Peg Drop
Balls fall through a grid of pegs, bouncing unpredictably left or right off each one,
and pile up in bins at the bottom. Every single collision is pure chance — but drop
enough balls and the bins settle into the same bell curve every time.
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Sound: On
How it works: this is a Galton board. Pegs are arranged in
offset rows so every falling ball is forced to hit one peg per row; each hit deflects
it left or right with roughly equal odds, completely independent of every other hit.
A single ball's final bin is unpredictable — but with N rows of pegs, reaching bin k
requires exactly k "right" deflections out of N coin flips, and the number of ways
that can happen follows the binomial distribution, which converges toward a bell
curve (the normal distribution) as more balls fall. That's the classic demonstration
of the Central Limit Theorem: total randomness at the level of one collision still
produces a smooth, predictable histogram at scale.