Why random bounces pile up into a bell curve: the Galton board
30seconds
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 same smooth bell curve.
Run the machine yourself. Change the number of rows, tilt the pegs, add a thousand balls at a time, and watch a dashed bell curve track the bars. Along the way you'll see why the middle slot wins, why the pile widens only with the square root of the rows, and what the central limit theorem says about adding up many small random pushes.
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