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Risk of Ruin Calculator

Probability your account ever hits a ruin-level drawdown, from win rate, payoff ratio, and risk % per trade.

Risk of Ruin

Live tool
1.9e-8%risk of ruinodds of ever hitting a 50% drawdown
Edge per trade (expectancy)0.25 R
Per-trade standard deviation1.25 R
1R losing steps to ruin68.97
Survival odds100.00%
Ruin equity level$12,500

Model: fixed-fractional, binary-outcome gambler’s-ruin approximation — the probability of ever hitting the threshold over unlimited trades. Assumptions and limits below.

How it works

Risk of ruin is the probability that your account ever falls to a drawdown level — the “ruin threshold” — from which you realistically cannot or will not continue. This calculator takes your win rate, your payoff ratio (average win ÷ average loss), and the percent of current equity you risk per trade, and estimates the odds of ever hitting that threshold. Because fixed-fractional sizing compounds, it first works out how many consecutive 1R losses it actually takes to reach the drawdown (more than the naive “threshold ÷ risk” count), then maps your unequal-payoff system onto an equivalent even-money coin-flip game and applies the classic gambler’s-ruin probability. Risk of ruin falls exponentially as risk per trade shrinks — which is why position sizing, not win rate alone, dominates long-run survival.

This tool uses the classic fixed-fractional, binary-outcome risk-of-ruin model — a gambler’s-ruin approximation on a normalized random walk. Its assumptions:

  • Binary outcomes — every trade either wins exactly payoffRatio × R or loses exactly 1R, where 1R is the amount risked on that trade; real trade distributions vary and are fat-tailed, so real ruin risk is typically higher than this estimate.
  • Constant risk % — the same fraction of current equity is risked on every trade, forever; no sizing down in drawdowns, no stopping.
  • Independence — trades are independent and identically distributed: no streak effects, no correlated positions, no edge decay.
  • Infinite horizon — this is the probability of ever hitting the ruin threshold over an unlimited number of trades; risk over any finite number of trades is lower.

The result is an approximation for reasoning about sizing, not a prediction.

The formula

Inputs are converted to decimals first: p = winRate ÷ 100 (win probability), q = 1 − p (loss probability), f = riskPct ÷ 100 (fraction of equity risked per trade), d = ruinThreshold ÷ 100 (ruin drawdown), and b = payoffRatio (already a plain ratio).

  1. Edge per trade: μ = p × b − q. The expected number of R-multiples gained per trade equals the win probability times the payoff ratio, minus the loss probability. If μ ≤ 0, ruin is certain (see below).
  2. Per-trade standard deviation: σ = (b + 1) × √(p × q). For a bet that either gains b R or loses 1 R, the standard deviation equals the gap between the two outcomes (b + 1) times √(p × q). This step is exact for binary outcomes, not itself an approximation.
  3. Loss units to ruin: U = ln(1 − d) ÷ ln(1 − f). Because fixed-fractional sizing compounds, losing a fraction f of equity U times in a row leaves (1 − f)U of equity; U solves (1 − f)U = 1 − d. A naive U = ruinThreshold ÷ riskPct ignores compounding and understates the units.
  4. Normalization: A = μ ÷ σ (the edge per trade in standard deviations) and n = U ÷ σ (the ruin distance in standard-deviation-sized steps). The unequal-payoff game is mapped onto an equivalent even-money coin-flip game matching its mean and variance — this mapping is the approximating step, accurate when riskPct is small and A is well below 1.
  5. Risk of ruin: RoR = ((1 − A) ÷ (1 + A))n, valid when 0 < A < 1 — the classic gambler’s-ruin probability that an even-money game with per-step edge A, played indefinitely, ever falls n steps below its starting point. riskOfRuinPct = RoR × 100.

Guards. If μ ≤ 0, risk of ruin is 100% — a driftless or downward-drifting account hits any finite drawdown barrier with probability 1 given enough trades. If A ≥ 1 (edge beyond one standard deviation per trade), the formula’s base goes non-positive and the approximation breaks down; instead of a specific figure, the tool shows the exact loss-streak lower bound RoR ≥ q⌈U⌉ — ⌈U⌉ consecutive opening losses are one specific way to be ruined, so the true ruin probability can never be lower than the chance of that streak.

Worked example

Inputs: win rate = 50%, payoff ratio = 1.5, risk per trade = 5%, ruin threshold = 50%, capital = $25,000.

  1. Conversions: p = 0.50, q = 0.50, f = 0.05, d = 0.50, b = 1.5.
  2. Edge: μ = 0.50 × 1.5 − 0.50 = 0.25 R per trade. Positive edge, so the model applies.
  3. Standard deviation: σ = (1.5 + 1) × √(0.50 × 0.50) = 2.5 × 0.50 = 1.25 R.
  4. Loss units to ruin: U = ln(0.50) ÷ ln(0.95) ≈ 13.513 — about 13.5 consecutive 5% losses halve the account, not 10 as the naive 50 ÷ 5 would say.
  5. Normalization: A = 0.25 ÷ 1.25 = 0.20; n = 13.513 ÷ 1.25 ≈ 10.811. A is well below 1.
  6. Risk of ruin: base = 0.80 ÷ 1.20 = 0.6667; RoR = 0.666710.811 ≈ 0.0125.
  7. Outputs: risk of ruin ≈ 1.25% (about a 1-in-80 chance of ever seeing a 50% drawdown); survival ≈ 98.75%; ruin equity level = $25,000 × 0.50 = $12,500.

Sensitivity contrast — same system at 1% risk per trade: U = ln(0.50) ÷ ln(0.99) ≈ 68.97; n ≈ 55.17; RoR = 0.666755.17 ≈ 2 × 10⁻¹⁰ — effectively zero. Cutting risk per trade from 5% to 1% took ruin risk from 1-in-80 to about 1-in-5-billion; risk of ruin falls exponentially as risk per trade shrinks.

FAQ

What is risk of ruin in trading?

It is the probability that an account ever falls to a drawdown level — the "ruin threshold" — from which the trader realistically cannot or will not continue. It depends on win rate, payoff ratio, and the percent of equity risked per trade.

Why does the calculator show 100%?

A win rate and payoff ratio that produce zero or negative expectancy mean the account drifts down on average. Over enough trades, hitting any drawdown threshold becomes a mathematical certainty — smaller position sizes only slow it down.

Is this an exact prediction?

No. The model assumes binary outcomes, a constant risk fraction, and independent trades, over an unlimited number of trades. Real trading has variable and fat-tailed outcomes and correlated losses, so real ruin risk is typically higher than the estimate.

What counts as "ruin"?

You choose the threshold; 50% is a common default because deep drawdowns require outsized gains to recover — a 50% loss needs a 100% gain just to get back to even — and many traders stop or change behavior before then.

How much does risking less per trade help?

Enormously — risk of ruin falls exponentially as risk per trade shrinks. In this tool's example system, risking 5% per trade gives roughly a 1.25% chance of a 50% drawdown; risking 1% makes the same event effectively impossible.

Does a higher win rate always mean lower risk of ruin?

No. Risk of ruin depends on the combination of win rate and payoff ratio. A 40% win rate with a 2.5 payoff ratio has positive expectancy, while a 55% win rate with a 0.7 payoff ratio has negative expectancy and certain eventual ruin.

Continue your analysis

Find the risk % your edge supports →Turn your risk % into a share count →Check the payoff ratio of your next setup →

Educational disclaimer

This calculator is for education only and is not financial, investment, or trading advice, and not a recommendation of any risk level. It uses the fixed-fractional, binary-outcome risk-of-ruin model, which assumes binary trade outcomes, a constant risk fraction, independent trades, and an infinite horizon; results are approximations. Real-world ruin risk is usually higher than the modeled figure due to fat-tailed outcomes, correlated positions, slippage, and behavioral deviation from the plan. When the model’s approximation limit is reached (edge beyond one standard deviation per trade), the displayed figure is a lower bound only. Outputs are long-run probabilities under idealized assumptions, not predictions for any specific account. US market conventions assumed.