Plinko / Galton Board

The Galton board was invented by English polymath Francis Galton in 1889 to visually demonstrate how independent random events combine into a predictable overall pattern. Each ball takes a random left/right path at every pin row, and the sum of many small random deflections is a binomial process. As the number of rows grows, that binomial distribution of final bin positions converges toward a smooth Gaussian (normal) "bell curve" — a direct visual proof of the Central Limit Theorem. Because each ball's path is independent and identically distributed, no single trial is predictable, yet the aggregate outcome across hundreds of balls is remarkably stable. Galton boards remain a staple of probability and statistics education for exactly this reason: they make an abstract theorem tangible.

Characteristics

• This board uses 12 rows of pins, a common count for classroom-scale demonstrations.
• Each pin gives roughly a 50/50 chance of deflecting a ball left or right.
• The standard deviation of the bin distribution grows with the square root of the number of rows.
• With 12 rows, the probability of landing in the center bin is the highest of all bins.
• The final histogram approximates Pascal's triangle / binomial coefficients row 12.
• More balls dropped over time make the bell-curve shape converge more closely to the ideal Gaussian.