Buffon's needle

The cracks in the floor are d apart, and a needle of length L no longer than d lands across one with chance 2L/πd; drop N needles, H of them across a line, and 2LN/dH estimates π. Drag N from a handful up to five thousand, or press play and let it climb: the estimate in the corner swings wildly at first and only slowly settles near 3.1, and another throw of the same number of needles settles on a different value. The error shrinks roughly as 1/√N, so every further correct digit costs a hundred times as many needles. Shorten the needle and fewer of them cross, and the same number of needles gives a shakier π.