Risk of ruin: when a good idea runs out of capital.
A positive average outcome is not a safety guarantee. A losing sequence may force you to stop trading long before a strategy's theoretical advantage has time to work.
What are we really measuring?
Imagine having 100 units of trading capital. You choose a level below which you would be unwilling or unable to continue—say, 50 units. The question is not simply whether your final balance might be below 50. It is: what is the chance that your balance touches 50 at any time in the next 200 trades?
That probability depends on three big assumptions: how often you win, how much you gain on a winner relative to what you lose, and how much of your current capital you risk per trade.
Our calculator computes this probability for an idealised model. It does not estimate those three assumptions from real markets.
Why risk per trade changes everything
If you risk 1% of current equity, a loss multiplies equity by 0.99. Ten consecutive losses leave about 90.44% of the starting balance, before costs. At 10% risk per trade, ten consecutive losses leave only about 34.87%. The winning strategy and market are not even part of this comparison—just position sizing.
Risk is recalculated on whatever capital is left. This is different from wagering a fixed cash amount on every trade.
How can a positive edge still lead to ruin?
Suppose you win 45% of trades and gain 1.5R on every winner, while losing 1R otherwise. Your simple expected payoff per trade is 0.45 × 1.5 − 0.55 = +0.125R before costs. But winners and losers can arrive in an unfortunate order. A sufficient cluster of losses may hit your capital floor before the long-run average matters.
Also, a positive *arithmetic* expectation need not imply positive compound growth if each trade risks a large fraction of capital. This is one reason serious risk management focuses on survival, not only average return.
What does the calculator actually do?
Every winning trade multiplies your current balance by 1 + f × R; every loss multiplies it by 1 − f. Here f is your risk fraction and R your winner's payoff in risk units. For each trade count, a dynamic program keeps the probabilities of sequences that have not yet touched the threshold. Probability mass that crosses the threshold is removed and counted as ruined.
This is an exact finite-horizon result under the model assumptions, not a Monte Carlo estimate that varies with random seeds.
When should you distrust the result?
Real strategies rarely have a perfectly constant win probability or exactly two possible payoffs. A win/loss rate measured on a small sample may be unreliable; outcomes can be correlated; stop orders may slip or gap; losses can exceed the planned amount. Fees, funding and changing volatility can turn a seemingly positive strategy negative.
Our model also uses a floor relative to your starting equity. It does not compute probability of a peak-to-trough drawdown, forced liquidation or the chance of going completely to zero.
Use it to test the sensitivity of your assumptions, not as a forecast or permission to increase leverage.
How close is your capital floor?
Change the assumed win rate, reward/risk, risk per trade and horizon. Compare different numbers; notice how the risk changes even though no market price is involved.
Method & scope
Original educational article and independent calculation engine, version exact-absorbing-binomial-dp-v1. The example values are hypothetical, not measured from exchanges. Assumes independent binary trades with constant probabilities and payoffs, fraction-of-current-equity position sizing, and a fixed threshold relative to initial capital. No external market data was used.
For more practical tools, visit Position Size and Risk / Reward.