The black hole in Interstellar was made by following rays of light through Einstein's curved space, one pixel at a time. This demo does the same in your browser, live: fly around the hole, then switch on the two effects the film left out on purpose, the gravitational...
Newton's method finds a root by sliding down the tangent, step after step. Start it everywhere in the complex plane at once, colour every starting point by the root it reaches, and the borders between the colours turn out to be fractals. This article and its...
The Mandelbrot set comes from one line of arithmetic: take a number c, start at zero, square and add c, again and again. Zoom into its edge as deep as you like, or click a point and watch its numbers either settle down or run away. This article and its interactive...
Unicorn Glitterluck is a dice race for small children, and it hides some real probability. Play a game on the board below, then let the computer play a hundred thousand and see how often the first unicorn home really wins, and how much it is worth to start. This...
Every roulette player can win tonight, and many do. The casino still knows its profit to the cent per thousand dollars wagered. Send players to the table, a few at first and then hundreds of thousands, and watch the casino's luck turn into arithmetic. This article and...
Two slot machines, both advertised with a 95 % return to player. One pays a little almost every third spin, the other hardly ever, but then a lot. Send ten thousand players with 100 coins to each and see how differently their evenings end. This article and its...
Craps looks wild, but the pass line bet runs on two dice and two simple rules. Roll through a few games, then add up the branches and see why this is one of the closest bets in a casino, and still a losing one. This article and its interactive demo were created with...
Six numbers out of 45, plus a bonus number: that is the Austrian Lotto. Pick your six, let the computer draw a million times, and compare what you would have won with what the counting says. This article and its interactive demo were created with the help of...
You pick one of three doors; behind one is a car, behind the others goats. The host, who knows where the car is, opens another door with a goat and offers you a switch. Play it yourself, keep score, then let the computer play a thousand rounds. This article and its...
Red has come up five times in a row. Is black due now, or is red on a hot streak? Spin the wheel thousands of times and look at what actually happened after every streak. This article and its interactive demo were created with the help of generative AI and editorially...
Martingale doubles after a loss, Reverse Martingale after a win, D'Alembert and Fibonacci climb more slowly. Give all five the very same spins, ten thousand times over, and compare what they do to your money, and what none of them can change. This article and its...
James Bond spreads $200 over three bets: $140 on the high numbers, $50 on 13 to 18 and $10 on zero, so most numbers win something. Build his bet, or any other mix, and see what each number pays and what the whole combination is worth on average. This article and its...
You have $100 at the roulette table and want to leave with $200. Is it safer to bet $1 at a time or everything at once? The exact chances say small bets are by far the worst way, and the reason is how much money passes over the table before you stop. This article and...
Double your bet after every loss, and the next win pays it all back. Give ten thousand simulated players the same bankroll and the same rule, send them to a roulette table, and watch what happens to their money over hours of play. This article and its interactive demo...
The Martingale system doubles the bet after every loss and goes back to the base bet after every win. Pick a number of rounds, and every possible sequence of wins and losses is listed with what it pays, so you can count the odds yourself and see what they cost. This...
Press Undo in any editor and your latest change disappears first. Send three documents to a printer and the first one comes out first. Behind these two everyday habits are two of the simplest and most useful structures in computing: the stack and the queue. Give both...
How does a computer find one word among millions without checking them all? With a hash table: the word itself is turned into a number that says which bucket to look in, so only the few words in that one bucket need checking. Insert your own words, watch two words...
How does a calculator find a square root? One of the oldest and fastest ways starts with any guess and keeps improving it: take the average of the guess and the number divided by the guess. This is Newton's method, and on a graph every step is a tangent line sliding...
In 1970 the mathematician John Conway invented a 'game' that plays itself: a grid of cells, each alive or dead, and four simple rules about how many live neighbours a cell has. Nothing else. Yet out of those rules come shapes that never change, shapes that blink, and...
Here is a way to find π without measuring a single circle: throw darts at a square at random, and count how many land inside a quarter circle drawn in it. Because the quarter circle covers π/4 of the square, four times that share comes out close to π. Throw a few...