A strategy with a positive expectancy can still blow up an account if each trade risks too much. The reason is order: you don't get the average, you get a sequence, and a bad sequence at the start can end the account before the average matters. Risk of ruin is the probability that sequence ends at zero, or at a loss limit like a prop firm's maximum drawdown, before you reach a target.
The simple formula and its assumptions
For even-money bets with a fixed win probability p, fixed dollar risk, and independent outcomes, the chance of eventually losing a stake worth N bets is approximately ((1 minus p) divided by p) raised to the power N, where N is capital divided by risk per trade. This formula needs those conditions. Most trades aren't even money, risk isn't always constant, and results aren't independent in every market. Treat the formula as an illustration of how sensitive ruin is to size, not as a forecast for your account.
Hypothetical numbers: win rate 55 percent, 1:1 payoff, $25,000 account, fixed dollar risk, ruin means reaching zero.
| Risk per trade | Bets in capital (N) | Approximate ruin chance |
|---|---|---|
| 1% ($250) | 100 | about 0.0000002% |
| 2% ($500) | 50 | about 0.005% |
| 5% ($1,250) | 20 | about 1.8% |
| 10% ($2,500) | 10 | about 13% |
Doubling the dollar risk halves the number of full losses the account can absorb. The ruin probability changes exponentially with that bet count. But everything above depends on a true 55 percent win rate that you can't observe. If the real number is 50 percent, ruin isn't small at any of these sizes, and a few dozen trades can't distinguish 50 from 55.
Streaks and drawdown arithmetic
Your next step
Check the math before you size up.
Use your recorded win rate, average win and loss, and trading costs in the free edge calculator. Estimates are a starting point, not proof of an edge.
With a 50 percent win rate, the chance of five losses in a row from a given starting point is about 3.1 percent, seven is about 0.78 percent, and ten is about 0.1 percent. Over hundreds of trades, long streaks happen. A rough estimate of the longest loss streak in N trades with loss rate q is ln(N) divided by ln(1/q). For N equal to 200 and q equal to 0.45 that's about 5.3 divided by 0.80, or roughly 6 to 7. For 1,000 trades it's about 8 to 9. These are typical values, not ceilings, so size for a longer run than the estimate.
What a streak costs depends on size. Ten straight losses at 1 percent risk leave 0.99 to the tenth power, about 90.4 percent of the account, a 9.6 percent drawdown. At 10 percent risk, 0.9 to the tenth is about 34.9 percent, a 65 percent drawdown that needs about a 187 percent gain to recover. Percentage losses and gains are asymmetric. A 40 percent drawdown needs a 67 percent gain just to get back.
Prop evaluations: ruin is defined by the rules
For an evaluation, ruin is hitting the drawdown limit. Read the firm's actual rule documents, because some limits trail the account high, some are fixed, some count open profit, and they vary by product and account vintage. Suppose a hypothetical $4,500 limit and $250 risk per trade, which is 18 bets. With a 55 percent win rate on even-money trades and a target of $9,000, the gambler's-ruin formula with a target gives roughly a 2.7 percent chance of hitting the limit first. At $1,000 risk, you only have about 4 bets of room and the same math gives roughly 40 percent. These come from an idealized model. Consistency rules, daily limits and trailing drawdowns change them, so they're an illustration of why sizing matters, not an estimate of passing odds. A funded account isn't a live account, and a payout isn't guaranteed.
Why Kelly needs caution
The Kelly fraction is p minus (1 minus p) divided by the payoff ratio b. With a hypothetical 55 percent win rate and a 1.8 to 1 payoff, that is 0.55 minus 0.45 divided by 1.8, which is 0.30, or 30 percent of the account risked per trade. Expectancy in that example is 0.55 times 1.8 minus 0.45, or plus 0.54R per trade. Full Kelly assumes your win rate and payoff are exactly right and that you'll never deviate. Estimates from small samples are noisy, overestimating an edge by a little makes the sizing far too large, and drawdowns at full Kelly are severe. If you use Kelly at all, treat a fraction of it as a ceiling, not a target. Many traders risk far less because the sample behind their estimate is small.
When to simulate instead
If your wins and losses vary in size, if you scale in, if risk is set by volatility, or if the drawdown limit trails, the simple formula doesn't apply. Run a Monte Carlo simulation: sample trade results from your logged R multiples, apply your actual sizing rule and loss limit, run thousands of sequences, and count how many hit the limit. Use a range of win rates around your estimate to see how fragile the answer is. The edge calculator can help you compute expectancy from your own numbers first.
What to do with this
Don't increase size during a drawdown to recover faster, since that's when sizing matters most. Set size so a streak longer than the estimate leaves you able to keep trading. And remember a futures margin requirement is collateral, not a cap on loss, and a stop order can fill beyond its price, so real risk per trade can exceed the planned amount.
About the Author
Founder, Young Money Investments · Quant Trader
Cameron trades ES, NQ, and futures across multiple market cycles. He founded Young Money Investments to teach systematic, data-driven trading and manages Magnum Opus Capital. His work emphasizes documented rules, risk controls, and review over outcome promises.
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Educational Purposes Only: The content provided in this blog is for educational and informational purposes only. It does not constitute financial, investment, or trading advice. Young Money Investments is not a registered investment advisor, broker-dealer, or financial analyst.
Risk Warning: Trading futures, forex, stocks, and cryptocurrencies involves a substantial risk of loss and is not suitable for every investor. The valuation of futures, stocks, and options may fluctuate, and as a result, clients may lose more than their original investment.
CFTC Rule 4.41 - Hypothetical or Simulated Performance Results: Certain results (including backtests mentioned in these articles) are hypothetical. Hypothetical performance results have many inherent limitations. No representation is being made that any account will or is likely to achieve profits or losses similar to those shown. In fact, there are frequently sharp differences between hypothetical performance results and the actual results subsequently achieved by any particular trading program.
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