Translate R outcomes into equity changes
One R is the reference amount risked before the outcome multiplier is applied. With equity fraction f, a winning step changes equity by the factor 1 + f × (average win R − cost R). A losing step uses 1 − f × (average loss R + cost R). Position amounts therefore shrink after losses and grow after gains. Costs apply to every simulated trade. Keep a loss step within the model's valid capital range; leverage liquidation rules are not reconstructed from this equation.
Interpret threshold breaches carefully
Here ruin is an operational drawdown threshold chosen by you, measured from each path's running equity peak. It need not mean an account reaches exactly zero. The reported breach share is the number of paths crossing that threshold divided by simulated paths. A larger path count reduces random sampling noise but cannot repair incorrect assumptions. A fixed seed makes an experiment reproducible; changing the seed explores a different finite sample. Terminal equity alone can conceal a serious drawdown earlier in a path.
Stress the assumptions, not only the seed
Every trade is drawn independently from the same win probability and two outcome sizes. Real trades can cluster by market regime, share exposures or experience larger losses during gaps. This model does not reproduce those dependencies, changing liquidity or varying payoff distributions. Compare lower win probabilities, larger losses and higher costs, then inspect how smaller equity fractions change the output. Illustrative defaults are not estimates of an existing strategy. A low simulated breach share is conditional on your inputs and is not account protection.