Risk of Ruin in Trading: Formula, Assumptions and Limits

Risk of ruin trading: Risk of ruin depends on the loss threshold, horizon, sizing rule and assumed return process.

What Is Risk of Ruin in Trading?

Risk of ruin is the probability that a trading account falls to a loss threshold you define as ruin, such as losing half of starting equity, before it recovers. It is the output of a model, not a measurement: it depends on a win probability, the size of wins and losses, how much you risk per trade and how many trades you take, and every one of those inputs is an estimate from past results. Used carefully, it shows how quickly position size can turn an ordinary losing streak into a decision to stop trading. Used carelessly, it produces precise-looking numbers that the data cannot support.

Key Takeaways

• With equal-sized wins and losses, ruin has a closed form. If the win probability is p, the loss probability is q = 1 - p and you can lose N units, the chance of ever losing all of them is (q ÷ p)^N when p is above 50%, and 100% when p is 50% or lower.
• No edge means ruin is only a matter of time. In a simulated zero-edge example risking 1% per trade, 3.8% of paths touched a 50% loss within 1,000 trades, while the long-run answer for a strategy with no edge is 100%.
• Position size dominates. In the simulated examples below, the same hypothetical strategy (40% winners, 2R payoff) went from under 0.1% to about 48% chance of a 50% loss when risk per trade moved from 1% to 10%.
• Your inputs are uncertain. A 40-trade log with 24 winners is consistent with a true win rate anywhere from about 45% to 74%. That range includes cases where the formula says ruin is certain and cases where it is negligible.
• Losing streaks are normal. With a 55% win rate, there is roughly a 17% chance of at least one run of 10 consecutive losses within 1,000 trades.

The Gambler's Ruin Formula for Equal Wins and Losses

The classic result comes from probability theory. In Grinstead and Snell's Introduction to Probability, section on gambler's ruin, a gambler starts with z units, wins one unit with probability p and loses one unit with probability q = 1 - p on each independent game, and plays against an infinitely rich opponent. The probability of eventually being ruined is (q ÷ p)^z when q is below p, and 1 when q is at least p.

Mapped to trading, the assumptions are strong:

• Every trade wins exactly 1 unit or loses exactly 1 unit, a unit being a fixed dollar amount of risk.
• Trades are independent and have the same win probability.
• Ruin means losing all N units, where N is your cushion divided by the dollars risked per trade.
• There is no time limit, so given enough trades even small probabilities accumulate.

Under those assumptions the table gives the probability of ever losing the whole cushion. The numbers are calculated from the formula, not observed results.

Hypothetical worked example. A $20,000 account where ruin is defined as falling to $10,000 has a $10,000 cushion. Risking $1,000 per trade gives N = 10 units, and a 55% win rate gives (0.45 ÷ 0.55)^10 ≈ 13.4%. Risking $500 gives N = 20 and about 1.8%. Risking $200 gives N = 50 and about 0.004%. The win rate did not change; only the size did.

Unequal Wins and Losses: Simulate, Do Not Guess

Real strategies rarely win and lose the same amount. With unequal payoffs and risk set as a percentage of current equity, there is no simple formula that is exact, so practitioners simulate. The table shows the share of 200,000 simulated 1,000-trade sequences in which equity touched 50% of its starting value. Each trade risks the stated fraction of current equity, a loss costs exactly that fraction, and a win pays the stated multiple of it. Trades are independent. The numbers come from the short script below and are illustrations of the method, not results of any strategy.

import numpy as np

def touch_probability(p_win, win_r, risk, trades=1000, paths=200_000, floor=0.5, seed=7):
    rng = np.random.default_rng(seed)
    equity = np.ones(paths)
    touched = np.zeros(paths, dtype=bool)
    for _ in range(trades):
        win = rng.random(paths) < p_win
        equity *= np.where(win, 1 + risk * win_r, 1 - risk)
        touched |= equity <= floor
    return touched.mean()

Three things are visible. First, the strategy with a positive expectancy of +0.2R per trade goes from effectively safe to a coin flip as size increases tenfold. Second, a strategy with no edge can look safe for a while: 3.8% over 1,000 trades at 1% risk is not the 100% the long-run formula gives. Third, a negative edge is ruinous even at small size, only more slowly. For how to compute the +0.2R in the first row, see the expectancy formula guide.

Losing Streaks Are Normal

A string of losses is the mechanism behind ruin, so it helps to know how common long streaks are. If trades are independent, the probability of at least one run of k or more consecutive losses within 1,000 trades is:

A 40% win-rate strategy that is perfectly healthy will usually produce a 10-trade losing run in 1,000 trades. If your size would not survive that run in the plan you wrote down, the size is the problem, not bad luck. Independence is an assumption: losses cluster when market conditions change, so real streaks can be longer or more frequent than this table.

Your Inputs Are Estimates

Every table above takes the true win rate and payoff as known. You only have a trade log. Take the hypothetical case of 24 winners in 40 trades (60%). As shown in the sample-size guide, the 95% interval for the true win rate is about 44.6% to 73.7%. In the equal-payoff model with N = 20:

• At a true win rate of 44.6%, ruin is certain (the win rate is below 50%).
• At 60%, ruin probability is about 0.03%.
• At 73.7%, it is effectively zero.

The same log supports "certain ruin" and "negligible ruin". The formula is not wrong, but its precision is not available to you. That is the reason to stress-test sizes against a lower, pessimistic estimate of the edge, rather than the single best estimate, and to wait for more trades before sizing up.

Common Formula Variants and a Caution

Many calculators write the result as ((1 - A) ÷ (1 + A))^N, where A is described as the trader's edge. That expression equals (q ÷ p)^N exactly when A = p - q, the win probability minus the loss probability, and wins and losses are the same size. With unequal payoffs it is an approximation, and depending on how a tool defines edge it can be materially off. Check what a calculator means by edge, what it assumes about payoffs, and what it counts as ruin before trusting the output.

What Risk of Ruin Cannot Tell You

• Gaps and slippage. A stop is a plan, not a guaranteed exit price. A loss larger than 1R is not in the model.
• Correlation. Several open positions that move together behave like one larger bet.
• Changing edge. Markets change. An edge estimated in one regime may not exist in the next.
• Costs. Spreads, fees and slippage reduce every win and enlarge every loss.
• Behavior. A plan you abandon after a streak is a different plan. Many traders reduce or stop trading well before the mathematical threshold.
• The threshold itself. Ruin might be a 20% drawdown for a trader with a hard personal limit, or a broker's minimum balance. The same strategy has a different risk of ruin for each definition.

Ways Traders Reduce Exposure to Ruin

This is a list of general ideas for study, not advice about your account:

1. Make risk per trade smaller. The tables show size has the strongest effect.
2. Limit total open risk. Portfolio heat caps the sum of risk across positions so correlated losses do not stack.
3. Set loss limits in advance. A daily loss limit and a drawdown rule stop a bad run from becoming a larger one. The maximum drawdown guide covers measuring and setting these.
4. Use a pessimistic estimate of edge. Plan with the lower end of your interval, not the average.
5. Review fractional sizing. Kelly sizing is sensitive to estimation error, and fractions of it are often used for that reason.
6. Measure realized results. Keep a trading journal of planned and realized R so the inputs improve.

The position sizing guide and advanced position sizing strategies go deeper on methods.

Using This With Paper-Tracked Signals

You can use paper tracking to test whether your sizing rules would have survived a realistic streak. Tradewink is a research and signals app: each signal lists an entry, stop, target and thesis, so you can write down the dollars risked before the outcome and record the realized R after. Run the streak and ruin arithmetic on that log, and compare it with the plan you wrote. Tradewink is not a broker and not a registered investment adviser, and a signal's confidence score is a ranking aid, not a win probability. Public subscriptions are paper-only; separately approved private beta accounts may submit live broker orders. Create a free account to paper-track signals and keep the log.

Risk of ruin trading: practical checks

State whether ruin means zero capital, a drawdown boundary or insufficient margin. Independent equal-payoff formulas are special cases; changing position size, dependence or payoff tails changes the calculation.

Read the Bailey et al., The Probability of Backtest Overfitting for the underlying definitions and limits. For a next step, use Block Bootstrap Backtests: Test Block-Length Sensitivity and Position Sizing: Risk Budget, ATR and Kelly Examples.

Frequently Asked Questions

What is a good risk of ruin?

There is no universal threshold. It depends on how you define ruin, how accurate your inputs are, and how much loss you can tolerate. Zero is not achievable, and an estimate based on a short trade log has a very wide margin of error. Compare scenarios, including a pessimistic edge, rather than trusting a single number.

Can a profitable strategy still lead to ruin?

Yes. A strategy with a positive expectancy can still ruin an account if size is too large for the variability of results, if the real edge is smaller than the estimate, or if costs, gaps or correlated positions add losses the model did not include. The simulated 40% win rate, 2R example reached a 50% loss in about 48% of sequences at 10% risk per trade.

How do I calculate risk of ruin for my own trading?

Define ruin as a specific loss level, estimate win rate and average win and loss after costs from a log with enough trades, then either use the gambler's ruin formula (for roughly equal-sized wins and losses) or simulate your actual distribution of R-multiples at your intended size. Run the calculation at the pessimistic end of your estimated edge as well as the center.

Is risk of ruin the same as maximum drawdown?

No. Maximum drawdown is a measured historical peak-to-trough decline. Risk of ruin is the modeled probability of reaching a defined loss threshold in future. A past drawdown informs the inputs but is not the same quantity. See the maximum drawdown guide.

Does the 1% rule make ruin impossible?

No. A 1% budget limits the planned loss on one trade, not the probability of a long run of losses, and gaps or slippage can exceed the plan. If each loss is exactly 1% of remaining equity, 69 consecutive losses leave about 49.98% of starting equity (0.99^69). Fewer losses mixed with small wins can reach similar levels, and the model excludes costs.

Why do some online risk of ruin tables disagree?

Different tools assume different payoffs, define edge differently, use different ruin thresholds and may be approximations. Some are exact only for equal-sized wins and losses. Always check the assumptions behind a number before comparing it with another.

Risk Disclaimer

Trading involves substantial risk of loss and is not suitable for everyone. This article is educational and is not investment advice. All numbers marked hypothetical or simulated are illustrations, not results or forecasts. Tradewink is not a broker and not a registered investment adviser. Signal confidence is not a win probability. Simulated results don't guarantee future results.