The Galton board

Each grain of sand that meets a peg goes right with chance p and left with chance 1 − p. The bars are each bin's exact chance, the gold curve is the bell curve with mean np and variance np(1 − p), and the ice-blue steps show what share of the sand dropped since your last change has landed in each bin. Drag p away from 0.5 and the pile moves to one side and narrows a little; with few rows and a strong lean the bars are plainly lopsided and miss the curve. Drag the rows up and the bars close in on it again: as long as p is neither 0 nor 1, enough rows always bring back the bell. The corner counts the grains, and their mean bin creeps towards np.