!!Con 2018: Estimating the Value of Pi with a Dartboard and (Not so Much) Luck! by Stephen Tu

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United States Confreaks
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Estimating the Value of Pi with a Dartboard and (Not so Much) Luck! by Stephen Tu

If you are like me and not very good at the game of darts, you might be able to use your skills towards estimating the value of pi. In this talk, we will look at a simple Monte Carlo algorithm which uses the (scaled) ratio of the number of darts that land on a dartboard over the number of darts that land within a square around the dartboard as an unbiased estimate for pi. We will understand why the algorithm works intuitively by appealing to the Law of Large Numbers. Furthermore, since we would like to not throw darts forever, we will use a large deviation inequality to derive an upper bound on the number of throws we need to estimate pi to within a desired accuracy with high probability.



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