Bet-size fraction maximising expected log-wealth growth: for a single risky asset, f^* = dfracμ - rσ^2, identical to the Merton fraction with risk-aversion γ = 1. Maximises mathbbE[ln W_T] — equivalently, the geometric mean of wealth — but is brutally aggressive: typical practical drawdowns at full Kelly are unacceptable to most investors, so practitioners use half-Kelly or fractional Kelly. Sensitive to estimation error in μ — overstating μ by 50% has more cost than under-betting by 50% (asymmetric loss in geometric growth).