>The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an upright board with evenly spaced nails (or pegs) driven into its upper half, where the nails are arranged in staggered order, and a lower half divided into a number of evenly-spaced rectangular slots. The front of the device is covered with a glass cover to allow viewing of both nails and slots. In the middle of the upper edge, there is a funnel into which balls can be poured, where the diameter of the balls must be much smaller than the distance between the nails. The funnel is located precisely above the central nail of the second row so that each ball, if perfectly centered, would fall vertically and directly onto the uppermost point of this nail’s surface (Kozlov and Mitrofanova 2002).

Statistically, how many times would you have to flip this thing until you’re likely to get the exact same distribution twice in a row, thus allowing for a perfectly looped gif?

From the [Wolfram Alpha](http://mathworld.wolfram.com/GaltonBoard.html):

>The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an upright board with evenly spaced nails (or pegs) driven into its upper half, where the nails are arranged in staggered order, and a lower half divided into a number of evenly-spaced rectangular slots. The front of the device is covered with a glass cover to allow viewing of both nails and slots. In the middle of the upper edge, there is a funnel into which balls can be poured, where the diameter of the balls must be much smaller than the distance between the nails. The funnel is located precisely above the central nail of the second row so that each ball, if perfectly centered, would fall vertically and directly onto the uppermost point of this nail’s surface (Kozlov and Mitrofanova 2002).

I could watch this all day.

[mp4 link](https://preview.redd.it/2vbc912kb1v21.gif?format=mp4&s=a7be2874fefe59aa1e1e31c25ca3de8584385e30)

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This mp4 version is 95.32% smaller than the gif (645.17 KB vs 13.47 MB).

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Statistically, how many times would you have to flip this thing until you’re likely to get the exact same distribution twice in a row, thus allowing for a perfectly looped gif?