Galton Board

0balls in the buckets

–landed in the middle zone (the green band), against – by theory

–chance of the far left bucket

Click a bucket to see its odds.

ball what theory expects for this many balls middle zone: within one spread of the centre

Run

Speed

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average bucket (theory )

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spread, buckets (theory )

balls in the air

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fit to theory

Spread is the standard deviation: about two thirds of balls land within one spread of the average. Fit is a chi-square test: "fair" means the gaps from the red curve are the size luck alone makes.

Board

Buckets Balls Tilt

Buckets sets the rows of pegs: one row fewer than buckets. Tilt is the chance to bounce right at each peg; 50% is a fair board. Changing the board starts a new run.

Show

red theory curve middle zone number of paths to each peg (Pascal's triangle) trail of the newest ball

Why it happens

To land in the far left bucket a ball must go left at every peg, and there is only one way to do that. To land in the middle it needs equal lefts and rights, in any order, and there are thousands of such orders. Count the ways (turn on Pascal's triangle) and you have the shape of the hill. Francis Galton built this board in 1873 to show how lots of small, random pushes add up to the bell curve, the shape of people's heights, measuring errors and exam scores.