The Simplest Derivation of the Kelly Formula: A Minimalist Perspective

Abstract

The Kelly criterion is a widely known decision formula in probability-based optimization. However, most derivations rely on logarithmic utility or information theory. In this note, we provide the simplest known derivation using only high school-level calculus and algebra. We also show that generalized loss models can be reduced to the classical form via variable substitution. This note is meant for educational and structural clarity.

Keywords: Kelly Formula, Optimal Betting, Expected Growth, Probability-Based Optimization, Elementary Calculus, Gambling Strategy, Structural Normalization, Wealth Allocation