A win rate summarises what was observed, but its precision depends on how many trades support it. Entering that rate as if it were known gives a ruin estimate that hides this uncertainty. Comparing the declared rate with the lower end of its interval shows how much the result depends on that assumption.
Ruin means touching a threshold within a horizon
Here ruin means the balance touches or falls below a threshold at any point within the horizon. It counts even if the balance later recovers. The threshold is relative to the initial balance; drawdown measures a fall from a previous peak and answers a different question.
With equal wins and losses, fixed steps, independence and a constant win probability p, the classic formula without a time limit is P(ruin) = (q / p)^B when p > q; when p ≤ q, it is 1. Here q = 1 − p and B is the distance to the threshold in loss units, rounded up. These are accumulated net losses, not necessarily consecutive ones. There is no upper exit barrier.
Simulation with a horizon answers a more specific question: under these assumptions, what fraction of paths touches the threshold before the horizon ends (here, 500 trades)? It also handles different win and loss sizes, where that classic formula does not apply.
How the three cases are calculated
In every case, 1R is 1 % of the initial balance, the threshold is a 30 % fall (a balance of 70 %) and the horizon is 500 trades. This is an illustrative scale, not position sizing advice. The trade count behind the rate is separate from the horizon.
Expectancy per trade is E = p × win − (1 − p) × loss, in R. Each probability uses 4,000 paths and seed 20261010, computed by the linked risk-of-ruin calculator. The second reading repeats the calculation at the lower bound of the two-sided 95 % Wilson interval, keeping all other inputs fixed.
Table: declared win rate and Wilson lower bound
Illustrative inputs and model results. Probabilities are frequencies of simulated paths; they are not measurements of a file.
| Win rate | Trades behind it | Win / loss | Expectancy (R) | Touch the threshold | Win rate: lower bound | Expectancy: lower bound (R) | Touch the threshold: lower bound |
|---|---|---|---|---|---|---|---|
| Declared · 55.0 % | Declared · 60 | Declared · 1.0R/1.0R | Declared · +0.10 R | Declared · 0.1 % | Declared · 42.5 % | Declared · -0.15 R | Declared · 98.9 % |
| Declared · 55.0 % | Declared · 300 | Declared · 1.0R/1.0R | Declared · +0.10 R | Declared · 0.1 % | Declared · 49.3 % | Declared · -0.01 R | Declared · 26.6 % |
| Declared · 45.0 % | Declared · 100 | Declared · 2.0R/1.0R | Declared · +0.35 R | Declared · 0.0 % | Declared · 35.6 % | Declared · +0.07 R | Declared · 9.7 % |
How to read the differences between rows
The first two rows have identical expectancy and risk at the declared rate. More trades narrow the interval and raise its lower bound, changing the three lower-bound columns. In both rows that bound still lies below break-even.
The third row combines fewer wins with a larger win than loss. Expectancy depends on both amounts, not just the win rate. More paths would reduce simulation noise without adding evidence about the declared win rate.
In that row, at the declared rate, 0 of 4,000 paths touched the threshold. The table rounds to one decimal, like the linked calculator, and that rounding does not distinguish no path from a single one. A zero does not make the event impossible.
What “compatible with the data” means
The Wilson interval contains rates these data do not exclude under that procedure and the independent-trade model. Its lower bound is one such compatible rate, not a new measurement or the rate the next history will necessarily have. The declared rate remains the reference for the comparison.
Confidence describes the procedure's approximate coverage over repeated samples, not a probability about this history's true rate. The table's two ruin probabilities are scenarios; they do not form a confidence interval for ruin risk. Only the rate changes: uncertainty about win sizes, loss sizes and dependence is left out.
How many trades put the lower bound above break-even
At a 55 % win rate with equal win and loss sizes, break-even before costs is 50.0 %. Evaluating each integer sample size with the win-rate calculator gives the first lower bound strictly above break-even at 385 trades, holding the declared rate fixed. This calculation uses a possibly rounded proportion; it does not reconstruct an integer win count.
If the rate must correspond exactly to an integer win count, the first compatible sample size meeting the condition is 400. The calculator shows 500 because it checks a grid of sizes, not every integer. These figures assume the same rate as data are added; they are not a universal minimum or a prediction of what will happen.
What an actual history adds
The model assumes independent trades, the same rate throughout the horizon and fixed win and loss sizes on the initial balance, without compounding. It adds no commissions, slippage, price gaps or regime changes. Correlated positions and clustered losses can substantially change the result.
With trades in their actual order, the report can measure streaks and drawdown in the supplied series instead of inferring them only from a rate. An incomplete history limits those measurements; measuring the past does not turn simulation into a forecast. Use the upload and synthetic sample report links to see the evidence each input provides. The challenge calculator adds targets and limits specific to that model.
FAQ
Is Wilson's lower bound the worst possible case?
It is a compatible scenario under the interval's assumptions. Outside the model, the rate, loss sizes and dependence can change. The table does not cover all those scenarios.
Why does positive expectancy not remove the risk of ruin?
Expectancy is the model's average per trade. A path can accumulate losses and touch the threshold before the horizon ends even when that average is positive. The order of outcomes matters.