probability

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.

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.

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.

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.

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.

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.

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.

A six-minute explainer from Undefined Behavior on range (score) voting. It follows an earlier video on Arrow's Theorem and shows how range voting seems to satisfy the criteria Arrow's Theorem says no ranked system can.

Primer uses simulations to compare voting systems such as first-past-the-post, approval, ranked choice and others. It shows how each system behaves and can be manipulated, with links to further voting theory resources.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.

A ten-minute explainer from Hypermind on the wisdom of crowds, covering Galton's discovery and the diversity theorem. It argues that collective intelligence comes from diversity, independence and aggregation.

Marcus du Sautoy of the BBC demonstrates the wisdom of the crowd, showing that averaging many guesses of jelly beans in a jar lands near the true count.

Vsauce asks whether music will ever run out of new melodies. It counts the possible note combinations and discusses how common chord progressions and remixing affect originality.

The poison goblet scene from The Princess Bride, in which Westley tricks Vizzini in a battle of wits. It is a famous example of nested reasoning.

Kurzgesagt animated explainer on the Dark Forest answer to the Fermi Paradox. It argues that if advanced civilizations exist, staying silent may be the safest strategy because revealing yourself invites a first strike.

Practical Engineering explains what a 100-year flood actually means, combining statistics, hydrology and how society treats risk. Grady walks through local drainage infrastructure and the caveats in estimating flood probability.