Place your chips, pull the lever, and watch hundreds of beans cascade through the pegs of a bean-machine, building a bell curve before your eyes.
Before each wave you stake chips on the outcome bins of a Galton board (a peg field where beans bounce left or right). Drop the wave and the beans pile up into a histogram that approximates a bell curve. A bet wins if its bin is among the three fullest of the wave. Center bins pay small but often; tail bins pay big but rarely. Survive the waves with chips in the bank.
Beanfall is a wagering game on the Galton board, an animated demonstration of how randomness sums into a bell curve.
The peg field where beans bounce left or right and pile into bins is the Galton board, invented by Francis Galton to demonstrate the central limit theorem: with enough trials, the binomial distribution approaches a normal curve.
Staking chips on outcome bins before dropping the wave is the original addition.
Betting first is what exposes the intuition gap. The bell shape is obvious once the beans have fallen and much less obvious in advance, because each bean's path is a sequence of coin flips and nothing about a single path suggests the shape the pile will take. Galton also designed the board to illustrate regression to the mean — which he called "reversion to mediocrity" and made part of his eugenist ideology, a piece of the device's history worth knowing alongside the mathematics.
Beanfall is a wagering game built on the Galton board, an animated demonstration of how randomness sums into a normal distribution. It's an original free browser game built for PlayPendium.