Galton Board
One ball’s path is a coin flip at every peg — pure chance. Drop enough of them and the chaos resolves into a curve you could set a clock by.
Why does a pile of random bounces make a smooth curve?
Each ball faces the same simple choice at every peg: bounce left or bounce right, decided independently of everything that came before. Any one ball’s route through the board is genuinely unpredictable — it is a small random walk. But once you drop thousands of balls and ask how many of them landed in each slot, something orderly appears. The number of “right” bounces a ball makes follows a binomial pattern, and far more paths lead to the middle bins than to the edges, since there are many more ways to mix six lefts and six rights than to go entirely one direction. As the board grows taller and more balls fall, that lumpy binomial pattern smooths into the familiar bell-shaped curve — the same convergence described by the central limit theorem.
What does this have to do with markets?
The same idea shows up well beyond physics demonstrations. If you treat a stream of small, independent price moves as a random walk — much like a ball ricocheting peg to peg — their cumulative effect settles into a predictable probability curve, even though no single move can be forecast. Option-pricing models such as Black–Scholes lean on exactly this property: they don’t try to guess tomorrow’s price, they work with the shape that a large number of small random shifts tends to produce.