Galton Board

Balls fall through a triangle of pegs. Each peg is a coin flip — left or right, nothing else. Do it a few thousand times and the pile at the bottom always draws the same shape: a bell curve. No one aims the balls. The shape is just what randomness looks like when you stack it up.

A triangle of pegs with balls falling into bins below. Your browser does not support canvas.
click a bin to inspect it
Board is focusable: Tab to it, then ← →.

Readout

0balls landed
0still falling
—average bin
—spread σ
idle
Curve predicts—
Inside ±1σ—
Tallest bin—

The badge turns green when the bars sit inside the wiggle room you would expect for this many balls. Small runs look lumpy — that is the point of dropping more.

The board

12 → 13 bins
250
50%

Changing the rows or the lean re-runs every ball that has landed through the new board, so the histogram never goes blank. With Animate off, drops fill in instantly.

Inspect a bin

bin 6 —
Landed
—
Curve says
—
Routes in
—

Click a bin, or focus the board and walk it with the arrow keys.

Why a bell?

A ball's whole life is a string of coin flips: L R R L R L ..., one per row. Where it lands depends only on how many rights it got, not which order they came in.

There is exactly one route to the far-left bin — go left every single time. But there are thousands of routes into the middle, because there are thousands of ways to mix an equal number of lefts and rights. The bins in the middle are simply easier to reach, and the bell curve is that count of routes, drawn to scale.

Drag bounce right off 50% and the whole pile slides sideways and narrows — the same machine, biased. That is the everyday version of this shape: heights, timings, measurement errors, anything built from many small independent nudges.