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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 read Why random dice rolls draw a perfect fractal: the chaos game and the Sierpiński triangle Pick three dots, then keep jumping halfway towards a randomly chosen one. It sounds like it should leave a grey smudge, but after a few thousand jumps a… Maths3 min read 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 read Why the most common word is twice as common as the next: Zipf's law Sort every word in a book from most to least common and a pattern appears: the top word is about twice as common as the second, three times as common as the… Language5 min read 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 read