# 3,408 needle drops gave him pi to six decimals. Lucky?

- Series: [The Better Guess](https://miu.fm/thebetterguess.md)
- Published: 2026-10-23
- Page: https://miu.fm/thebetterguess/3-408-needle-drops-gave-him-pi-to-six-decimals-lucky

## Story

3,408 needle drops gave him pi to six decimals. Lucky?

The game is older. In 1733 the Count of Buffon asked: drop a needle on a wooden floor, how often does it land across a crack? With a needle as long as a board is wide, the answer has pi in it: two divided by pi, about 64 drops in 100. Later Pierre-Simon Laplace turned it around: drop enough needles, count the crossings, and you can work out pi.

So we tried. Our own run said 3.39 after 100 needles, 3.19 after 1,000 and 3.13 after 10,000. Every extra digit costs about a hundred times more needles.

In 1901 Mario Lazzarini reported 3,408 drops and 1,808 crossings, which make 355/113: pi to six decimals. Honest counting that sharp would need tens of trillions of drops, and one crossing more or fewer gives 3.1398 or 3.1433. Mathematicians who checked, Gridgeman in 1960 and Badger in 1994, say he almost certainly kept going until the count came out perfect, and stopped.

Every count wobbles. Before you trust a result, ask how much a count that size should wobble.

Buffon himself never dropped needles to find pi; he only asked how often. Our runs are seeded simulations.

So, lucky or not? What did you say?

Sources: Julyan Cartwright, "La Baguette Mathémagique", arXiv, 2021; Lee Badger, "Lazzarini's Lucky Approximation of pi", Mathematics Magazine, 1994; N. T. Gridgeman, Scripta Mathematica, 1960; Buffon, Essai d'arithmétique morale, 1777; Laplace, Théorie analytique des probabilités, 1812.
Sounds: our own, made in code (earshot, CC0).

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