The notebook
One variable at a time
Detailed derivations and practical notes on the probability, payoff shape, path, and position size behind a tail edge.
How a 30% win rate can produce positive expectancy
Derive breakeven hit rate, profit factor, variance, and the sample-size problem from one clean payoff model.
Read the derivation →The losing streak your backtest owes you
Calculate exact run probabilities and learn why a valid low-hit-rate strategy will regularly look broken.
Study the probabilities →Skew, fat tails, and where the return really comes from
Mean versus median, positive skew, outlier dependence, and what happens when the best trades disappear.
Follow the right tail →Position size for the path, not the average
Fixed-fraction drawdown, geometric growth, Kelly sizing, model uncertainty, and the difference between survival and comfort.
Size the risk →The complete mathematics of a tail edge
All of the core equations, assumptions, and failure modes assembled into one rigorous primer.
Open the primer →The source shelf for randomness and asymmetry
Reviewed books on tail events, expectancy, systematic trading, decision quality, and risk.
Browse the shelf →