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Why a treatment can win in every group and still lose overall: Simpson's paradox Treatment B beats Treatment A overall, yet A wins for small stones and for large stones. That is Simpson's paradox, and it is real data from a kidney-stone… Maths4 min read3 Nov Why real coin flips look fake: streaks and the way we imagine randomness Ask people to write down 100 random coin flips and they almost never include a streak of six, yet a real coin makes one about four times in five. Our gut… Mind4 min read29 Oct Why a dropped stick can find π: Buffon's needle Drop a stick on a floor of planks and count how often it lands across a seam. The count secretly contains π: for a needle as long as the plank width, the… Maths4 min read21 Oct Why swapping cards at random is not a fair shuffle: Fisher–Yates and the 27 paths Shuffling three cards by swapping each one with a random card from the whole row looks fair, but it is not. It makes 3 × 3 × 3 = 27 equally likely paths for… Computing4 min read20 Oct Why 23 people are enough for a shared birthday: counting pairs, not people Put 23 people in a room and the chance that two share a birthday is already 51%. It feels far too low a number, because we picture one person matching our… Maths3 min read16 Oct Why random bounces pile up into a bell curve: the Galton board Every ball in a Galton board makes the same blind choice at each peg: left or right, a coin flip. Yet drop enough of them and the pile always grows into the… Maths4 min read13 Oct Why switching doors wins twice as often: the Monty Hall problem Three doors, one car. You pick one, the host opens a goat door, and offers a swap. Most people say it's 50/50. It isn't: switching wins twice as often as… Maths4 min read10 Oct How dropping needles on a floor reveals the number π: Buffon's needle Toss a match onto a plank floor and ask: does it touch a crack? Do it thousands of times and the fraction that do will quietly spell out π, though no circle is… Maths3 min read4 Oct How a Bloom filter says "definitely not" using just a few bits How can a computer check whether a word is on a huge list using only a few bits per entry? A Bloom filter flips a handful of switches for every word you add… Computing3 min read3 Oct Why 23 people are enough for two to share a birthday Put 23 people in a room and there's a better-than-even chance that two of them share a birthday. That sounds wrong, because 23 is tiny next to 365. The catch… Maths4 min read29 Sep Why seven shuffles are enough to mix a deck of cards A 52-card deck can be put in about 8 × 10^67 different orders, yet a few quick shuffles leave a lot of the old order behind. In 1992 Dave Bayer and Persi… Maths4 min read27 Sep