What risk of ruin means here
Reaching a fixed line below starting equity; a later recovery does not undo it.
The floor, and what it is not
Here, ruin means reaching a fixed line below starting equity. A 30% threshold is crossed when equity reaches or falls below 70% of its starting value. A later recovery would not undo that crossing. The line never rises with a new peak: it is different from the running-peak drawdown in the Monte Carlo simulator. This is a model you specify, not a check of a prop firm's actual rules. A ruin probability is not a cap on losses either: a gap or slippage can make one loss larger than the planned risk.
The risk of ruin formula
Risk of ruin = ((1 − p) ÷ p)N, where N = (capital − ruin floor) ÷ risk per trade
Where it comes from, its assumptions and payoffs above 1R
The classic formula comes from the gambler's ruin problem in probability theory. It assumes you risk the same fixed amount on every trade and that each trade either wins or loses that amount (a 1:1 payoff).
p is the win rate as a fraction and N is the number of losses in a row that would take your capital down to the floor; if N is not a whole number, round it up. The formula holds when p is above 50%. At 50% or below it gives 100%: with no edge and no limit on the number of trades, the floor is eventually reached. Example: a 60% win rate, $10,000 capital, a $5,000 floor and $500 risked per trade give N = 10 and (0.4 ÷ 0.6)10 ≈ 1.7%. Written with the edge A = p − (1 − p), the same formula reads ((1 − A) ÷ (1 + A))N.
When a win pays more than the risk. For a payoff of R times the risk, with R a whole number, replace (1 − p) ÷ p with θ, the number between 0 and 1 that solves p × (θ + θ² + … + θR) = 1 − p. Risk of ruin is θN. For 1R this gives back (1 − p) ÷ p. For 2R the quadratic formula gives θ = (√(p² + 4p(1 − p)) − p) ÷ 2p; for 3R and above the calculator solves for θ numerically. If p × R is not above 1 − p, the strategy has no positive expectancy and the formula gives 100%. For a payoff that is not a whole number, such as 1.5R, the last loss can overshoot the floor by part of a bet, and there is no exact formula of this kind; the calculator says so and leaves that case to the simulation.
Assumptions: the same risk amount on every trade, not a percentage of current equity; independent trades; a constant win rate and payoff; an unlimited number of trades; and no loss larger than the planned risk. Source: the classical ruin problem in W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, chapter XIV.
Risk of ruin table
The classic formula with a fixed risk amount, unlimited trades and a floor 50% below the start.
| Win rate | Payoff | 1% risk | 2% risk | 5% risk |
|---|---|---|---|---|
| 40% | 1R | 100% | 100% | 100% |
| 40% | 2R | < 0.01% | 0.76% | 14.2% |
| 40% | 3R | < 0.01% | < 0.01% | 2.5% |
| 50% | 1R | 100% | 100% | 100% |
| 50% | 2R | < 0.01% | < 0.01% | 0.81% |
| 50% | 3R | < 0.01% | < 0.01% | 0.23% |
| 60% | 1R | < 0.01% | < 0.01% | 1.7% |
| 60% | 2R | < 0.01% | < 0.01% | 0.04% |
| 60% | 3R | < 0.01% | < 0.01% | 0.02% |
Method, and how to read 100% and < 0.01%
Method: the classic formula above, with a fixed risk amount per trade (a percentage of starting capital) and unlimited trades. Ruin floor: equity 50% below starting capital, so N = 50 ÷ risk %: 50, 25, 10 losses for 1%, 2%, 5% risk.
100% marks the rows with no positive expectancy: 40% at 1R loses on average, and 50% at 1R breaks even before costs, so with no limit on trades both reach the floor. "< 0.01%" is a model result, not a promise: it is only as good as the win rate and payoff you assume, and the real ones change.
Why the simulation gives different numbers
The calculator risks a share of current equity over a set number of trades; the formula a fixed amount forever.
| Win rate · payoff · risk | Formula (fixed amount, unlimited trades) | Simulation (fixed %, 1,000 trades) |
|---|---|---|
| 50% · 1R · 2% | 100% | 38.0% (761 of 2,000 paths) |
| 40% · 2R · 5% | 14.2% | 11.1% (222 of 2,000 paths) |
| 60% · 1R · 5% | 1.7% | 0.45% (9 of 2,000 paths) |
| 40% · 1R · 2% | 100% | 100% (2,000 of 2,000 paths) |
Sizing, horizon and sampling, with the settings
The calculator above simulates a different, more common sizing rule. Each trade risks a fixed percentage of current equity, so the risk amount shrinks after losses and grows after wins. Each path is checked only up to the trade count you set. Equity multiplies by 1 + risk% × reward R on a win and by 1 − risk% on a loss. Each path stops at its first threshold crossing or at the trade horizon. The estimate is the number of paths that crossed divided by the total path count.
Three things separate the two answers. Sizing: at 2% risk, a fixed amount reaches a 50% floor after 25 losses in a row; a fixed percentage needs 35, because 0.9835 ≈ 0.49. Horizon: the formula counts unlimited trades, the simulation stops at your trade count, so a strategy with no edge can show well under 100%. Sampling: the formula is exact for its assumptions; a simulation is an estimate that changes with the seed. The table compares rows from the grid above, with the same 50% floor.
Simulation settings: 2,000 paths, seed 7, 1,000 trades per path. Neither method includes costs, changing win rates, correlated losing streaks or gaps. More simulated paths reduce sampling variation under those assumptions; they do not make uncertain trading inputs true.
Enter dollars instead of percentages
$10,000 capital, $200 risk and a $5,000 floor become 2% risk and a 50% threshold.
How the amounts are converted
Choose Dollar amounts and type your starting capital, the risk per trade and the ruin floor. The calculator converts them to the same model: risk % = risk per trade ÷ capital, and threshold = (capital − floor) ÷ capital. $10,000 capital, $200 risk and a $5,000 floor become 2% risk and a 50% threshold, 25 losses from the floor. In the simulation the first trade risks $200 and later trades risk 2% of current equity; the classic-formula line keeps $200 on every trade.
Reproduce the example, then change one input
The worked example: 7 of 2,000 paths cross, 0.35%; at 5% risk, 12.4%.
The steps, and why later paths shift
Load the worked example, then press Run simulation: 50% win rate, 1.5R reward, 2% risk, a 30% threshold, 200 trades, seed 7 and 2,000 paths. Seven paths cross the line: 7 ÷ 2,000 = 0.35%, displayed as 0.4%. With the other settings held fixed, 5% risk gives a rounded 12.4% crossing frequency in its sample. These are conditional model results, not forecasts. Because each ruined path stops drawing random numbers early, changing inputs can also change where later paths begin in the generator's stream. A 1.5R payoff has no exact classic value, so the formula line points you to this simulation.
Keep the run, including a zero count
The JSON download keeps the full-precision result, the seed and the threshold definition.
What the download holds, and what a zero means
Download the JSON to retain the full-precision result, event count, inputs, seed, engine version and threshold definition; in dollar mode it also records the amounts you typed and how they were converted. Repeating the same settings reproduces that sample; New sample seed clears the previous result and supplies a different seed for your next explicit run. If no paths cross, the count is zero observations in the finite sample, not proof of zero probability. Even a precise simulation estimate leaves uncertainty about the win rate, payoff and model itself. Nothing in the download establishes an account's authenticity or future outcome.