Galton board
Drop a thousand balls. Randomness has a shape.
Changing the board clears the bins.
- Balls dropped
- 0
- Most common bin
- –
Each ball makes 12 coin-flip choices. Most land in the middle because there are far more paths there.
balls expected shape
What's going on
Every peg is a coin flip: bounce left or bounce right. After 12 rows, the bin a ball lands in depends only on how many of its flips went right. There is exactly one path to the far-left bin (left, left, left… every time), but 924 different paths to the middle bin. More paths means more balls, and when you count paths for every bin you get the binomial distribution, which looks more and more like a smooth bell curve as the rows add up.
Francis Galton built this machine, which he called a quincunx, and described it in Natural Inheritance in 1889. He used it to show how lots of small, independent nudges add up to a predictable shape, even though no single ball is predictable.
That is why so many things in nature look bell-shaped. Adult height, measurement errors, or how long a reaction takes are each the sum of many small, mostly independent influences. Add enough of them together and the extremes cancel out more often than they stack up. Tilt the board with the bias slider and the bell slides sideways, but it keeps its shape.