Let w and l be average gross win and gross loss in units of pre-cost risk (R), and c be cost per trade in R. Net outcomes are W = w − c and L = l + c. Expectancy = pW − (1 − p)L. Break-even win rate = L / (w + l). With b = W / L, full Kelly account-loss fraction is max(0, min(1, p − (1 − p)/b)); it is zero when W ≤ 0. The win-rate buffer is subtracted from the entered win probability and clipped at zero; it is a user-selected stress scenario, not a statistical confidence interval. Selected account risk is the lesser of full Kelly × fraction and the entered account-risk cap. Growth is p ln(1 + bf) + (1 − p) ln(1 − f), with f the fraction of account lost on a losing trade including costs. This two-outcome approximation treats the averages as fixed payoffs and assumes stable, known probabilities and independent repeats. Estimated inputs and correlated losses are not risk-constrained by this model.

Stanford: the Kelly criterion