In the 18th century, Georges-Louis Leclerc, Count of Buffon, proposed an experiment to estimate . The experiment (now somewhat famous as it appears in almost all probability textbooks) consists in dropping randomly matches on a floor made of parallel floorboards and using the number of time the matches land across a junction to estimate .

To perform the Count’s experiment, you do not need a lot of math. You only need to test if

with and are both uniform random variables, and is the width of the floorboards. You may remark that we use and that it looks like a circular definition until you think that radians is 45°, and you can estimate it using other means. Then you start throwing zillions of virtual matches and count the number of intersections, then use a laboriously obtained probability distribution to estimate .

Lucky for us, there’s a variant that does not require the call to sines, not complicated integrals. Just squaring, counting, and a division. Let’s have a look.

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