This project compares the mathematical structure of the Kelly Criterion, meant to maximize expected logarithmic wealth in two settings: a repeated biased coin toss model and the stock market modeled as a stochastic process. This project derives the optimal fraction in each case and demonstrates that both solutions follow the same structural principle: optimal allocation equals expected excess return divided by variance. By looking at both examples side by side, this project shows how the same mathematical idea can be applied to simple games of chance as well as real-world investing decisions.