Kelly Criterion Simulator

gist

Kim Birch’s simulator uses Monte Carlo runs to show how bankrolls evolve under full or fractional Kelly sizing. Repeated multiplicative bets turn one fixed probability and odds assumption into a distribution of outcomes, exposing growth, volatility, drawdowns, and tail risk. Kelly can be growth-optimal under the model while remaining sensitive to probability error and producing severe interim losses. The simulator is a teaching tool, not betting advice.

ideas

• Growth-optimal does not mean smooth. Maximizing expected logarithmic growth can still produce deep drawdowns and wide outcome dispersion.
• Fractional Kelly buys robustness. Smaller fractions sacrifice some modeled long-run growth for lower volatility and less sensitivity to estimation error.
• Input quality dominates the formula. An overstated edge produces an oversized stake, which can turn a sound allocation rule into overbetting.
• Read distributions, not one path. Median, mean, tail outcomes, and drawdown depth reveal more than a single simulated bankroll.
• The model has strict limits. Fixed independent trials omit changing odds, correlation, costs, liquidity, execution, adaptation, and structural breaks.