Estimating the Value of Pi with a Dartboard and (Not so Much) Luck!

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" summary

Uniform random throws over a square-inscribed circle yield an unbiased Monte Carlo estimate for pi given by 4·(inside)/n, implemented in two lines of NumPy and empirically producing a Gaussian-like spread (CLT). A large-deviation bound gives sample counts: ~1/epsilon^2 scaling, concretely 2,000 (ε=0.1), 200,000 (ε=0.01), 20,000,000 (ε=0.001). Allowing a larger surrounding square multiplies samples by H^2, and the empirical runs match the predicted error-sample tradeoff.

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" chapters (6)

1. 0:00Start
2. 0:15What the game of darts is supposed to look like...
3. 1:10A comparison of area
4. 2:03Algorithm v1
5. 3:20Aside: Monte-Carlo Integration
6. 4:04How accurate is this algorithm?

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