Essays

Twenty years of writing about probability, data, investing, and the systems that shape decisions. Several of these include simulations you can run yourself.

Data & AI
Where the Value Will Be If AI commoditizes execution, three things become expensive: the ability to judge, proof of origin, and willingness to guarantee. Dec 2025 An Analytics Renaissance is Coming Most companies' data was built for humans reading dashboards. AI needs something different. The gap is where the real work is. Sep 2025 Don't Outsource Your Thinking How I use AI as a sparring partner. Why the distinction from ghostwriting matters more than people think. Sep 2025
Probability & Statistics
Interactive Goodhart's Law When a measure becomes a target, it stops being a good measure. Watch the proxy and the goal diverge in real time. Mar 2026 Interactive The Prosecutor's Fallacy "99.9% accurate" sounds airtight until you realize what it actually means. A common reasoning error with serious consequences. Mar 2026 Interactive Regression to the Mean Why exceptional performances tend to be followed by ordinary ones. Watch a basketball shooter prove it. Mar 2026 Interactive Simpson's Paradox Aggregated data can show the opposite of what every subgroup says. Build your own counterexample with sliders. Mar 2026 Interactive P-Hacking: Finding "Significant" Results in Random Noise How researchers find statistically significant results in data with no real effects. Try it yourself. Jan 2020 Interactive The Birthday Problem Only 23 people are needed for a 50% chance of a shared birthday. The math is counterintuitive but the simulator makes it real. Dec 2010 Interactive Finding Pi With Randomness Throw random darts at a square and watch π emerge. The Monte Carlo method made tangible. Sep 2009 Interactive The Monty Hall Problem Switching wins 2/3 of the time. Play the game and watch the stats prove it. Jan 2008
Systems & Strategy
Interactive Dice Influence and Variance Why the "if it worked, casinos would be bankrupt" argument misses how variance hides small edges. Dec 2019 Interactive Blackjack Basic Strategy The math behind every blackjack decision, computed from first principles. Train against perfect strategy. Mar 2026 Interactive Schelling's Segregation Model Even mild individual preferences for similarity produce extreme collective segregation. Run the model yourself. Oct 2006 Power To The People Crowdsourcing human cognition for machine learning. An early take on what would become a major theme. May 2007 Ethics of Fantasy Sports What counts as cheating when the rules are software-defined? A piece about systems and incentive design. Apr 2007
Investing
Variable Dollar Cost Averaging A simple system for investing more when prices are low and less when they're high, without trying to time the market. Oct 2018 The Big Deal About Risk Parity Why allocating by risk instead of by capital changes everything about portfolio construction. Mar 2018 The Cognitive Biases That Plague Investors A field guide to the systematic errors that cost individual investors money. With practical mitigations. May 2017 Socially Responsible Investing Will Soon Be The Norm Why a $30 trillion wealth transfer to millennials makes ESG investing inevitable, with empirical evidence. May 2016 Roboadvisors are Good Investment Vehicles A detailed rebuttal of the case against automated investing, including the often-overlooked psychological protections. Jul 2015 Wealthfront vs Schwab Intelligent Portfolios A close comparison of two early roboadvisors, including the hidden costs of cash drag. May 2015 Tried and True Investing Advice The boring fundamentals that work for most people. Diversification, low costs, and a tolerance for waiting. Aug 2012