1. Precise numbers and weak assumptions
If you assume independent trades, a 45% win rate, 1.5R winners and 2% risk of current equity, the mathematics of an idealized sequence is unambiguous. But a real strategy's win rate, realized payoff and execution quality may change. A sensitivity matrix recalculates the same exact risk model with deliberately altered inputs. The cells are not confidence intervals for a measured trading edge.
2. Losing streaks are not the same as ruin
A run of K consecutive losses can start anywhere in N trades. In our exact calculation, each surviving state keeps the current run length 0, 1, …, K−1. Any win resets the run to zero; a loss extends it by one. Reaching K counts the event once, regardless of what later trades do. This is a finite-state absorbing dynamic program rather than a random sample.
The right-hand expression is only the chance that one specified block of K trades consists entirely of losses. In a longer trading horizon, many blocks can contain the same streak and they overlap; adding their individual probabilities also gives the wrong answer. A losing streak does not necessarily imply reaching a selected equity floor.
3. Worked example: two position-sizing rules
Start with $10,000 and assume five consecutive losses at 2% risk. Under fixed-fraction sizing, each loss removes 2% of the then-current capital, leaving $10,000 × 0.985 = approximately $9,039.21. Under a fixed dollar risk of $200 per trade, the same five losses leave $9,000. Neither illustration estimates how likely the streak is.
Now suppose five consecutive winners follow, each paying 1.5R. The fractional method compounds a +3% return on the changing equity each time. The fixed-dollar method adds $300 per winner if its original risk stake remains affordable. This particular loss-then-win ordering is deterministic and not a forecast or a random simulation.
4. Stress cases and mathematical log growth
The calculator tests a 5-percentage-point reduction in assumed win rate, a 20% reduction in gross winning payout, a 50% increase in risk fraction, and all three changes together. These are illustrative stress choices, not historically calibrated shocks or confidence limits.
Expected logarithmic growth per trade follows the win and loss equity multipliers. This is not a simple expected dollar return and may be negative even when arithmetic expectancy is positive.
5. What the model cannot tell you
Real strategies include changing win rates, variable returns, spread, fees, partial fills, stop gaps, volatility clustering, correlated outcomes and changing market regimes. Cross margin, mark-price liquidations, funding and exchange maintenance rules are not modeled. Do not interpret a conditional risk estimate as the real chance of losing money, or use it as personalized investment advice.
For sampled outcome distributions, try Monte Carlo Simulator →. For a single first-passage result, see Risk of Ruin →. The complete calculation conventions are published in Methodology →.