Risk of Ruin Calculator

The calculator above estimates ruin probability by Monte Carlo simulation, which handles uneven payoffs, drawdown thresholds and streak-dependent position sizing. Behind it sit two classic closed-form results worth knowing. For an even-payoff game where you win each trade with probability p > 0.5 and risk one unit per trade, starting U units away from ruin (the gambler's ruin formula):

RoR = ((1 − p) / p) ^ U

For strategies with arbitrary payoffs, the diffusion approximation is the standard generalization — μ is your expected profit per trade, σ² the variance of per-trade outcomes, and b the amount of capital you can lose before hitting your ruin threshold:

RoR = exp(−2 · μ · b / σ²)

Worked example: a strategy with a 55% win rate and 1:1 payoff risking 1% per trade ($100 on a $10,000 account) has μ = $10 and σ² ≈ 9,900 per trade. With ruin defined as losing half the account (b = $5,000), RoR = exp(−2 × 10 × 5,000 / 9,900) ≈ 0.004%. The same strategy risking 5% per trade gives μ = $50, σ² ≈ 247,500 and RoR = exp(−2.02) ≈ 13.3% — a >3,000× jump in ruin probability from position size alone, with an identical edge. This exponential sensitivity to position size is the entire argument for sizing discipline.

Because the exponent scales with μ/σ², anything that improves expectancy or reduces outcome variance collapses the ruin probability. The Kelly criterion calculator finds the growth-optimal risk fraction for your edge, and the prop firm challenge calculator applies the same survival math to challenge drawdown limits, where the ruin barrier b is the prop firm's maximum drawdown instead of your full account.