Probability

September 2026

• Sep 7, 2026ConceptsOccam's Razor: When the Simplest Explanation WinsWilliam of Ockham never wrote the Latin sentence attached to his name; later writers coined it, and Aristotle had argued in the Posterior Analytics for the demonstration resting on fewer postulates. The razor earns its keep probabilistically, since each added assumption is another chance to be wrong, and statistically, since fewer parameters resist overfitting. Medicine keeps a counterweight: Hickam's dictum, that a patient can have as many diseases as they please.15 MIN833

March 2026

• Mar 3, 2026ConceptsRisk vs Uncertainty: What People ConfuseFrank Knight's 1921 line between known probabilities and genuine uncertainty, mapped across a five-step spectrum from casino games to questions no distribution covers. The page explains why optimization gives way to robustness, optionality and heuristics once probabilities stop being meaningful, and uses LTCM's roughly $4.6 billion loss in 1998, the Challenger launch decision and COVID-19 preparedness to show what happens when uncertainty gets dressed up as calculable risk.24 MIN65.4k

June 2025

• Jun 19, 2025ExplainersOrigins of Decision Theory: Key DevelopmentsMost people prefer a certain million to a gamble with a higher expected value, then reverse that preference when both options become unlikely, which breaches the independence axiom underpinning expected utility. Savage produced the pattern himself. This page traces the field from Pascal and Fermat through Bernoulli's utility solution to the St. Petersburg paradox, von Neumann and Morgenstern's axioms, and the Ellsberg and prospect theory challenges.38 MIN67.5k
• Jun 3, 2025ExplainersUsing Decision Theory in Everyday ChoicesDecision theorists split choices into four worlds by how much you know: certainty, risk, uncertainty and ignorance. Most practical tools, expected value and expected utility, were built for risk, where probabilities are known. Outside gambling that case is rare; real decisions make you estimate them instead. Even a certain choice between two apartments is hard, because weighing a commute against pet permission compares incommensurable things.51 MIN47.3k

December 2024

• Dec 3, 2024ConceptsThe Representativeness Heuristic: Judging by AppearancesAdding feminist activist to bank teller makes the description fit the prototype better while mathematically making it less likely, and people follow the resemblance. The page covers the cab problem and the engineer-lawyer studies, where vivid case detail swamps the base rate entirely. It also gives Gigerenzer's critique real weight, since presenting the mammogram problem as natural frequencies largely dissolves the error.21 MIN4.9k

November 2024

• Nov 21, 2024ConceptsGambler's Fallacy: Misconceptions About RandomnessTheir 2016 study found the same corrective pattern in loan officers approving applications and umpires calling pitches, controlling for the merits of each case. A roulette wheel has no memory, but the people watching it keep a ledger, and so do professionals trained for case-by-case objectivity. The page is careful on the hot hand too, noting Miller and Sanjurjo's 2018 correction and that the debate continues rather than treating it as settled illusion.24 MIN1.9k

November 2022

• Nov 18, 2022ConceptsThinking About Risk: A Practical Framework ExplainedRisk and uncertainty are not the same thing, a distinction Frank Knight drew in 1921. Under risk the probabilities can be estimated from data or theory; under uncertainty they cannot, and you may not even know the full range of possible outcomes, so standard tools become unreliable. Volatility is not risk either: a cash deposit with zero nominal volatility can carry enormous purchasing power risk during high inflation.20 MIN4.8k

August 2022

• Aug 6, 2022ConceptsMonte Carlo Method: How Randomness Solves Complex ProblemsUsing random sampling where direct calculation will not work. Rather than enumerate every possible state, you run a model many times with randomly drawn inputs and read the distribution of results. Ulam had the idea playing Canfield solitaire in 1946, and with von Neumann and Metropolis applied it to neutron transport, publishing in 1949. Accuracy improves with the square root of the sample count, so halving the error takes four times the runs.16 MIN7.3k