The Galton Board

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This is a probability experiment – and like a lot of physics and maths, it’s a thought experiment. In other words, it’s an idealised situation, which it would be very hard to replicate in the real world. For a real-world experiment with some striking similarities, go to the NAG board – but stay here first, and find out what it’s all about.

[VIDEO WITH GRAPHIC AND/OR COMPUTER GALTON BOARD – Video 4V]

In a Galton board, we have an imaginary ball, and imaginary pins in an imaginary board – ok. It’s a thought experiment, so please just keep the ‘imaginary’ thing in your mind. If we keep on saying everything is imaginary, it’s going to get really wordy and annoying.

So…

A Galton board is a board with pins in it, in a criss-crossing pattern. When you drop a ball in at the top, there is a 50-50 chance that it will go in either direction at each pin. Let’s unpack that.

[graphic of Galton board for next para to point to; one pin highlighted]

Let’s look at this pin – it could be any pin, but let’s choose this one. There are two ways the ball could go here – to the left of the pin, or to the right. There is a fifty-fifty chance of it going either way.

At the pin the ball hits in the next row, the odds are the same. And so on all the way down the board until the ball reaches the bottom. By adding up the probabilities at each level of pins, we can come to a probability for the ball landing in each marked pocket at the bottom of the board.

Try out the Galton board here.  [link to Galton board interactive]
As this is a thought experiment, it works in a ‘perfect world’ – so the probabilities are right; that is to say they accurately reflect what will happen. It might take a large number of balls to get the proportion of balls in each pocket that the sums predict, but the sums do work.

The Galton board reflects some basic statistical concepts of uncertainties in measurements. You can play games with it just like tossing a coin (Game 1), or tossing a coin lots of times and seeing how confident you are about predicting what will happen (Game 2).

Once you’ve got an idea of how the Galton board works, we can make it more interesting by changing both the board and the games.

For that we need a NAG board; something that looks just like a Galton board, but isn’t – well, not quite…

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