probability

Lecture 1 of Harvard's Statistics 110 with Joe Blitzstein, introducing sample spaces, the naive definition of probability, counting, binomial coefficients and the sampling table.

A 2015 talk by David Deutsch with slides and audio about constructor theory and how physics, in particular the many-worlds interpretation, can be framed without probability.

Sid Meier's GDC 2010 keynote on how players perceive probability in games, including how Civilization's odds were adjusted because players misjudged them.

Matt Parker analyzes the Minecraft speedrunning controversy in which Dream was accused of cheating via improbably lucky drops. He walks through the probability and the statistical arguments in the original accusation and the reply.

Veritasium explains Bayes' theorem with examples and introduces the 'Bayesian trap', where repeated events get mistaken for inevitable ones. It discusses how priors shape our expectations and behavior.

Numberphile interviews Grant Sanderson of 3blue1brown about Bertrand's paradox, where different reasonable ways of picking a random chord of a circle give different probabilities.

Mathematician singingbanana shows how he flipped ten heads in a row, with the full uncut video and answers to viewers' questions. The point is that unlikely events happen given enough attempts.

A doctor from Medlife Crisis explains in under three minutes why even a rich patient should not simply order every medical test, touching on pre-test probability and Bayesian reasoning. False positives make blanket testing counterproductive.

3Blue1Brown explains why positive results on accurate medical tests are often false positives, and reframes Bayes' rule using likelihood ratios (Bayes factors) to update odds. It uses visual examples to make the reasoning intuitive.

Numberphile with Simon Pampena on how humans misunderstand randomness, including coin-flip sequences, run lengths and the gambler's fallacy.

Julia Galef uses pictures to explain Bayes' rule, then tells three personal stories showing how she applies it to improve her thinking.

Persi Diaconis explains on Numberphile the mathematics of card shuffling, including why seven riffle shuffles are needed to randomize a deck and how different shuffles compare.

3Blue1Brown presents Bayes' theorem through a geometric diagram, showing how evidence should update beliefs. It works through the Kahneman and Tversky style questions and base rates.

David Spiegelhalter, Professor of the Public Understanding of Risk, uses statistics to weigh everyday risks such as bacon sandwiches and cycling. The six-minute piece introduces micromorts as a way to compare the risk of dying.

Veritasium explores why the number 37 turns up so often, drawing on Tom Magliery's collection of 37 sightings and a poll of about 200,000 people asked to pick a random number. It covers how humans choose numbers and why 37 stands out.

Mathematician Hannah Fry's TED talk on patterns in dating and mate-seeking, including optimal stopping and three math-backed tips for finding a partner.

Numberphile talks with Grant Sanderson of 3Blue1Brown about a darts puzzle with a shrinking bullseye. Solving it takes the volumes of high-dimensional spheres, and the answer turns up Euler's number.

A Veritasium video on how a feud between Russian mathematicians led to Markov chains and the modern prediction algorithms built on them. It covers the history and the math behind them.

Matt Parker of Stand-up Maths examines the Texas Supreme Court filing claiming Biden's 2020 win had a one-in-a-quadrillion chance. He walks through why the statistical argument is flawed.

Nassim Taleb argues that evidence on terrorism risk presented in media is statistically naive, using extreme value theory without math to separate fat-tailed risks like Ebola and terrorism from thin-tailed ones.

Robert Miles examines whether the case for AI safety is a Pascal's mugging, a tiny probability of an enormous payoff. He argues it is not, because AI risk does not depend on vanishingly small probabilities.

CGP Grey explains first-past-the-post voting and why it pushes elections toward two dominant parties. It is the first in his series on electoral systems.

Veritasium examines the role of luck in success, with simulations and examples showing how small advantages and chance can compound. It argues that top outcomes are disproportionately luck-driven while still crediting effort.

Veritasium explores the Prisoner's Dilemma and Axelrod's tournaments, showing why tit-for-tat and forgiving strategies win in repeated games. It extends the ideas to cooperation in evolution and conflict.

A short CGP Grey explainer on the alternative vote (instant runoff voting) versus first past the post, made around the 2011 UK referendum. It shows how ranked ballots are tallied and why they avoid spoiler effects.

A Golden Balls episode in which one contestant announces he will steal, leading to an unexpected outcome in the split-or-steal prisoner's dilemma.

An animated simulation comparing single-winner voting methods such as plurality, instant runoff and STAR. Colored regions show which candidate wins as a randomized electorate shifts across a two-dimensional political space, building on Ka-Ping Yee's earlier diagrams.

The Center for Election Science explains favorite betrayal in instant-runoff voting: in some elections, ranking your favorite first can cause your least favorite to win. It contrasts this with plurality voting's spoiler problem.

Stanford biologist Robert Sapolsky lectures on the evolution of behavior, including the Prisoner's Dilemma and tit-for-tat strategies in animals. It is part of his Human Behavioral Biology course.

A short animated TED-Ed lesson in which two competing ice cream vendors on a beach illustrate why rival shops cluster together. It introduces game theory and the Nash equilibrium through the Hotelling model.

John Rauser's Strata 2014 keynote argues that programmers can learn statistics quickly by simulating random processes and shuffling data. He explains p-values through resampling rather than formulas.

Derren Brown's TV special in which he convinces a person he has a system for predicting horse race winners, demonstrating how survivorship bias and selective outcomes can fake predictive powers.

Mathematician Colin Wright demonstrates juggling and explains the mathematics of juggling patterns, including notation that led to new throwing patterns. It is a public presentation at the Museum of Mathematics aimed at a general audience.

Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

Primer simulates green beard altruism, where individuals recognize and help others carrying a shared marker, and shows how imposters affect its evolution. It is an animated evolution simulation based on published papers.

Isaac Arthur examines the Dark Forest theory, Cixin Liu's proposed solution to the Fermi Paradox in which civilizations stay silent and may destroy any that reveal themselves. He tests the theory's underlying assumptions and arguments.

A short CGP Grey animation showing how the US electoral college lets a candidate win the presidency with as little as about 22 percent of the popular vote. It lays out the arithmetic of winning states by narrow margins.

A short clip of Jordan Peterson explaining Pareto distributions, using Soviet farm collectivization and the resulting famine as context. It also covers how outcomes concentrate in a few people.

Vsauce explores math through card tricks and big numbers, including an animation of how enormous 52 factorial, the number of deck orderings, really is.

Chris Stucchio presents the ethical principles behind algorithmic decision making and shows with examples from lending, criminology and education that they cannot all be satisfied at once. The talk frames AI fairness as a set of quantitative tradeoffs.