watch a large number of small balls fall between the nailboards and eventually change from disorder to a regular curve:

(video source: Index Fund Advisors, Inc.)

this demonstration device, called Galton board, was invented by Francis Galton to verify the central limit theorem. A small ball falling from a funnel-shaped mouth will encounter a series of "nails" arranged in triangles. Whenever the ball falls from the top to a "nail", it always has a 50% chance of running to the left and a 50% chance of going to the right. After several such random "left and right selections", the ball fell into the grid below.

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finally, the number of small balls in the lattice directly reflects the probability distribution of this process. The probability of a ball falling into a grid fits a binomial distribution, and when there are enough nails, squares and balls, the ball's distribution is close to the normal distribution-the bell-shaped curve we see in the video.

apart from visualizing the probability distribution, I think the main advantage of the Galton board is that it looks very comfortable. This device also has a small desktop toy version, which can be placed on the desk and watch the tiny beads slowly change from chaos to regular curve. It feels like a lot of time can be wasted.

(mini desktop version)

recently I really want to make a Galton plate by myself, and then pour it into it with a basin of glass balls (although I haven't started making _ (: desktop) ∠ at all)