Estimate Pi at Home

Try Buffon's needle. Draw parallel lines on paper, spaced one needle-length apart, then drop a needle of that exact length about 100 times. Count how often it lands across a line.

The odds of a crossing work out to 2/pi, roughly 0.64. So if 63 of 100 drops cross, your estimate is 2 x 100 / 63, about 3.17 — already near 3.14. More drops sharpen it.

This is Monte Carlo estimation in its oldest form, the same trick now used to price options and model reactors.