Category
Fundamentals.
Master the building blocks of probabilistic thinking. From Bayes theorem and expected value calculations to base rates and conditional probability, these guides lay the mathematical and conceptual foundation you need to make better decisions under uncertainty. Whether you are new to probability or brushing up, start here.
22 posts in Fundamentals
law of large numbers
The Law of Large Numbers: Why Casinos Always Win
The Law of Large Numbers explains why a single bet is wildly volatile but casinos profit reliably - the maths behind insurance and long-run averages.
probability
The Monty Hall Problem: Why You Should Always Switch
The Monty Hall problem looks 50/50 and isn't - switching doors wins two-thirds of the time. Here's why, with five proofs and the famous controversy.
fundamentals
Risk vs Uncertainty: The Distinction That Matters
Risk is measurable; uncertainty is not. Confusing the two produces overconfident forecasts and brittle portfolios. Here's how to tell them apart.
bayes theorem
The False Positive Paradox: Why Positive Tests Mislead
When a test for a rare condition comes back positive, it's often more likely wrong than right. The false positive paradox, explained with real numbers.
bayesian thinking
Bayesian vs Frequentist Statistics: What's the Difference?
Bayesian vs frequentist statistics - the philosophical split that decides whether you get p-values or posteriors, and when each one actually wins.
probability
Conditional Probability Explained Simply, With Examples
Conditional probability is the chance one event happens given another already has. Worked examples in medical testing, weather, and the Monty Hall problem.
books
12 Best Books on Probabilistic Thinking and Decision-Making
A curated reading list on probability, decision-making under uncertainty, and rational thinking - from Kahneman to practical guides for forecasters.
ergodicity
Ergodicity Explained: Why Time Averages Matter Most
Ergodicity separates sensible bets from catastrophic ones. The difference between ensemble averages and time averages - and why ignoring it can ruin you.
bayes theorem
Bayes Theorem Explained: Formula and 5 Worked Examples
Bayes theorem explained from the formula up: derivation, intuitive examples (medical tests, spam filters), and the base-rate trap that fools experts.
expected value
Expected Value vs Expected Utility: When EV Isn't Enough
Pure expected value can lead to ruinous decisions. Here's why expected utility, risk aversion, and the St Petersburg paradox matter for real-life choices.
Expected Value Thinking: Better Decisions Under Uncertainty
Expected value thinking: the most important concept in decision-making under uncertainty. What it is, how to calculate it, when to apply it.
kelly criterion
The Kelly Criterion: How to Size Your Bets Optimally
The Kelly Criterion tells you exactly how much to stake when you have an edge. Formula derivation, fractional Kelly, history, and worked examples for 2026.
expected value
Expected Value Formula: Derivation and 5 Worked Examples
The expected value formula is E[X] = Σ(p × x). Full derivation and five worked examples - coin flip, lottery, insurance, poker, and stock investment.
monte carlo
Monte Carlo Thinking: How to Stress-Test Decisions
Monte Carlo simulation lets you stress-test decisions across thousands of scenarios. A practical guide to using it for retirement, projects and investing.
nassim taleb
Nassim Taleb's Ideas: Black Swan, Antifragile & More
A guide to Nassim Taleb's key ideas - Black Swans, Antifragile, Skin in the Game, fat tails, barbell strategy and the Lindy effect - and where to start.
regression to the mean
Regression to the Mean: Why Extremes Don't Last
Why extreme performance - sporting peaks, market gains, viral hits - almost always reverts to average. Galton's discovery, examples, and how to spot it.
probability
Probability vs Odds: The Difference and Why It Matters
Probability and odds describe the same uncertainty differently - and confusing them costs people money. How each works, conversions, and bookmaker tricks.
correlation
Correlation vs Causation: A Probabilistic Thinking Guide
Correlation is not causation - the most-quoted line in statistics, and the most misunderstood. What it really means, and how to think clearly about cause.
probability
Probabilistic Thinking in Daily Life: 7 Practical Uses
How to apply probabilistic thinking to medical decisions, career bets, insurance, investing, dating, sports betting and travel. 7 worked examples.
insurance
How Insurance Companies Use Probability to Make Money
Insurance is a negative-EV bet - for you. Here's how actuarial science, risk pooling, and the law of large numbers turn that into reliable profit.
prediction markets
How Prediction Markets Work: Probability Meets Money
Prediction markets turn questions about the future into tradeable contracts whose prices behave like probabilities. How they work, and how to use them.
expected value
Negative Expected Value: Why Lottery Tickets Always Lose
Why every lottery ticket, roulette spin and slot pull is mathematically a loss in expectation. The maths behind why the house always wins.