random

Matt Parker's LMS popular lecture on how seemingly incredible results can be meaningless random patterns. He ranges from ancient Woolworths civilisations to shoelaces and DNA.

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

Tom Scott visits Cloudflare's San Francisco office to show the wall of lava lamps whose camera feed is used as a source of entropy for random number generation. It is a short explainer on how this helps secure internet encryption.

Stephan T. Lavavej's GoingNative 2013 talk explaining why calling rand() and using rand() % 100 is bad in C++, and how the C++11 <random> header does the job properly.

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.

Civilization creator Sid Meier's GDC 2010 talk on applying psychology to game design. He discusses player perception, randomness, and win states, and why designers must account for how players experience events.

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.

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.

Dr Mike Pound explains the suspected backdoor in the Dual_EC_DRBG random number generator and how elliptic curve constants could let someone predict its output.

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.

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

Nassim Nicholas Taleb talks at Google about his book Antifragile, on systems that gain from disorder and volatility. It draws on themes from his earlier books.

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.

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 one-minute clip from The IT Crowd (S03E02) in which Roy and Moss memorize fake football jargon to pass as real men. The scene's punchline is the ludicrous made-up football talk.