prop firm breach?
It can estimate probability under its assumptions, not predict a particular account’s outcome. Check whether it models daily resets, trailing drawdown, open equity, profit targets and the way you size trades. A generic fixed-floor calculator does not automatically account for those features.
Put the Account Rules Into the Calculation
A useful risk estimate starts with the boundary you actually trade against. Before choosing a ThinkCapital programme, review its loss limits, payout conditions and trading rules. Then test your strategy against those conditions rather than relying on a generic percentage.
Explore ThinkCapital’s programme rules and FAQs
Disclaimer
CFDs are complex instruments and come with a high risk of losing money rapidly due to leverage. You should consider whether you understand how CFDs work and whether you can afford to take the high risk of losing your money. Past performance and backtested or simulated results do not indicate future results.
This article provides general education about trading risk measurement. It does not constitute investment advice, a trade recommendation, or a solicitation. All figures shown are illustrative model calculations, not representations of achievable results or any specific trader’s outcome. ThinkCapital offers access to funded accounts in a simulated trading environment. The examples do not recommend a particular strategy or position size.
