The Bean Machine: One Ball vs 100

A bean machine drops balls through a triangle of pegs — each ball bounces left or right by pure chance at every peg. One ball is impossible to call: it could land almost anywhere. But drop a hundred and they always pile into a smooth BELL. First predict how spread-out a board full of balls will be — then find out. How TALL the board is (how many pegs each ball bounces off) decides how wide that bell spreads.

1. A Short Board (4 rows of pegs)5 bins

2. A Medium Board (9 rows of pegs)10 bins

3. A Tall Board (16 rows of pegs)17 bins

Three boards. A taller board has more rows of pegs for each ball to bounce off.

Where this tool comes from

Galton’s board

Francis Galton, an English scientist, built this board in the 1870s to show how chance adds up. He described it in his book Natural Inheritance (1889) and called it a quincunx; “bean machine” is a later nickname.

One thing to hold: A board with rows of pins. Lead shot pours in at the top, bounces through the pins and lands in a row of slots.

Why it matters: Each ball goes left or right by chance, yet together the balls pile into the same hump-shaped curve every time. One run is lumpy; the shape shows up when many balls fall.

Sources: Francis Galton, Natural Inheritance (1889) · Stephen M. Stigler, The History of Statistics (1986)